OECD Education Working Papers No.

268

When practice meets policy William H. Schmidt,

in mathematics education: A Richard T. Houang,
19 country/jurisdiction case William F. Sullivan,
study Leland S. Cogan
https://dx.doi.org/10.1787/07d0eb7d-en
Organisation for Economic Co-operation and Development
EDU/WKP(2022)6

Unclassified English - Or. English

4 March 2022
DIRECTORATE FOR EDUCATION AND SKILLS

When Practice Meets Policy in Mathematics Education: A 19

Country/Jurisdiction Case Study

OECD Education Working Paper No. 268

William H. Schmidt (Michigan State University), Richard T. Houang (Michigan State

University), William F. Sullivan (Michigan State University), Leland S. Cogan (Michigan
State University).

This working paper has been authorised by Andreas Schleicher, Director of the Directorate
for Education and Skills.

This document is only available as a pdf.

OECD Future of Education and Skills 2030 Project [Education2030@oecd.org]

JT03490657
OFDE

This document, as well as any data and map included herein, are without prejudice to the status of or sovereignty over any territory,
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Table of contents

Acknowledgements ................................................................................................................................ 4
Abstract .................................................................................................................................................. 5
1. Introduction ....................................................................................................................................... 6
2. Research questions............................................................................................................................. 6
3. Methods .............................................................................................................................................. 8
4. Information Relative to the Various Graphics and Tables Presented throughout the Results Section
............................................................................................................................................................... 14
5. Results: Country/jurisdiction reports ............................................................................................ 17
6. Discussion ....................................................................................................................................... 111
References........................................................................................................................................... 113
Annex A. Mathematics Curriculum Document Analysis (MCDA) Framework .......................... 115
Annex B. Contributors list ................................................................................................................ 118

Tables
Table 1. 21st Century Competencies Related to Mathematics Education 13
Table 2. Country/jurisdiction reports 18

Figures
Figure 1. Example of a real-world application exercise 9
Figure 2. Example of a real-world application exercise 9
Figure 3. Example of a real-world application exercise 10
Figure 4. Example of a real-world application exercise 10
Figure 5. Example of a math-world application exercise 11
Figure 6. Example of a math-world application exercise 11
Figure 7. Example of a math-world application exercise 11
Figure 8. Example of a math-world application exercise 12

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Acknowledgements

We, the authors, wish to acknowledge the country/jurisdiction representatives who have given a great
deal of their time, especially to the five, week-long training/coding meetings. Their hard work in
coding their curriculum standards and a widely used 8th grade textbook (4 countries coded two
textbooks) using rigorous and very specifically defined definitions with scientific procedures enabled
us to produce the data that follows in this report. We thank them.
The OECD countries and jurisdictions participating in the study included: Australia, Estonia, Greece,
Hungary, Israel, Korea, Latvia, Lithuania, the Netherlands, New Zealand, Norway, Portugal, Sweden.
The OECD partner countries and economies participating in the study included: Argentina, Hong Kong
(China), Kazakhstan. Additionally, for the following countries/economies, data were provided by
independent researchers: Japan, Chinese Taipei, and the United States.
We also wish to thank the OECD Secretariat, in particular, Miho Taguma and Kelly Makowiecki for
their comments, and Cassandra Morley for her help formatting the document.
We also wish to especially acknowledge the work of Jennifer R. Cady. This study would not be
completed if it were not for her efforts. She is the Executive Assistant of one of the authors who
ostensibly became the executive assistant to the project itself. It is not just the logistics of the study
that she managed, but she also contributed to the development of the report, the editing of all
documents, the designing of the graphical displays, the immense amount of work involved here which
she did with Richard T. Houang produced a policy-relevant document that is readily useable and
interpretable to government and policy makers in education. For her contribution the four authors say,
thank you. We also thank Jiachen Liu, Xuran Wang and Augustus Sampah without whom this report
would not be possible.
We further wish to acknowledge that this study was funded in part by a research grant to William H.
Schmidt at Michigan State University in addition to OECD funding.

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Abstract

The OECD Future of Education and Skills 2030 (E2030) project’s overall goal is that of looking to the
future in terms of how school curricula should evolve given the technological advances and other
changes that societies are now facing. Towards that end, the E2030 project centres on the idea that
education needs to equip students with the knowledge, skills, attitudes and values they need to become
active, responsible and engaged citizens.
Mathematics is considered a highly relevant subject for achieving the above stated goals, as such it
requires further and more detailed analysis. As a result, it has been chosen as one of the E2030 project’s
subject-specific analyses. 1 The project has been named the Mathematics Curriculum Document
0F

Analysis (MCDA) study as per the request of participating countries. This working paper presents the
findings of the MCDA study, which involves participants from 19 countries and jurisdictions.

1
OECD countries and jurisdictions participating in the E2030 project: Australia, Belgium, Canada (British
Columbia, Manitoba, Quebec, Saskatchewan), Chile, Czech Republic, Denmark, Estonia, Finland, France,
Germany, Hungary, Iceland, Ireland, Israel, Italy, Japan, Korea, Latvia, Lithuania, Luxembourg, Mexico, the
Netherlands, New Zealand, Norway, Poland, Portugal, Slovenia, Spain, Sweden, United Kingdom (Scotland,
Wales), United States; OECD partner countries and economies participating in the E2030 project: Argentina,
China (People’s Republic of), Costa Rica, Hong Kong (China), Indonesia, Kazakhstan, Lebanon, Russia, Saudi
Arabia, Singapore, South Africa, United Arab Emirates, Viet Nam.

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1. Introduction

The world in which we now live has become increasingly complicated, not just in terms of artificial
intelligence (AI), computers, robotics and other forms of technology, but in terms of the ways in which
we acquire the knowledge we need to live, work and respond to the complicated issues that now
confront the world’s population. Pandemics rage, economies plunge, and the occurrence of floods,
hurricanes, tornadoes, and earthquakes increase exponentially in conjunction with climate change.
Understanding these issues not only requires literacy in the sense of being able to comprehend what
you read, but also requires mathematics literacy, such that a person is able to comprehend the necessary
information that increasingly is numerical in nature and is often presented in graphical or tabular form.
Such data include a background surrounding the following mathematics topics: fractions, rates, ratios,
percentages and proportionality, which need to be interpreted correctly to understand the given issue.
Nothing illustrates the need for such mathematics literacy more than the current COVID-19 pandemic.
Data are presented daily with respect to the number of cases, the number of hospitalisations, the
number of deaths, and the number of vaccinations for different countries, regions and cities. People
look to see how their region compares to others or use it to make decisions about whether to get
vaccinated, when to wear a mask, or where to travel. To effectively use this information, a person must
understand what the denominator of the percentage is in order to make reasoned comparisons among
issues involving quantities, medicines, areas, deaths, etc.
Mathematics literacy includes knowledge of statistical procedures and statistical reasoning (based
primarily on probability) that is increasingly more important in making informed decisions related to
both the world of work as well as to personal decisions about health, family finances, schooling
options, and filing tax returns, but also societal issues such as climate change, inflation rates, income
tax policies and country budgets. For example, those who refuse to get vaccinated because they believe
it is dangerous due to possible side-effects often fail to take into account that not getting the vaccination
is not free of risk either. The more thoughtful response would be for the person to compare the
probability of each. It is this type of statistical reasoning – a key component of mathematics literacy –
that must be provided to all children by their schooling no matter their socio-economic status.
Mathematics education must continue to provide all children with the formal ideas, concepts,
algorithms and procedures that define formal mathematics, but also focus on providing students
opportunities to experience quantitative reasoning (including mathematics, statistics, geometric, and
algorithmic reasoning) in the solution of real-world applications. Perhaps then, we would no longer
hear our children say, “Why do I have to learn math? I’m never going to use it!”

2. Research questions

The OECD Future of Education and Skills 2030 (E2030) project’s overall goal is that of looking to the
future in terms of how school curricula should evolve given the technological advances and other
changes that societies now are expected to face. Towards that end, the E2030 project centres on the
idea that education needs to equip students with the knowledge, skills, attitudes and values they need
to become active, responsible and engaged citizens.
Some 25 years ago, as a part of the Trends in International Mathematics and Science Study (TIMSS)
1995 project, a special curriculum study was conducted that coded over 40 countries’ national curricula
standards over grades 1-12 (Schmidt et al., 2001[1]; Schmidt et al., 1997[2]). Reports of that work
characterised what topics were covered at particular grades as well as important characteristics of the
curricula of the top-performing countries on the TIMSS assessment – such as focus, rigor, and
coherence (Schmidt, Wang and McKnight, 2005[3]). The study also included a very thorough and
detailed document analysis of 4th and 8th grade mathematics textbooks (Schmidt et al., 1997[2]).

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Building on that opportunity, the first research question for the MCDA study is: how much and in what
ways has the mathematics curriculum changed in terms of its coverage of formal mathematics over the
first 8 grades of schooling. Clearly, technology has impacted the mathematics curriculum with the
advent of high-powered computers and calculators. On one hand, the part of formal mathematics that
is the basis for school mathematics has not changed. On the other hand, the inclusion or exclusion of
particular topics or the amount of time allocated to those topics as indicated by the number of grades
in which they are covered might have changed. In addition, other topics not covered in the past could
have been added to the mathematics curriculum.
As the TIMSS-95 curriculum study showed, there were distinctive differences among countries in
terms of their coverage of mathematics especially over the first eight grades which in most countries
includes primary- and lower-secondary schooling. It is to these additions, deletions, and differences
among countries that the first data collection is designed to address. Simply put the research question
is – has the timing, focus and organisation of school mathematics changed over the last 25 years?
A related but second research question centres on the inclusion of topics that were not typically taught
in the mathematics curriculum some 25 years ago. One example is the inclusion of formal statistics
which other than defining mean, median and mode and various data displays, was not typically covered
25 years ago. There are several other topics such as non-linear models, measuring irregular geometric
shapes, algorithmic reasoning, and human perspectives on the history of mathematics that fall into the
same category. The research question is: to what extent and in what grades have these topics been
added to curricula in the early part of the 21st century?
The third research question and the one most central to this working paper concerns the extent to which
issues related to the development of mathematics literacy are now being included in countries’ and
jurisdiction's national curriculum standards and in the textbooks used by the teachers. The research
question becomes – to what extent quantitative reasoning (including mathematics, statistical,
algorithmic, and geometric reasoning), higher-order real-world applications, and 21st century
competencies (knowledge, skills, attitudes and values) related to mathematics literacy have been added
to the 19 countries’ and jurisdiction's national standards and textbooks. Put another way, to what extent
have these countries started to shift their mathematics curriculum toward real-world applications
involving personal and societal issues given the increasing amount of information relative to these
issues that are often presented in a data-oriented format. The purpose of this research is to provide an
answer to the proverbial student question rephrased as follows, “am I ever going to use mathematics
outside of school.”
The fourth research question centres on the 8th grade mathematics textbooks used by the 19 countries
and jurisdictions. In mathematics, as shown originally in the TIMSS 95 study (Schmidt et al., 1997[2];
Valverde et al., 2002[4]), most mathematics classes around the world use textbooks as the medium for
providing the exercises that students need to do in order to learn mathematics. Each country selected
the most typically used textbook for analysis (four countries selected two). We focused on the exercises
contained in the textbook as these are what provide the relevant opportunities to learn both formal
mathematics and mathematics literacy. We categorised the exercises as to the nature of the opportunity
provided. It was with those data that we used to examine the research question: to what extent do the
19 countries and jurisdictions provide teachers with textbooks that provide opportunities to learn both
the formal topics of mathematics as well as those aspects related to mathematics literacy?
The fifth research question examines the degree of consistency between the emphasis found in the
national/jurisdictional curriculum standards and that found in the textbooks used by each
country/jurisdiction . Such a lack of consistency would likely have a negative effect on student
learning. Finally, the last question centres on the curriculum decision making as done in the TIMSS-
95 study (Schmidt et al., 2001[1]). In other words, who makes what decisions? It examines the strength
and breadth of curriculum decision making and whether countries vary in their patterns of making
curricular decisions across 14 areas of the curriculum.

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3. Methods

Document analysis procedures, developed originally in the TIMSS-95 study were used to code the
national curriculum standards and at least one 8th grade mathematics textbook from the 19 countries
and jurisdictions. The mathematics framework used in the current coding for formal mathematics was
based on the TIMSS-95 framework but included both newly emerging mathematics topics as well as
aspects related to the development of mathematics literacy.
The formal part of the framework adds topics that were not typically taught 25 years ago such as those
related to statistics, non-linear models, computational methods, and irregular geometric shapes. Three
dimensions were added to the framework characterising mathematics literacy: quantitative reasoning
including mathematics, statistics, geometric, and algorithmic reasoning, higher-order real-world
applications, and 21st century competencies (see Annex A for the Mathematics Curriculum Document
Analysis (MCDA) Framework).
Representatives with mathematics backgrounds from each country were selected to do the coding of
both the national standards documents in place in 2019 and at least one 8th grade textbook. Each
country selected a commonly used textbook to be analysed (some countries chose two such commonly
used textbooks). The training took place over five days in 2019 with the first two days consisting of
training and testing to a criterion reflecting a high level of accuracy and interrater reliability. On days
3, 4 and 5 of the work sessions the coders, using the mathematics framework, first coded their
curriculum standards as to the coverage of the formal mathematics content specified in the framework.
The coding identified for each topic in the framework the grade or grades in which that topic was to
be covered as specified in the standards. The coders were instructed to conduct “low-inference” coding
by which we meant that the coders were not to use their own opinions or other information they might
have as to whether or not the topics were covered at particular grades. They were to base their coding
solely on the actual words used in the documents – in other words strictly a literal interpretation of the
actual words used in the curriculum standards. This same principle was applied to the coding of the
textbooks.
For the textbooks, parts of the same mathematics framework were used but the methodology was
different. The first task for the coders was to go through the textbook, page-by-page counting the
number of exercises included in each chapter or section of the textbook (depending on the country’s
specific organisational textbook structure). The exercises were then coded as either computational or
word problems. Any exercise that simply required a computation or the application of procedures or
algorithms was coded as computational (including the solving of simple linear equations). Following
the identification of the exercises as being computational, they were then further classified into two
categories: straightforward computation or higher-order math-world applications. The country
representatives also further sorted the word problems into two categories: simple word problems or
higher-order real-world applications.
The coders were again instructed to strictly follow the following definitions of the two higher-order
designations and to not read more into the exercises than was literally included in the exercise. Each
definition is followed by several examples of that specific type of higher-order application (see Figures
1 – 6 below).

Higher-order real-world applications

Problems presented in a realistic, authentic, real-world context that require more than identifying the
mathematics needed to arrive at an acceptable solution. The problem needs to simulate the real world
in its messy, complex way requiring the student to conceptualise, organise, and extract the relevant
information before formulating a mathematical equation representing the problem and then finding the
correct answer. In fact, the latter may well be the least challenging and the least important in terms of
the development of mathematics literacy.

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Figure 1. Example of a real-world application exercise

Source:(Pearson Australia, 2014[5]), Pearson Mathematics Student Book 8 , (1st edition)

Figure 2. Example of a real-world application exercise

Source: Adapted from (Pearson Australia, 2014[5]), Pearson Mathematics Student Book 8, (1st edition)

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Figure 3. Example of a real-world application exercise

Source:(Eszterhazy Karoly University, 2018[6]), Matematika 8.

Figure 4. Example of a real-world application exercise

Source: (France, Lace and and Slokenberga, 2017[7]). Matematika 8 Klasei, Lielvārds.

Higher-order math-world applications

Problems are situated only within mathematics (not the real world) but require the student to
conceptualise, organise, extract the relevant information, and develop a logical approach before
finding a solution. A good example is a geometric proof where the goal is to formally construct a
deductive proof using the relevant information and then develop a logical approach to solving the

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problem. One key aspect of such solutions is the recognition of relevant theorems and axioms and how
they can be combined logically in a proof.

Figure 5. Example of a math-world application exercise

Source: (Great Minds, 2015[8]) Eureka Math! Grade 8 Modules 1 and 2 (Student Edition).

Figure 6. Example of a math-world application exercise

Source: Author’s own work

Figure 7. Example of a math-world application exercise

Source: (Eszterhazy Karoly University, 2018[6]), Matematika 8

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Figure 8. Example of a math-world application exercise

Source: (Great Minds, 2015[9]), Eureka Math! Grade 8 Modules 3,4, and 5 (Student Edition).

In both the real-world and the math-world applications, the designation of higher-order has a similar
meaning. In the case of the real-world as specified above, it demands the use of quantitative reasoning
and having to not only think through which of the information provided is relevant, but also how to
set up the problem mathematically. The actual mathematics computation is perhaps the least important
element of the exercise.
Higher-order real-world applications (HoRw) do not come with only the relevant information and the
specific required numbers you need in order to find the solution as is typical with word problems.
HoRw applications come from a messier context in which there may be multiple numbers, multiple
facets defining the situation, and even multiple solutions to the problem. Part of the task associated
with the exercise is to discern what is relevant and what is not and how to formulate the problem in
mathematical terms thus leading to the solution.
Similarly in the higher-order math-world applications (HoMw) a student must actually reason their
way through multiple steps to figure out what mathematics to put together in order to find the solution
to the stated problem. These are the types of items that demand at least one of the four types of
reasoning: mathematics, statistics, geometric, or algorithmic.
The higher-order real-world exercises were subjected to one additional coding to assure consistency
in comparisons across countries. The set of higher-order items that were identified by the country
coders were further classified as to whether they met the definition of higher-order by two of the
researchers themselves – both of whom have degrees in mathematics and statistics.
Both the national curriculum standards and the exercises identified as higher-order real-world
applications were coded with respect to the three dimensions related to mathematics literacy – in other
words the standards and the higher-order exercises were both coded as to whether they included
quantitative reasoning and 21st century competencies. The curriculum standards were additionally
coded as to whether and to what extent they included higher-order real-world applications. In the case
of the 21st century competencies, seven were identified which we hypothesised were likely to be related
to the mathematics curriculum (see Table 1).
In the case of the national curriculum standards, each of these three framework dimensions were not
only coded so as to indicate their presence in the standards, but also for the degree of emphasis that

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they received. The size of the emphasis code also reflected the degree to which each of the three
framework dimensions were formally integrated with specific mathematics topics and specific grade
levels. If the whole mathematics section of the national curriculum standards only mentioned a
framework dimension once it would produce the lowest score (1), the only lower score (0) indicates
there was no mention of the framework dimension at all.

Table 1. 21st Century Competencies Related to Mathematics Education

21st Century Definitions
Competencies
Communication Communication requires individuals to be both knowledgeable in the mathematics substance involved in the communication
as well as being knowledgeable about the audience for the communication and how best to craft the mathematics
substance of the communication for the targeted audience.

Creativity Creativity is defined as the ability to approach problems or situations with fresh perspectives resulting in seemingly
unorthodox solutions. Creative thinking is the process through which one develops novel ideas, approaches or information
(Mumford, Medeiros and Partlow, 2012[10]). Creativity has been central to the evolution of the discipline of mathematics, as
innovations in the rules and methods have brought us from its origins to the present-day practice of the discipline. From
complex mathematics problems to higher-order real-world applications, creativity becomes essential.

Critical thinking Critical thinking is defined as questioning and evaluating ideas and solutions (OECD, 2016[11]). Critical thinking is a higher-
order cognitive skill and includes inductive and deductive reasoning, making correct analyses, inferences and evaluations
(Facione, Giancarlo and Facione, 1995[12]; Liu, Frankel and Roohr, 2014[13]). Mathematics requires critical thinking when
individuals must draw on knowledge, logic and plausible reasoning to make sense of and form a response or solution to a
problem.

Information use Information use in mathematics increasingly demands digital literate students. They must have the knowledge,
understanding, skills and dispositions to use digital devices effectively and appropriately in both the world of mathematics,
but especially in higher-order real-world applications.

Reflection Reflection is the ability to take a critical stance before deciding, choosing and acting, such as, by stepping back from the
assumed, known, apparent, and accepted, comparing a given situation from other, different perspectives, and looking
beyond the immediate situation to the long-term and indirect effects of one’s decisions and actions.Mathematics problems
calling for reasoning and argument benefit from reflection.

Resistance/ Resilience is the disposition required to maintain effort or interest in an activity in the face of difficulties encountered, the
resilience length of time or steps involved or when opposed by someone or something. Resilience is the process of adapting well in
the face of adversity, trauma, threats or significant sources of stress (American Psychological Association, 2017[14]).

Systems thinking Systems thinking is the ability to think about a system as a whole, rather than only considering the parts individually
(Sterman, 2000[15]). The student is able to situate the mathematics problem or the real-world application in a well-defined
context and articulate the relationships among the various variables defining the mathematics problem or the higher-order
real-world application.

What created a larger emphasis code for a framework dimension was a more frequent mention of it
and even more so the number of times the framework dimension was integrated with a specific
mathematics topic in a particular grade. In short, the more frequently the framework topic is mentioned
in connection with specific topics in specific grades, the larger the measure of emphasis.
The same basic approach was taken with textbooks. The coding procedure described above classified
the exercises as higher-order applications or not. Those identified as higher-order real-world
applications were further coded as to the type of quantitative reasoning required and for the inclusion
of any of the seven 21st century competencies identified in Table 1.
The figures and graphics outlined in the following section present in detail data indicating the formal
mathematics content and the three additional dimensions related to mathematics literacy as they
occurred in both the countries’ national curriculum standards document and in a lower-secondary

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textbook. Those data reflect decisions made by the country with respect to what it is that schools should
teach in mathematics. The final question we address is who makes the various decisions related to
curriculum. To address this question, we developed a form that lists 4 major areas of curriculum
including: the goals of the system, the content to be included in the instruction, the instructional
methods used in the teaching of mathematics, and development of the framework and assessment items
both within the classroom and for the country as a whole. Each of these four categories, had between
two and five sub-areas identified.
The country representative was asked for each of the 14 aspects of curriculum, to identify the amount
of influence each of five loci had on that particular decision. The five loci represented different levels
of the system with correspondingly different actors. These included: the national centre (often referred
to as the Ministry of Education or Secretary of Education), the regional school office in charge of the
curriculum, the school headmaster or principal or other school-level official in charge of the
curriculum, a formal committee of the teachers chosen for the activity, and finally the individual
teacher his or herself.
For each curriculum area and locus of control, the country representative was asked to indicate the
degree of influence that the particular office or individual had. They responded on a four-point scale
indicating: no formal control; advice and recommendation; constrain or veto/modify recommendation;
and final authority or approval.
We have chosen to present the results of the analyses as country reports. We present the data
graphically to make them more accessible to those outside of the area of mathematics such as education
leaders, government authorities, and policy analysts. The next section of this report provides details
regarding each of the figures in the report and illustrates the interpretation that goes with each of the
graphics found throughout the report.

4. Information Relative to the Various Graphics and Tables Presented throughout the Results
Section

4.1. Guide to the Mathematics Curriculum Analysis Displays

Figures 1-4 and 7-8

Notes: The light grey bars show the Range for each of the seven sets of variables. Figure 1 includes the number of topics
covered at each grade level. Figures 2-4 indicate the intensity of effort in the standards associated with reasoning and 21st
century competencies. Figures 2-4 include and represent all grades. Figures 7-8 show the number of Higher-Order Real-
World textbook exercises that were classified as reasoning and 21st century competencies. The dark grey bars show the Inter-
Quartile Range (25th percentile-75 percentile) found within the number of textbook exercises across the 19 countries and
jurisdictions. The stars show the number of higher-Order Real World exercises that are presented in each
country’s/jurisdiction’s textbook with the specific type of Quantitative Reasoning and the specific Competencies. For Figure
1, the counts for each grade are defined in terms of the MCDA Mathematics Framework.

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Figures 5-6. Textbook composition

Notes: Figure 6 shows the results of the classification of all of the exercises found in a country’s/jurisdiction’s eighth-grade
mathematics textbook. Figure 5 is the classification of the said exercises cumulatively across the 19 participating
countries’/jurisdiction's textbooks. For countries/jurisdictions that analysed two textbooks, they are included in Figure 5 (and
6) as an average, not separately (but each textbook is also reported separately at the end of the individual country/jurisdiction
report) in that way Figure 5 represents the distribution of type of exercises with country/jurisdiction as the unit of analysis.
The classification includes three categories which sum to 100%: Computational Exercises, Higher-Order Math Applications,
and Word Problems. The additional pie shows the two types of problems – Standard Word and Higher Order Real World –
that make up Word Problems.

Figure 9. Roles played in curriculum decision making at five education levels

Notes: Country/jurisdiction curriculum decision making involves individuals from different levels of the educational system
(the five levels, e.g. national, define the columns in the above figure) having different levels of responsibility as a part of the
general decision-making process. The four different types of responsibilities are included in the key at the top of the display
and are numbered from 0 (no responsibility) to 3 (final authority/approval). Curriculum decisions involve multiple facets
such as content, examinations, etc. We have identified 13 subcategories of the four facets which define the rows of the above
figure. Each country/jurisdiction was asked to choose the type of responsibility that each level of the education system has
for each facet.

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Figures 10 and 11. Average influence of each educational level on four general curriculum facets

Notes: Transforming the four levels of responsibility as defined in Figure 9 to their numerical equivalent (i.e., no formal role
is coded as 0, final authority/approval is coded as 3, we then calculated for each combination of education level and the four
broad curriculum facets. The results are displayed in Figure 10. The average over all 19 countries and jurisdictions is
presented in Figure 11.

Figure 12. Comparing the patterns of topic coverage over 25 years

Notes: The above juxtaposed three figures characterise topic coverage for each of grades 1-8. The rows represent the set of
topics typically covered world-wide in mathematics while the columns indicate grade level. The green cells indicate coverage
by two-thirds of the top achieving countries in TIMSS-95 – termed TIMSS A+ (Schmidt, Wang and McKnight, 2005[3]).
Orange cells indicate coverage by a simple majority of the 19 countries and jurisdictions in the OECD2020 study (10 or
more). Blue cells indicate specific country/jurisdiction coverage (Figure 12).

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Figure 13. Moving into the future: Coverage of topics defining a new literacy

Notes: Like Figure 12, the rows define a set of topics and the columns grades 1-8. What is different in this table is that these
are mathematics topics that have not been commonly covered across the world in grades 1-8. These topics were identified by
consultants coming from four major sectors of the world’s economy: financial, medical, communications, and high-tech
manufacturing, as well as mathematicians and mathematics teachers. The three juxtaposed figures correspond to those in
Figure 12. The difference is that a colored cell indicates at least one country/jurisdiction intends to cover that topic at that
grade. The third set of data included represents, as in Figure 12, the results for a specific country/jurisdiction. In that case,
the colored cell means that the country/jurisdiction intended coverage of that topic at that grade. The absence of green cells
indicates no coverage of any of these topics in TIMSS95. For the OECD2020 results the orange-colored cell together with
the imbedded numbers indicate the number of countries and jurisdictions (of 19) currently covering the topic.

5. Results: Country/jurisdiction reports

This section contains the individual reports for each of the 19 countries/jurisdictions in the study. See
Table 2 below for the specific page numbers for each country/jurisdiction.

Unclassified
18  EDU/WKP(2022)6

Table 2. Country/jurisdiction reports

Country/jurisdiction Page numbers
OECD
Australia 19-26
Estonia 27-30
Greece 31-34
Hungary 35-38
Israel 39-42
Japan 43-46
Korea 47-50
Latvia 51-56
Lithuania 57-60
Netherlands 61-64
New Zealand 65-68
Norway 69-76
Portugal 77-80
Sweden 81-84
United States 85-90

Partner
Argentina 91-94
Chinese Taipei 95-100
Hong Kong (China) 101-106
Kazakhstan 107-110

Unclassified
 EDU/WKP(2022)6  19

Australia
Curriculum Standards
Index
 Page 1 portrays the composition of the country’s/ Figure 2. Degree of Emphasis for the Coverage of
jurisdiction’s curriculum standards. Four Types of Quantitative Reasoning
 Page 2 portrays the composition of a representative 8 th
grade mathematics textbook.
 Page 3 portrays the curriculum decision making authority
within the educational system.
 Page 4 portrays the mathematics topic coverage of the
country’s/jurisdiction’s curriculum standards across
grades 1-8 in comparison to the 1995 TIMSS A+
benchmark curriculum.

Figure 1. Number of Topics to be Covered at each Grade Figure 3. Degree of Emphasis for the Coverage of
Higher-Order Applications

Figure 4. Degree of Emphasis for the Coverage of 21st

Century Competencies/Skills

Notes for Figure 1:

 Light Greay bars show the range for the number of topics that each
of the 19 countries/jurisdictions intended to cover.
 Dark Grey bars show the Inter-Quartile Range (25th to 75th
Percentile) found within the broader range for the number of
topics that each of the 19 countries/jurisdictions intended to
cover.
 The stars show the number of topics that the country/
jurisdiction intended to cover at each of the grades.
Notes for Figures 2-4:
 The structure of these figures is the same as described in the note for Figure
1.
 The variable represented in each of these figures is a measure of the
intensity/emphasis that the curriculum standards for each of the
countries/jurisdictions placed on each of these three dimensions of
mathematics literacy.
 The measure is defined with 0 indicating no mention of the
dimension and 1-75 indicating the degree of emphasis (see
methods section of the introduction to the country/jurisdiction
reports).

Unclassified
20  EDU/WKP(2022)6

8th Grade Textbook Exercises

Textbook Exercise Composition
Characteristics of Higher-Order Real-World
Figure 5. Totals Over All Participants’ Application Textbook Exercises
Textbooks
Figure 7. Types of Quantitative Reasoning

Figure 8. Types of 21st Century Competencies

Figure 6. Country/Jurisdiction Textbook

Notes for Figures 7 & 8:

 Light Grey bars show the range for the number of Higher-Order Real-World
application exercises of each type for each country/jurisdiction.
Notes for Figures 5 (total number of exercises across all countries/jurisdictions)  Dark Grey bars show the Inter-Quartile Range (25th to 75th percentile).
& 6 (country/jurisdiction specific):  Special case: in cases where the majority of the country’s/jurisdiction’s
 The Blue pie diagram shows the total number of different types of values were 0, the light grey bar encompasses the dark grey bar.
exercises.  The stars show the number of Higher-Order Real-World application
 The Grey pie diagram shows the number of standard word problems exercises of each type that are included.
(an expansion of the light-blue wedge).
 The Orange wedge represents the number of Higher-Order Math- Notes for Figures 9 & 10 (next page):
World applications.  The Australian Curriculum, Assessment and Reporting Authority (ACARA) is
 The Yellow wedge represents the number of Higher-Order Real- responsible for the development and monitoring of the national curriculum
World applications. and the National Assessment Program. This includes the National
 For countries/jurisdictions that coded 2 textbooks, the average Assessment Program – Literacy and Numeracy (NAPLAN) which is an
number of exercises of the two textbooks was used in Figures 5, annual assessment for all Australian students in Years 3, 5, 7 and 9 and
6, 7 and 8. three-yearly NAP sample assessments in science literacy, civics and
citizenship, and ICT literacy for selected groups of students in Years 6 and
10. Jurisdictions, systems and schools are responsible for the
implementation of the Australian Curriculum and determine how student
learning is assessed and reported.

Unclassified
 EDU/WKP(2022)6  21

Curriculum Decision Making

0 1 2 3
Constrain, veto or
Advice & Final authority or
No formal role modify
Decision role recommendations approval
recommendations

[\\\\\\] zz\\\\\] [\zzzzzz zzzzzzzz

Figure 9. Who Makes What Decisions?
Locus of Curriculum Decisions
National Regional School Teachers Teachers
Collectively Individually
Goals for Pupils
A By overall system completion zz\\\\\] zz\\\\\] [\zzzzzz [\zzzzzz [\zzzzzz

B For intermediate stages zz\\\\\] zz\\\\\] [\zzzzzz [\zzzzzz [\zzzzzz

C For differentiated programme types zz\\\\\] [\zzzzzz zzzzzzzz [\zzzzzz [\zzzzzz

D To be reached in a given grade [\\\\\\] [\zzzzzz zzzzzzzz [\zzzzzz [\zzzzzz

E To apply for a specific school [\\\\\\] [\\\\\\] zzzzzzzz [\\\\\\] [\\\\\\]

Content of Instruction
F Course (grade level) offerings zzzzzzzz zzzzzzzz [\zzzzzz [\zzzzzz [\zzzzzz
G Auxiliary content outside of syllabi zzzzzzzz zzzzzzzz [\zzzzzz [\zzzzzz [\zzzzzz
H Student course assignment rules zzzzzzzz zzzzzzzz [\zzzzzz [\zzzzzz [\zzzzzz
I Course content (syllabi) zz\\\\\] zz\\\\\] [\zzzzzz [\zzzzzz [\zzzzzz
Methods of instruction
J Textbook selection [\\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz [\zzzzzz
K Instructional methods/techniques [\\\\\\] zz\\\\\] [\zzzzzz zz\\\\\] [\zzzzzz
Examinations
L Content of examinations zzzzzzzz [\zzzzzz [\zzzzzz [\zzzzzz zz\\\\\]
M Examination performance standards zzzzzzzz [\zzzzzz [\\\\\\] [\\\\\\] [\\\\\\]
N School Examination standards zz\\\\\] zz\\\\\] zzzzzzzz [\zzzzzz zz\\\\\]

Figure 10. Country/Jurisdictions: Relative Importance for each of the Four Facets
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 20% 40% 87% 53% 53%
Content of instruction 83% 83% 67% 67% 67%
Methods (including textbooks) 0% 17% 83% 67% 67%
Examinations 78% 56% 56% 44% 22%
Note. The denominator for the percentages is the number of subcategories (as defined in Figure 9) within each category x 3. The numerator (x) is the sum of
the values assigned for each chosen subcategory; for example, for cell (1,1) the formula is x/15. Note. The facet Methods of Instruction includes textbook
selection as well.
Figure 11. Relative Importance Averaged Across All 19 Countries/Jurisdictions
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 52% 24% 40% 29% 33%
Content of instruction 46% 19% 43% 42% 53%
Methods (including textbooks) 28% 18% 55% 50% 74%
Examinations 55% 16% 30% 40% 41%
Note for Figures 9, 10 & 11. In the above figures looking across rows tells who has what role while looking down the columns especially in Figures 10 and 11,
indicates over which facets each locus has the most influence.We acknowledge David E. Wiley’s contribution to the study of curriculum decision making.

Unclassified
22  EDU/WKP(2022)6

Coverage of Mathematics Topics in the Standards

Figure 12. Comparing the Patterns of Coverage over 25 Years
Majority
TIMSS95 Australia
OECD2020
Mathematics Topic 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
Whole Number: Meaning 1 1 1 1 1 0 0 0 19 19 17 14 12 9 5 4 1 1 1 1 0 1 0 0

Whole Number: Operations 1 1 1 1 1 0 0 0 19 19 19 19 14 12 11 9 1 1 1 1 1 1 0 1

Measurement Units, Estimation & Errors 1 1 1 1 1 1 1 0 17 17 18 17 15 11 9 9 1 1 1 1 1 0 0 1

Common Fractions 0 0 1 1 1 1 0 0 4 8 15 15 16 14 4 3 1 1 1 1 1 1 0 0

Equations & Formulas 0 0 1 1 1 1 1 1 8 8 10 11 16 17 19 19 1 1 0 1 1 1 1 1

Data Representation & Analysis 0 0 1 1 1 1 0 1 8 10 12 14 17 17 18 18 0 0 0 0 0 0 1 1

2-D Geometry: Basics 0 0 1 1 1 1 1 1 14 17 14 13 12 14 13 9 0 0 0 0 0 1 1 0

2-D Geometry: Polygons & Circles 0 0 0 1 1 1 1 1 11 14 14 15 19 18 15 15 1 1 1 1 1 1 1 1

Measurement: Perimeter, Area & Volume 0 0 0 1 1 1 1 1 11 14 14 15 19 18 15 15 1 1 1 1 1 1 1 1

Rounding & Significant Figures 0 0 0 1 1 0 0 0 0 0 4 9 12 8 6 7 0 0 0 0 1 1 1 0

Estimating Computations 0 0 0 1 1 1 0 0 5 7 10 11 13 12 7 6 0 0 0 0 1 1 0 0

Whole Numbers: Properties of Operations 0 0 0 1 1 0 0 0 12 14 16 18 15 13 10 7 1 1 1 1 0 1 0 0

Decimal Fractions 0 0 0 1 1 1 0 0 0 0 4 12 19 16 10 7 0 0 0 1 1 1 1 1

Relation of Common & Decimal Fractions 0 0 0 1 1 1 0 0 0 0 5 9 14 16 8 6 0 0 0 0 1 1 0 0

Properties of Common & Decimal Fractions 0 0 0 0 1 1 0 0 0 0 5 9 14 16 8 6 0 0 0 0 1 1 0 0

Percentages 0 0 0 0 1 1 0 0 0 0 4 12 19 16 10 7 0 0 0 1 1 1 1 1

Proportionality Concepts 0 0 0 0 1 1 1 1 1 1 1 5 11 16 16 13 0 0 0 1 1 0 1 1

Proportionality Problems 0 0 0 0 1 1 1 1 1 1 1 5 11 16 16 13 0 0 0 1 1 0 1 1

2-D Geometry: Coordinate Geometry 0 0 0 0 1 1 1 1 0 0 1 4 5 9 11 12 0 0 0 0 0 0 0 0

Geometry: Transformations 0 0 0 0 0 1 1 1 4 7 5 7 6 7 8 8 0 1 0 1 1 0 1 0

Negative Numbers, Integers, & Their Properties 0 0 0 0 0 1 1 0 3 3 4 5 6 11 14 12 0 0 0 0 0 1 1 1

Exponents, Roots & Radicals 0 0 0 0 0 0 1 1 0 0 0 1 3 4 13 13 0 0 0 0 0 0 0 0

Exponents & Orders of Magnitude 0 0 0 0 0 0 1 1 1 2 3 4 5 3 11 11 0 0 0 0 0 0 1 1

Geometry: Congruence & Similarity 0 0 0 0 0 0 0 1 1 1 1 2 3 5 9 12 0 0 0 0 0 0 0 0

Rational Numbers & Their Properties 0 0 0 0 0 0 0 1 0 0 2 4 5 8 10 8 0 0 0 0 0 0 0 1

Patterns, Relations & Functions 0 0 0 0 0 0 0 1 0 0 0 2 2 3 11 16 0 0 0 0 0 0 0 0

Proportionality: Slope & Trigonometry 0 0 0 0 0 0 0 1 0 0 0 1 1 3 9 16 0 0 0 0 0 0 0 0

Real Numbers, Their Subsets & Properties 0 0 0 0 0 0 0 0 0 0 0 0 0 1 6 13 0 0 0 0 0 0 0 1

Note. Green cells indicate coverage defined by TIMSS A+; Orange cells indicate coverage defined by at least a simple majority of the 19
countries/jurisdictions; Blue cells indicate specific country/jurisdiction coverage.
Figure 13. Moving into the Future: Current Coverage of Topics Defining a New
Literacy

Note. Orange cells indicate the number of countries that cover that topic at that grade level. The accompanying column indicates the number of
countries/jurisdictions that included that topic at any grade level; Blue cells indicate specific country/jurisdiction coverage.
The absence of green cells indicates the lack of coverage of those topics in TIMSS95.

Unclassified
 EDU/WKP(2022)6  23

Australia
Revised curriculum standards*
Index Figure 2. Degree of Emphasis for the Coverage of
 Page 1 portrays the composition of the country’s/ Four Types of Quantitative Reasoning
jurisdiction’s curriculum standards.
 Page 2 portrays the composition of a representative 8 th
grade mathematics textbook.
 Page 3 portrays the curriculum decision-making authority
within the educational system.
 Page 4 portrays the mathematics topic coverage of the
country’s/jurisdiction’s curriculum standards across
grades 1-8 in comparison to the 1995 TIMSS A+
benchmark curriculum.

Figure 1. Number of Topics to be Covered at each Grade Figure 3. Degree of Emphasis for the Coverage of
Higher-Order Applications

Figure 4. Degree of Emphasis for the Coverage of 21st

Century Competencies/Skills

Notes for Figure 1:

 Light Grey bars show the range for the number of topics that each
of the 19 countries/jurisdictions intended to cover.
 Dark Grey bars show the Inter-Quartile Range (25th to 75th
Percentile) found within the broader range for the number of
topics that each of the 19 countries/jurisdictions intended to
cover.
 The stars show the number of topics that the country/
jurisdiction intended to cover at each of the grades.

Note regarding curriculum standards:

Notes for Figures 2-4:
 *The Australian Revised Curriculum Standards are the ones  The structure of these figures is the same as described in the note for Figure
categorised on this page (page 1) and page 4 of this report. 1.
They are formally entitled “Australian Curriculum Standards -  The variable represented in each of these figures is a measure of the
Consultation version 2021” and were available during a 10 intensity/emphasis that the curriculum standards for each of the
week open public consultation period from April to July 2021. countries/jurisdictions placed on each of these three dimensions of
Further refinements have been made to the curriculum mathematics literacy.
following analysis of the consultation feedback. The final  The measure is defined with 0 indicating no mention of the
revisions are awaiting ministerial endorsement. When endorsed, dimension and 1-75 indicating the degree of emphasis (see
it will become known as Australian Curriculum (version 9). methods section of the introduction to the country/jurisdiction
reports).

Unclassified
24  EDU/WKP(2022)6

8th Grade Textbook Exercises

Textbook Exercise Composition Characteristics of Higher-Order Real-World
Application Textbook Exercises
Figure 5. Totals Over All Participants’ Figure 7. Types of Quantitative Reasoning
Textbooks

Figure 8. Types of 21st Century Competencies

Figure 6. Country/Jurisdiction Textbook

Notes for Figures 7 & 8:

 Light Grey bars show the range for the number of Higher-Order Real-World
application exercises of each type for each country/jurisdiction.
 Dark Grey bars show the Inter-Quartile Range (25th to 75th percentile).
Notes for Figures 5 (total number of exercises across all countries/jurisdictions)  Special case: in cases where the majority of the country’s/jurisdiction’s
& 6 (country/jurisdiction specific): values were 0, the light grey bar encompasses the dark grey bar.
 The Blue pie diagram shows the total number of different types of  The stars show the number of Higher-Order Real-World application
exercises. exercises of each type that are included.
 The Grey pie diagram shows the number of standard word problems
(an expansion of the light-blue wedge). Notes for Figures 9 & 10 (next page):
 The Orange wedge represents the number of Higher-Order Math-  The Australian Curriculum, Assessment and Reporting Authority (ACARA) is
World applications. responsible for the development and monitoring of the national curriculum
 The Yellow wedge represents the number of Higher-Order Real- and the National Assessment Program. This includes the National
World applications. Assessment Program – Literacy and Numeracy (NAPLAN) which is an
 For countries/jurisdictions that coded 2 textbooks, the average number of annual assessment for all Australian students in Years 3, 5, 7 and 9 and
exercises of the two textbooks was used in Figures 5, 6, 7 and 8. three-yearly NAP sample assessments in science literacy, civics and
citizenship, and ICT literacy for selected groups of students in Years 6 and
10. Jurisdictions, systems and schools are responsible for the
implementation of the Australian Curriculum and determine how student
learning is assessed and reported.

Unclassified
 EDU/WKP(2022)6  25

Curriculum Decision Making

0 1 2 3
Advice & Constrain, veto Final authority
No formal role recommendati or modify
Decision or approval
ons recommendati
Role: ons
[\\\\\\] zz\\\\\] [\zzzzzz zzzzzzzz
Figure 9. Who Makes What Decisions?
Locus of Curriculum Decisions
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils
A By overall system completion
zz\\\\\] zz\\\\\] [\zzzzzz [\zzzzzz [\zzzzzz
B For intermediate stages
zz\\\\\] zz\\\\\] [\zzzzzz [\zzzzzz [\zzzzzz
C For differentiated programme types
zz\\\\\] [\zzzzzz zzzzzzzz [\zzzzzz [\zzzzzz
D To be reached in a given gradE
[\\\\\\] [\zzzzzz zzzzzzzz [\zzzzzz [\zzzzzz
E To apply for a specific school
[\\\\\\] [\\\\\\] zzzzzzzz [\\\\\\] [\\\\\\]
Content of Instruction
F Course (grade level) offerings
zzzzzzzz zzzzzzzz [\zzzzzz [\zzzzzz [\zzzzzz
G Student course assignment rules
zzzzzzzz zzzzzzzz [\zzzzzz [\zzzzzz [\zzzzzz
H Course content (syllabi)
zzzzzzzz zzzzzzzz [\zzzzzz [\zzzzzz [\zzzzzz
I Auxiliary content outside of syllabi
zz\\\\\] zz\\\\\] [\zzzzzz [\zzzzzz [\zzzzzz
Methods of instruction
J Textbook selection
[\\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz [\zzzzzz
K Instructional methods/techniques
[\\\\\\] zz\\\\\] [\zzzzzz zz\\\\\] [\zzzzzz
Examinations
L Content of examinations
zzzzzzzz [\zzzzzz [\zzzzzz [\zzzzzz zz\\\\\]
M Examination performance standards
zzzzzzzz [\zzzzzz [\\\\\\] [\\\\\\] [\\\\\\]
N School Examination standards
zz\\\\\] zz\\\\\] zzzzzzzz [\zzzzzz zz\\\\\]
Figure 10. Country/Jurisd: Relative Importance for each of the Four Facets
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 20% 40% 87% 53% 53%
Content of instruction 83% 83% 67% 67% 67%
Methods (including textbooks) 0% 17% 83% 67% 67%
Examinations 78% 56% 56% 44% 22%
Note. The denominator for the percentages is the number of subcategories (as defined in Figure 9) within each category x 3.
The numerator (x) is the sum of the values assigned for each chosen subcategory; for example, for cell (1,1) the formula is x/15.
The facet Methods of Instruction includes textbook selection as well.
Figure 11. Relative Importance Averaged Across All 19 Countries/Jurisdictions
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 52% 24% 40% 29% 33%
Content of instruction 46% 19% 43% 42% 53%
Methods (including textbooks) 28% 18% 55% 50% 74%
Examinations 55% 16% 30% 40% 41%
Note for Figures 9, 10 & 11. In the above figures looking across rows tells who has what role while looking down the columns
especially in Figures 10 and 11, indicates over which facets each locus has the most influence.
We acknowledge David E. Wiley’s contribution to the study of curriculum decision making.

Unclassified
26  EDU/WKP(2022)6

Coverage of Mathematics Topics in the Standards

Figure 12. Comparing the Patterns of Coverage over 25 Years
Majority
TIMSS95 Australia (Revised)
OECD2020
Mathematics Topic 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
Whole Number: Meaning 1 1 1 1 1 0 0 0 19 19 17 14 12 9 5 4 1 1 1 1 0 0 1 0

Whole Number: Operations 1 1 1 1 1 0 0 0 19 19 19 19 14 12 11 9 1 1 1 1 1 1 1 0

Measurement Units, Estimation & Errors 1 1 1 1 1 1 1 0 17 17 18 17 15 11 9 9 0 1 1 1 1 0 0 0

Common Fractions 0 0 1 1 1 1 0 0 4 8 15 15 16 14 4 3 0 1 1 1 1 1 0 0

Equations & Formulas 0 0 1 1 1 1 1 1 8 8 10 11 16 17 19 19 0 0 0 0 0 1 1 1

Data Representation & Analysis 0 0 1 1 1 1 0 1 8 10 12 14 17 17 18 18 0 0 0 0 1 1 1 0

2-D Geometry: Basics 0 0 1 1 1 1 1 1 14 17 14 13 12 14 13 9 0 1 1 1 1 1 1 1

2-D Geometry: Polygons & Circles 0 0 0 1 1 1 1 1 11 14 14 15 19 18 15 15 0 0 1 1 1 0 0 0

Measurement: Perimeter, Area & Volume 0 0 0 1 1 1 1 1 11 14 14 15 19 18 15 15 0 0 1 1 1 1 1 1

Rounding & Significant Figures 0 0 0 1 1 0 0 0 0 0 4 9 12 8 6 7 0 0 0 0 0 0 1 1

Estimating Computations 0 0 0 1 1 1 0 0 5 7 10 11 13 12 7 6 0 0 0 0 0 1 1 1

Whole Numbers: Properties of Operations 0 0 0 1 1 0 0 0 12 14 16 18 15 13 10 7 0 1 1 1 1 1 1 1

Decimal Fractions 0 0 0 1 1 1 0 0 0 0 4 12 19 16 10 7 0 0 0 0 0 0 0 1

Relation of Common & Decimal Fractions 0 0 0 1 1 1 0 0 0 0 5 9 14 16 8 6 0 0 0 0 0 0 0 0

Properties of Common & Decimal Fractions 0 0 0 0 1 1 0 0 0 0 5 9 14 16 8 6 1 1 1 1 1 1 1 0

Percentages 0 0 0 0 1 1 0 0 0 0 4 12 19 16 10 7 0 0 0 0 0 0 1 1

Proportionality Concepts 0 0 0 0 1 1 1 1 1 1 1 5 11 16 16 13 0 0 0 0 0 0 0 0

Proportionality Problems 0 0 0 0 1 1 1 1 1 1 1 5 11 16 16 13 1 1 1 1 1 1 1 1
2-D Geometry: Coordinate Geometry 0 0 0 0 1 1 1 1 0 0 1 4 5 9 11 12 1 1 1 1 1 1 1 1

Geometry: Transformations 0 0 0 0 0 1 1 1 4 7 5 7 6 7 8 8 1 1 1 1 1 1 1 1

Negative Numbers, Integers, & Their Properties 0 0 0 0 0 1 1 0 3 3 4 5 6 11 14 12 0 0 0 0 1 1 1 1

Exponents, Roots & Radicals 0 0 0 0 0 0 1 1 0 0 0 1 3 4 13 13 0 0 0 0 0 0 0 1

Exponents & Orders of Magnitude 0 0 0 0 0 0 1 1 1 2 3 4 5 3 11 11 0 0 1 1 1 0 0 0

Geometry: Congruence & Similarity 0 0 0 0 0 0 0 1 1 1 1 2 3 5 9 12 0 1 1 1 1 1 1 0

Rational Numbers & Their Properties 0 0 0 0 0 0 0 1 0 0 2 4 5 8 10 8 0 0 0 0 0 0 0 1

Patterns, Relations & Functions 0 0 0 0 0 0 0 1 0 0 0 2 2 3 11 16 0 0 0 0 0 0 1 1

Proportionality: Slope & Trigonometry 0 0 0 0 0 0 0 1 0 0 0 1 1 3 9 16 0 0 0 0 0 0 0 1

Real Numbers, Their Subsets & Properties 0 0 0 0 0 0 0 0 0 0 0 0 0 1 6 13 0 0 0 0 0 1 1 0

Note. Green cells indicate coverage defined by TIMSS A+; Orange cells indicate coverage defined by at least a simple majority of the 19
countries/jurisdictions; Blue cells indicate specific country/jurisdiction coverage.

Figure 13. Moving into the Future: Current Coverage of Topics Defining a New
Literacy

Note. Orange cells indicate the number of countries that cover that topic at that grade level. The accompanying column indicates the number of
countries/jurisdictions that included that topic at any grade level; Blue cells indicate specific country/jurisdiction coverage. The absence of green
cells indicates the lack of coverage of those topics in TIMSS95.

Unclassified
 EDU/WKP(2022)6  27

Estonia
Curriculum Standards
Figure 2. Degree of Emphasis for the Coverage of
Index Four Types of Quantitative Reasoning
 Page 1 portrays the composition of the country’s/
jurisdiction’s curriculum standards.
 Page 2 portrays the composition of a representative 8 th
grade mathematics textbook.
 Page 3 portrays the curriculum decision-making authority
within the educational system.
 Page 4 portrays the mathematics topic coverage of the
country’s/jurisdiction’s curriculum standards across
grades 1-8 in comparison to the 1995 TIMSS A+
benchmark curriculum. Figure 3. Degree of Emphasis for the Coverage of
Higher-Order Applications
Figure 1. Number of Topics to be Covered at each Grade

Figure 4. Degree of Emphasis for the Coverage of 21st

Century Competencies/Skills

Notes for Figures 2-4:

Notes for Figure 1:  The structure of these figures is the same as described in the note for Figure
 Light Grey bars show the range for the number of topics that each 1.
of the 19 countries/jurisdictions intended to cover.  The variable represented in each of these figures is a measure of the
 Dark Grey bars show the Inter-Quartile Range (25th to 75th intensity/emphasis that the curriculum standards for each of the
Percentile) found within the broader range for the number of countries/jurisdictions placed on each of these three dimensions of
topics that each of the 19 countries/jurisdictions intended to mathematics literacy.
cover.  The measure is defined with 0 indicating no mention of the
 The stars show the number of topics that the country/ dimension and 1-75 indicating the degree of emphasis (see
jurisdiction intended to cover at each of the grades. methods section of the introduction to the country/jurisdiction
reports).

Unclassified
28  EDU/WKP(2022)6

8th Grade Textbook Exercises

Textbook Exercise Composition
Characteristics of Higher-Order Real-World
Figure 5. Totals Over All Participants’ Application Textbook Exercises
Textbooks
Figure 7. Types of Quantitative Reasoning

Figure 6. Country/Jurisdiction Textbook Figure 8. Types of 21st Century Competencies

Notes for Figures 5 (total number of exercises across all countries/jurisdictions)

& 6 (country/jurisdiction specific):
 The Blue pie diagram shows the total number of different types of
exercises.
 The Grey pie diagram shows the number of standard word problems
(an expansion of the light-blue wedge).
 The Orange wedge represents the number of Higher-Order Math- Notes for Figures 7 & 8:
World applications.  Light Grey bars show the range for the number of Higher-Order Real-World
 The Yellow wedge represents the number of Higher-Order Real- application exercises of each type for each country/jurisdiction.
World applications.  Dark Grey bars show the Inter-Quartile Range (25th to 75th percentile).
 For countries/jurisdictions that coded 2 textbooks, the average  Special case: in cases where the majority of the country’s/jurisdiction’s
number of exercises of the two textbooks was used in Figures 5, values were 0, the light grey bar encompasses the dark grey bar.
6, 7 and 8.  The stars show the number of Higher-Order Real-World application
exercises of each type that are included.

Unclassified
 EDU/WKP(2022)6  29

Curriculum Decision Making

0 1 2 3

No formal Advice & Constrain, veto Final authority

or modify
Decision role recommendations or approval
recommendatio
Role: ns
[\\\\\\] zz\\\\\] [\zzzzzz zzzzzzzz
Figure 9. Who Makes What Decisions?
Teachers Teachers
National Region School
Collectively Individually
al
Goals for pupils
A By overall system completion
zz\\\\\] zz\\\\\] [\zzzzzz [\zzzzzz [\zzzzzz
B For intermediate stages
zz\\\\\] zz\\\\\] [\zzzzzz [\zzzzzz [\zzzzzz
C For differentiated programmetypes
zz\\\\\] [\zzzzzz zzzzzzzz [\zzzzzz [\zzzzzz
D To be reached in a given grade programme types
[\\\\\\] [\zzzzzz zzzzzzzz [\zzzzzz [\zzzzzz
E To apply for a specific school
[\\\\\\] [\\\\\\] zzzzzzzz [\\\\\\] [\\\\\\]
Content of instruction
F Course (grade level) offerings
zzzzzzzz zzzzzzzz [\zzzzzz [\zzzzzz [\zzzzzz
H Student course assignment rules
zzzzzzzz zzzzzzzz [\zzzzzz [\zzzzzz [\zzzzzz
H Course content (syllabi)
zzzzzzzz zzzzzzzz [\zzzzzz [\zzzzzz [\zzzzzz
I Auxiliary content outside of syllabi
zz\\\\\] zz\\\\\] [\zzzzzz [\zzzzzz [\zzzzzz
Methods of instruction
J Textbook selection
[\\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz [\zzzzzz
K Instructional methods/techniques
[\\\\\\] zz\\\\\] [\zzzzzz zz\\\\\] [\zzzzzz
Examinations
L Content of examinations
zzzzzzzz [\zzzzzz [\zzzzzz [\zzzzzz zz\\\\\]
M Examination performance standards
zzzzzzzz [\zzzzzz [\\\\\\] [\\\\\\] [\\\\\\]
N School Examination standards
zz\\\\\] zz\\\\\] zzzzzzzz [\zzzzzz zz\\\\\]
Figure 10. Country/Jurisdictions: Relative Importance for each of the Four Facets
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 20% 40% 87% 53% 53%
Content of instruction 83% 83% 67% 67% 67%
Methods (including textbooks) 0% 17% 83% 67% 67%
Examinations 78% 56% 56% 44% 22%

Note. The denominator for the percentages is the number of subcategories (as defined in Figure 9) within each category x 3. The numerator (x) is the sum of the values
assigned for each chosen subcategory; for example, for cell (1,1) the formula is x/15. The facet Methods of Instruction includes textbook selection as well.
Figure 11. Relative Importance Averaged Across All 19 Countries/Jurisdictions
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 52% 24% 40% 29% 33%
Content of instruction 46% 19% 43% 42% 53%
Methods (including textbooks) 28% 18% 55% 50% 74%
Examinations 55% 16% 30% 40% 41%
Note for Figures 9, 10 & 11. In the above figures looking across rows tells who has what role while looking down the columns especially in Figures 10 and 11,
indicates over which facets each locus has the most influence. We acknowledge David E. Wiley’s contribution to the study of curriculum decision making.

Unclassified
30  EDU/WKP(2022)6

Coverage of Mathematics Topics in the Standards

Figure 12. Comparing the Patterns of Coverage over 25 Years

Note. Green cells indicate coverage defined by TIMSS A+; Orange cells indicate coverage defined by at least a simple majority of
the 19 countries/jurisdictions; Blue cells indicate specific country/jurisdiction coverage.

Figure 13. Moving into the Future: Current Coverage of Topics

Defining a New Literacy

Note. Orange cells indicate the number of countries that cover that topic at that grade level. The accompanying column indicates the
number of countries/jurisdictions that included that topic at any grade level; Blue cells indicate specific country/jurisdiction
coverage. The absence of green cells indicates the lack of coverage of those topics in TIMSS95.

Unclassified
 EDU/WKP(2022)6  31

Greece
Curriculum Standards
Index Figure 2. Degree of Emphasis for the Coverage of
 Page 1 portrays the composition of the country’s/ Four Types of Quantitative Reasoning
jurisdiction’s curriculum standards.
 Page 2 portrays the composition of a representative 8 th
grade mathematics textbook.
 Page 3 portrays the curriculum decision-making
authority within the educational system.
 Page 4 portrays the mathematics topic coverage of the
country’s/jurisdiction’s curriculum standards across
grades 1-8 in comparison to the 1995 TIMSS A+
benchmark curriculum.

Figure 1. Number of Topics to be Covered at each Figure 3. Degree of Emphasis for the Coverage of
Grade Higher-Order Applications

Figure 4. Degree of Emphasis for the Coverage of

21st Century Competencies/Skills

Notes for Figure 1: Notes for Figures 2-4:

 Light Grey bars show the range for the number of topics that  The structure of these figures is the same as described in the note for
each of the 19 countries/jurisdictions intended to cover. Figure 1.
 Dark Grey bars show the Inter-Quartile Range (25th to 75th  The variable represented in each of these figures is a measure of the
Percentile) found within the broader range for the number intensity/emphasis that the curriculum standards for each of the
of topics that each of the 19 countries/jurisdictions intended countries/jurisdictions placed on each of these three dimensions of
to cover. mathematics literacy.
 The stars show the number of topics that the country/  The measure is defined with 0 indicating no mention of the
jurisdiction intended to cover at each of the grades. dimension and 1-75 indicating the degree of emphasis (see
methods section of the introduction to the
country/jurisdiction reports).

Unclassified
32  EDU/WKP(2022)6

8th Grade Textbook Exercises

Textbook Exercise Composition Characteristics of Higher-Order Real-
World Application Textbook Exercises
Figure 5. Totals Over All Participants’ Figure 7. Types of Quantitative Reasoning
Textbooks

Figure 8. Types of 21st Century Competencies

Figure 6. Country/Jurisdiction Textbook

Notes for Figures 5 (total number of exercises across all

countries/jurisdictions) & 6 (country/jurisdiction specific):
 The Blue pie diagram shows the total number of different types Notes for Figures 7 & 8:
of exercises.
 The Grey pie diagram shows the number of standard word  Light Grey bars show the range for the number of Higher-Order Real-
problems (an expansion of the light-blue wedge). World application exercises of each type for each
country/jurisdiction.
 The Orange wedge represents the number of Higher-Order
Math-World applications.  Dark Grey bars show the Inter-Quartile Range (25th to 75th
percentile).
 The Yellow wedge represents the number of Higher-Order Real-
World applications.  Special case: in cases where the majority of the country’s/jurisdiction’s
values were 0, the light grey bar encompasses the dark grey bar.
 For countries/jurisdictions that coded 2 textbooks, the average
number of exercises of the two textbooks was used in Figures  The stars show the number of Higher-Order Real-World application
5, 6, 7 and 8. exercises of each type that are included.

Unclassified
 EDU/WKP(2022)6  33

Curriculum Decision Making

0 1 2 3
Constrain, veto or
Advice & Final authority or
No formal role modify
Decision recommendations approval
recommendations
Role:
[\\\\\\] zz\\\\\] [\zzzzzz zzzzzzzz
Figure 9. Who Makes What Decisions?
Teachers Teachers
National Regional School
Collectively Individually
Goals for pupils
A By overall system completion [\\\\\\]
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\]
B For intermediate stages
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
C For differentiated programme types
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
D To be reached in a given grade
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
E To apply for a specific school
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
Content of instruction
F Course (grade level) offerings
G
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
Student course assignment rules
[\zzzzzz [\\\\\\] [\\\\\\] [\\\\\\] zzzzzzzz
H Course content (syllabi)
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
I Auxiliary content outside of syllabi
[\zzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
Methods of instruction
J Textbook selection
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
K Instructional methods/techniques
zz\\\\\] [\\\\\\] [\\\\\\] zz\\\\\] zzzzzzzz
Examinations
L Content of examinations
zzzzzzzz [\\\\\\] [\\\\\\] zzzzzzzz [\zzzzzz
M Examination performance standards
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
N School Examination standards
[\\\\\\] [\\\\\\] [\\\\\\] zzzzzzzz [\zzzzzz
Figure 10. Country/Jurisdictions: Relative Importance for each of the Four Facets
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 100% 0% 0% 0% 0%
Content of instruction 83% 0% 0% 0% 25%
Methods (including textbooks) 67% 0% 0% 17% 50%
Examinations 67% 0% 0% 67% 44%
Note. The denominator for the percentages is the number of subcategories (as defined in Figure 9) within each category x 3. The numerator (x) is the sum of the
values assigned for each chosen subcategory; for example, for cell (1,1) the formula is x/15. The facet Methods of Instruction includes textbook selection as well.

Figure 11. Relative Importance Averaged Across All 19 Countries/Jurisdictions

National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 52% 24% 40% 29% 33%
Content of instruction 46% 19% 43% 42% 53%
Methods (including textbooks) 28% 18% 55% 50% 74%
Examinations 55% 16% 30% 40% 41%

Note for Figures 9, 10 & 11. In the above figures looking across rows tells who has what role while looking down the columns especially in Figures 10 and 11,
indicates over which facets each locus has the most influence. We acknowledge David E. Wiley’s contribution to the study of curriculum decision making.

Unclassified
34  EDU/WKP(2022)6

Coverage of Mathematics Topics in the Standards

Figure 12. Comparing the Patterns of Coverage over 25 Years

Note. Green cells indicate coverage defined by TIMSS A+; Orange cells indicate coverage defined by at least a simple
majority of the 19 countries/jurisdictions; Blue cells indicate specific country/jurisdiction coverage.

Figure 13. Moving into the Future: Current Coverage of Topics Defining a
New Literacy

Note. Orange cells indicate the number of countries that cover that topic at that grade level. The accompanying column
indicates the number of countries/jurisdictions that included that topic at any grade level; Blue cells indicate specific
country/jurisdiction coverage. The absence of Green cells indicates the lack of coverage of those topics in TIMSS95.

Unclassified
 EDU/WKP(2022)6  35

Hungary
Curriculum Standards
Index Figure 2. Degree of Emphasis for the Coverage of
 Page 1 portrays the composition of the country’s/ Four Types of Quantitative Reasoning
jurisdiction’s curriculum standards.
 Page 2 portrays the composition of a representative 8 th
grade mathematics textbook.
 Page 3 portrays the curriculum decision making authority
within the educational system.
 Page 4 portrays the mathematics topic coverage of the
country’s/jurisdiction’s curriculum standards across
grades 1-8 in comparison to the 1995 TIMSS A+
benchmark curriculum.

Figure 1. Number of Topics to be Covered at each Grade Figure 3. Degree of Emphasis for the Coverage of
Higher-Order Applications

Figure 4. Degree of Emphasis for the Coverage of 21st

Century Competencies/Skills

Notes for Figure 1:

 Light Grey bars show the range for the number of topics that each
of the 19 countries/jurisdictions intended to cover.
 Dark Grey bars show the Inter-Quartile Range (25th to 75th
Percentile) found within the broader range for the number of
topics that each of the 19 countries/jurisdictions intended to
cover.
 The stars show the number of topics that the country/
jurisdiction intended to cover at each of the grades.
Notes for Figures 2-4:
 The structure of these figures is the same as described in the note for Figure
Note for Curriculum Standards: 1.
 The variable represented in each of these figures is a measure of the
 Hungary adopted a new mathematics curriculum for grades 1, 5 intensity/emphasis that the curriculum standards for each of the
and 9 in 2020, but the 8th grade textbook in this report is based countries/jurisdictions placed on each of these three dimensions of
on the 2012 National Curriculum. mathematics literacy.
 The measure is defined with 0 indicating no mention of the
dimension and 1-75 indicating the degree of emphasis (see
methods section of the introduction to the country/jurisdiction
reports).

Unclassified
36  EDU/WKP(2022)6

8th Grade Textbook Exercises

Characteristics of Higher-Order Real-World
Textbook Exercise Composition Application Textbook Exercises
Figure 5. Totals Over All Participants’ Figure 7. Types of Quantitative Reasoning
Textbooks

Figure 8. Types of 21st Century Competencies

Figure 6. Country/Jurisdiction Textbook

Notes for Figures 5 (total number of exercises across all countries/jurisdictions)

& 6 (country/jurisdiction specific):
 The Blue pie diagram shows the total number of different types of Notes for Figures 7 & 8:
exercises.  Light Grey bars show the range for the number of Higher-Order Real-World
 The Grey pie diagram shows the number of standard word problems application exercises of each type for each country/jurisdiction.
(an expansion of the light-blue wedge).  Dark Grey bars show the Inter-Quartile Range (25th to 75th percentile).
 The Orange wedge represents the number of Higher-Order Math-  Special case: in cases where the majority of the country’s/jurisdiction’s
World applications. values were 0, the light grey bar encompasses the dark grey bar.
 The Yellow wedge represents the number of Higher-Order Real-  The stars show the number of Higher-Order Real-World application
World applications. exercises of each type that are included.
 For countries/jurisdictions that coded 2 textbooks, the average
number of exercises of the two textbooks was used in Figures 5, Note for Textbook:
6, 7 and 8.
 Hungary adopted a new mathematics curriculum for grades 1, 5 and 9 in
2020, but the 8th grade textbook in this report is based on the 2012
National Curriculum.

Unclassified
 EDU/WKP(2022)6  37

Curriculum Decision Making

0 1 2 3

No formal Advice & Constrain, veto Final authority

or modify
Decision role recommendations or approval
recommendation
Role: s
[\\\\\\] zz\\\\\] [\zzzzzz zzzzzzzz
Figure 9. Who Makes What Decisions?
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils
A By overall system
zzzzzzzz [\\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
B For intermediate stages
zzzzzzzz [\\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
C For differentiated programe types
[\zzzzzz [\\\\\\] zzzzzzzz zz\\\\\] zz\\\\\]
D To be reached in a given grade
[\\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
E To apply for a specific school
[\zzzzzz [\\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
Content of instruction
F Course (grade level) offerings
zzzzzzzz [\\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
G Student course assignment rules
[\\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
H Course content (syllabi)
zzzzzzzz [\\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
I Auxiliary content outside of syllabi
[\\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
Methods of instruction
J Textbook selection
zz\\\\\] [\\\\\\] [\zzzzzz zzzzzzzz zzzzzzzz
K Instructional methods/techniques
[\\\\\\] [\\\\\\] [\zzzzzz [\zzzzzz zzzzzzzz
Examinations
L Content of examinations
zzzzzzzz [\\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
M Examination performance standards
zzzzzzzz [\\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
N School Examination standards
[\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
Figure 10. Country/Jurisdictions: Relative Importance for each of the Four Facets
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 67% 0% 100% 87% 87%
Content of instruction 50% 0% 100% 100% 100%
Methods (including textbooks) 17% 0% 67% 83% 100%
Examinations 67% 0% 67% 67% 67%
Note. The denominator for the percentages is the number of subcategories (as defined in Figure 9) within each category x 3. The numerator (x) is the sum of the
values assigned for each chosen subcategory; for example, for cell (1,1) the formula is x/15. Note. The facet Methods of Instruction includes textbook selection as
well.
Figure 11. Relative Importance Averaged Across All 19 Countries/Jurisdictions
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 52% 24% 40% 29% 33%
Content of instruction 46% 19% 43% 42% 53%
Methods (including textbooks) 28% 18% 55% 50% 74%
Examinations 55% 16% 30% 40% 41%

Note for Figures 9, 10 & 11. In the above figures looking across rows tells who has what role while looking down the columns especially in Figures 10 and 11,
indicates over which facets each locus has the most influence. We acknowledge David E. Wiley’s contribution to the study of curriculum decision making.

Unclassified
38  EDU/WKP(2022)6

Coverage of Mathematics Topics in the Standards

Figure 12. Comparing the Patterns of Coverage over 25 Years
Majority
TIMSS95 Hungary
OECD2020
Mathematics Topic 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
Whole Number: Meaning 1 1 1 1 1 0 0 0 19 19 17 14 12 9 5 4 1 1 0 0 0 0 0 0

Whole Number: Operations 1 1 1 1 1 0 0 0 19 19 19 19 14 12 11 9 1 1 1 1 0 0 0 0

Measurement Units, Estimation & Errors 1 1 1 1 1 1 1 0 17 17 18 17 15 11 9 9 0 0 1 1 0 0 0 1

Common Fractions 0 0 1 1 1 1 0 0 4 8 15 15 16 14 4 3 0 0 1 1 1 1 0 0

Equations & Formulas 0 0 1 1 1 1 1 1 8 8 10 11 16 17 19 19 0 0 0 0 1 1 1 1

Data Representation & Analysis 0 0 1 1 1 1 0 1 8 10 12 14 17 17 18 18 0 0 0 0 1 1 1 1

2-D Geometry: Basics 0 0 1 1 1 1 1 1 14 17 14 13 12 14 13 9 1 1 0 0 1 1 0 0

2-D Geometry: Polygons & Circles 0 0 0 1 1 1 1 1 11 14 14 15 19 18 15 15 0 1 1 1 1 1 1 1

Measurement: Perimeter, Area & Volume 0 0 0 1 1 1 1 1 11 14 14 15 19 18 15 15 0 1 1 1 1 1 1 1

Rounding & Significant Figures 0 0 0 1 1 0 0 0 0 0 4 9 12 8 6 7 0 0 1 1 1 0 0 0

Estimating Computations 0 0 0 1 1 1 0 0 5 7 10 11 13 12 7 6 0 0 1 1 1 1 0 0

Whole Numbers: Properties of Operations 0 0 0 1 1 0 0 0 12 14 16 18 15 13 10 7 0 0 1 1 1 1 0 0

Decimal Fractions 0 0 0 1 1 1 0 0 0 0 4 12 19 16 10 7 0 0 0 0 1 1 0 0

Relation of Common & Decimal Fractions 0 0 0 1 1 1 0 0 0 0 5 9 14 16 8 6 0 0 0 0 1 1 0 1

Properties of Common & Decimal Fractions 0 0 0 0 1 1 0 0 0 0 5 9 14 16 8 6 0 0 0 0 1 1 0 1

Percentages 0 0 0 0 1 1 0 0 0 0 4 12 19 16 10 7 0 0 0 0 1 1 0 0

Proportionality Concepts 0 0 0 0 1 1 1 1 1 1 1 5 11 16 16 13 0 0 0 1 1 1 0 0

Proportionality Problems 0 0 0 0 1 1 1 1 1 1 1 5 11 16 16 13 0 0 0 1 1 1 0 0

2-D Geometry: Coordinate Geometry 0 0 0 0 1 1 1 1 0 0 1 4 5 9 11 12 0 0 0 0 0 1 1 1

Geometry: Transformations 0 0 0 0 0 1 1 1 4 7 5 7 6 7 8 8 0 0 0 0 0 0 1 1

Negative Numbers, Integers, & Their Properties 0 0 0 0 0 1 1 0 3 3 4 5 6 11 14 12 0 0 0 0 1 1 0 0

Exponents, Roots & Radicals 0 0 0 0 0 0 1 1 0 0 0 1 3 4 13 13 0 0 0 0 0 0 1 1

Exponents & Orders of Magnitude 0 0 0 0 0 0 1 1 1 2 3 4 5 3 11 11 0 0 0 0 0 1 1 0

Geometry: Congruence & Similarity 0 0 0 0 0 0 0 1 1 1 1 2 3 5 9 12 0 0 0 0 0 1 1 1

Rational Numbers & Their Properties 0 0 0 0 0 0 0 1 0 0 2 4 5 8 10 8 0 0 0 1 1 1 0 0

Patterns, Relations & Functions 0 0 0 0 0 0 0 1 0 0 0 2 2 3 11 16 0 0 0 0 0 0 1 1

Proportionality: Slope & Trigonometry 0 0 0 0 0 0 0 1 0 0 0 1 1 3 9 16 0 0 0 0 0 0 0 1

Real Numbers, Their Subsets & Properties 0 0 0 0 0 0 0 0 0 0 0 0 0 1 6 13 0 0 0 0 0 0 0 1

Note. Green cells indicate coverage defined by TIMSS A+; Orange cells indicate coverage defined by at least a simple majority of the 19
countries/jurisdictions; Blue cells indicate specific country/jurisdiction coverage.
Figure 13. Moving into the Future: Current Coverage of Topics Defining a New
Literacy

Note. Orange cells indicate the number of countries that cover that topic at that grade level. The accompanying column indicates the number of
countries/jurisdictions that included that topic at any grade level; Blue cells indicate specific country/jurisdiction coverage. The absence of green
cells indicates the lack of coverage of those topics in TIMSS95.

Unclassified
 EDU/WKP(2022)6  39

Israel
Curriculum Standards
Index
 Page 1 portrays the composition of the country’s/ Figure 2. Degree of Emphasis for the Coverage of
jurisdiction’s curriculum standards. Four Types of Quantitative Reasoning
 Page 2 portrays the composition of a representative 8 th
grade mathematics textbook.
 Page 3 portrays the curriculum decision-making authority
within the educational system.
 Page 4 portrays the mathematics topic coverage of the
country’s/jurisdiction’s curriculum standards across
grades 1-8 in comparison to the 1995 TIMSS A+
benchmark curriculum.

Figure 1. Number of Topics to be Covered at each Grade

Figure 3. Degree of Emphasis for the Coverage of
Higher-Order Applications

Figure 4. Degree of Emphasis for the Coverage of 21st

Century Competencies/Skills

Notes for Figure 1:

 Light Grey bars show the range for the number of topics that each
of the 19 countries/jurisdictions intended to cover.
 Dark Grey bars show the Inter-Quartile Range (25th to 75th Notes for Figures 2-4:
Percentile) found within the broader range for the number of
 The structure of these figures is the same as described in the note for Figure
topics that each of the 19 countries/jurisdictions intended to
1.
cover.
 The variable represented in each of these figures is a measure of the
 The stars show the number of topics that the country/
intensity/emphasis that the curriculum standards for each of the
jurisdiction intended to cover at each of the grades.
countries/jurisdictions placed on each of these three dimensions of
mathematics literacy.
 The measure is defined with 0 indicating no mention of the
dimension and 1-75 indicating the degree of emphasis (see
methods section of the introduction to the country/jurisdiction
reports).

Unclassified
40  EDU/WKP(2022)6

8th Grade Textbook Exercises

Textbook Exercise Composition Characteristics of Higher-Order Real-World
Application Textbook Exercises

Figure 5. Totals Over All Participants’ Figure 7. Types of Quantitative Reasoning

Textbooks

Figure 8. Types of 21st Century Competencies

Figure 6. Country/Jurisdiction Textbook

Notes for Figures 5 (total number of exercises across all countries/jurisdictions)

& 6 (country/jurisdiction specific):
 The Blue pie diagram shows the total number of different types of
exercises.
 The Grey pie diagram shows the number of standard word problems Notes for Figures 7 & 8:
(an expansion of the light-blue wedge).
 Light Grey bars show the range for the number of Higher-Order Real-World
 The Orange wedge represents the number of Higher-Order Math-
application exercises of each type for each country/jurisdiction.
World applications.
 Dark Grey bars show the Inter-Quartile Range (25th to 75th percentile).
 The Yellow wedge represents the number of Higher-Order Real-
 Special case: in cases where the majority of the country’s/jurisdiction’s
World applications.
values were 0, the light grey bar encompasses the dark grey bar.
 For countries/jurisdictions that coded 2 textbooks, the average
 The stars show the number of Higher-Order Real-World application
number of exercises of the two textbooks was used in Figures 5,
exercises of each type that are included.
6, 7 and 8.

Unclassified
 EDU/WKP(2022)6  41

Curriculum Decision Making

0 1 2 3

Advice & Constrain, veto or modify Final authority

Decision Role: No formal role
recommendation recommendations or approval

[\\\\\\] zz\\\\\] [\zzzzzz zzzzzzzz

Figure 9. Who Makes What Decisions?
Teachers Teachers
National Regional School
Collectively Individually
Goals for pupils
A By overall system completion
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
B For intermediate stages
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
C For differentiated programme types
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
D To be reached in a given grade
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
E To apply for a specific school
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
Content of Instruction
F Course (grade level) offeringS
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
G s Student course assignment rules
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
H Course content (syllabi)
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
I Auxiliary content outside of syllabi
[\zzzzzz [\zzzzzz zzzzzzzz [\\\\\\] zzzzzzzz
Methods of instruction
J Textbook selection
[\zzzzzz [\\\\\\] zzzzzzzz zzzzzzzz [\\\\\\]
K Instructional methods/techniques
zz\\\\\] zz\\\\\] [\zzzzzz [\zzzzzz zzzzzzzz
Examinations
L Content of examinations
zz\\\\\] zz\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
M Examination performance standards
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
N School Examination standards
zz\\\\\] zz\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
Figure 10. Country/Jurisdictions: Relative Importance for each of the Four Facets
Teachers Teachers
National Regional School
Collectively Individually
Goals for pupils 100% 0% 0% 0% 0%
Content of instruction 92% 17% 25% 0% 25%
Methods (including textbooks) 50% 17% 83% 83% 50%
Examinations 56% 22% 67% 67% 67%
Notes. The denominator for the percentages is the number of subcategories (as defined in Figure 9) within each category x 3. The numerator (x)
is the sum of the values assigned for each chosen subcategory; for example, for cell (1,1) the formula is x/15. The facet Methods of Instruction
includes textbook selection as well.
Figure 11. Relative Importance Averaged Across All 19 Countries/Jurisdictions
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 52% 24% 40% 29% 33%
Content of instruction 46% 19% 43% 42% 53%
Methods (including textbooks) 28% 18% 55% 50% 74%
Examinations 55% 16% 30% 40% 41%
Notes for Figures 9, 10 & 11. In the above figures looking across rows tells who has what role while looking down the columns especially in
Figures 10 and 11, indicates over which facets each locus has the most influence. We acknowledge David E. Wiley’s contribution to the study of
curriculum decision making.

Unclassified
42  EDU/WKP(2022)6

Coverage of Mathematics Topics in the Standards

Figure 12. Comparing the Patterns of Coverage over 25 Years

Note. Green cells indicate coverage defined by TIMSS A+; Orange cells indicate coverage defined by at least a simple majority of the 19
countries/jurisdictions; Blue cells indicate specific country/jurisdiction coverage.
Figure 13. Moving into the Future: Current Coverage of Topics Defining a New
Literacy

Note. Orange cells indicate the number of countries that cover that topic at that grade level. The accompanying column indicates the number of
countries/jurisdictions that included that topic at any grade level; Blue cells indicate specific country/jurisdiction coverage. The absence of green
cells indicates the lack of coverage of those topics in TIMSS95.

Unclassified
 EDU/WKP(2022)6  43

Japan
Curriculum Standards
Index Figure 2. Degree of Emphasis for the Coverage of
 Page 1 portrays the composition of the country’s/ Four Types of Quantitative Reasoning
jurisdiction’s curriculum standards.
 Page 2 portrays the composition of a representative 8 th
grade mathematics textbook.
 Page 3 portrays the curriculum decision-making authority
within the educational system.
 Page 4 portrays the mathematics topic coverage of the
country’s/jurisdiction’s curriculum standards across
grades 1-8 in comparison to the 1995 TIMSS A+
benchmark curriculum.
Figure 3. Degree of Emphasis for the Coverage of
Figure 1. Number of Topics to be Covered at each Grade Higher-Order Applications

Figure 4. Degree of Emphasis for the Coverage of 21st

Century Competencies/Skills

Notes for Figure 1:

 Light Grey bars show the range for the number of topics that each
of the 19 countries/jurisdictions intended to cover.
 Dark Grey bars show the Inter-Quartile Range (25th to 75th
Percentile) found within the broader range for the number of
topics that each of the 19 countries/jurisdictions intended to
cover.
 The stars show the number of topics that the country/
jurisdiction intended to cover at each of the grades.
 The numbers presented in Figure 1 are based on data from the
coding of the MCDA Framework and as a result are not
Notes for Figures 2-4:
associated with changes made to Figure 12.
 The structure of these figures is the same as described in the note for Figure
1.
\  The variable represented in each of these figures is a measure of the
intensity/emphasis that the curriculum standards for each of the
countries/jurisdictions placed on each of these three dimensions of
mathematics literacy.
 The measure is defined with 0 indicating no mention of the
dimension and 1-75 indicating the degree of emphasis (see
methods section of the introduction to the country/jurisdiction
reports).

Unclassified
44  EDU/WKP(2022)6

8th Grade Textbook Exercises

Textbook Exercise Composition Characteristics of Higher-Order Real-World
Application Textbook Exercises
Figure 5. Totals Over All Participants’ Figure 7. Types of Quantitative Reasoning
Textbooks

Figure 8. Types of 21st Century Competencies

Figure 6. Country/Jurisdiction Textbook

Notes for Figures 5 (total number of exercises across all countries/jurisdictions)

& 6 (country/jurisdiction specific):
 The Blue pie diagram shows the total number of different types of
exercises. Notes for Figures 7 & 8:
 The Grey pie diagram shows the number of standard word problems  Light Grey bars show the range for the number of Higher-Order Real-World
(an expansion of the light-blue wedge). application exercises of each type for each country/jurisdiction.
 The Orange wedge represents the number of Higher-Order Math-  Dark Geay bars show the Inter-Quartile Range (25th to 75th percentile).
World applications.  Special case: in cases where the majority of the country’s/jurisdiction’s
 The Yellow wedge represents the number of Higher-Order Real- values were 0, the light grey bar encompasses the dark grey bar.
World applications.  The stars show the number of Higher-Order Real-World application
 For countries/jurisdictions that coded 2 textbooks, the average exercises of each type that are included.
number of exercises of the two textbooks was used in Figures 5,
6, 7 and 8.

Unclassified
 EDU/WKP(2022)6  45

Curriculum Decision Making

0 1 2 3

No formal Advice & Constrain, veto or

modify Final authority or approval
role recommendations
Decision Role: recommendations

[\\\\\\] zz\\\\\] [\zzzzzz zzzzzzzz

Figure 9. Who Makes What Decisions?
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils
A By overall system completion
zzzzzzzz zz\\\\\] zz\\\\\] [\\\\\\] [\\\\\\]
B For intermediate stages
zzzzzzzz zz\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
C For differentiated programme types
zzzzzzzz zz\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
D To be reached in a given grade
zzzzzzzz zz\\\\\] zz\\\\\] [\\\\\\] [\\\\\\]
E To apply for a specific school
[\\\\\\] zz\\\\\] zzzzzzzz [\\\\\\] [\\\\\\]
Content of instruction
F Course (grade level) offerings
zzzzzzzz zz\\\\\] zzzzzzzz [\zzzzzz [\zzzzzz
G Student course assignment rules
zzzzzzzz zz\\\\\] zzzzzzzz [\zzzzzz [\zzzzzz
H Course content (syllabi)
zz\\\\\] [\zzzzzz zzzzzzzz [\zzzzzz [\zzzzzz
1 Auxiliary content outside of syllabi
zz\\\\\] [\zzzzzz zzzzzzzz [\zzzzzz [\zzzzzz
Methods of instruction
J Textbook selection
zzzzzzzz [\zzzzzz [\\\\\\] [\\\\\\] [\\\\\\]
K Instructional methods/techniques
zz\\\\\] [\zzzzzz [\zzzzzz [\zzzzzz zzzzzzzz
Examinations
L Content of examinations
zz\\\\\] zz\\\\\] zz\\\\\] zz\\\\\] zzzzzzzz
M Examination performance standards
standards zz\\\\\] zz\\\\\] zz\\\\\] zz\\\\\] [\\\\\\]
N School Examination
zz\\\\\] zz\\\\\] [\zzzzzz [\zzzzzz zzzzzzzz
Figure 10. Country/Jurisdictions: Relative Importance for each of the Four Facets
National Regional School Teachers Collectively Teachers Individually
Goals for pupils 80% 33% 33% 0% 0%
Content of instruction 67% 50% 100% 67% 67%
Methods (including textbooks) 67% 67% 33% 33% 50%
Examinations 33% 33% 44% 44% 67%
Notes:The denominator for the percentages is the number of subcategories (as defined in Figure 9) within each category x 3. The numerator (x)
is the sum of the values assigned for each chosen subcategory; for example, for cell (1,1) the formula is x/15. The facet Methods of Instruction
includes textbook selection as well.
Figure 11. Relative Importance Averaged Across All 19 Countries/Jurisdictions
National Regional School Teachers Collectively Teachers Individually
Goals for pupils 52% 24% 40% 29% 33%
Content of instruction 46% 19% 43% 42% 53%
Methods (including textbooks) 28% 18% 55% 50% 74%
Examinations 55% 16% 30% 40% 41%
Note for Figures 9, 10 & 11. In the above figures looking across rows tells who has what role while looking down the columns especially in
Figures 10 and 11, indicates over which facets each locus has the most influence. Given Japan’s Ministry of Education’s request for changes in
Figure 9, Figure 11 does not include their revised data. We acknowledge David E. Wiley’s contribution to the study of curriculum decision
making.

Unclassified
46  EDU/WKP(2022)6

Coverage of Mathematics Topics in the Standards

Figure 12. Comparing the Patterns of Coverage over 25 Years

Note. Green cells indicate coverage defined by TIMSS A+; Orange cells indicate coverage defined by at least a simple majority of the 19
countries/jurisdictions; Blue cells indicate specific country/jurisdiction coverage. At the request of the Japanese Ministry of Education, changes
were made to the data collected at the original work session. The modifications are identified by a change in the color of each cell for which a
change was requested. The new colors for each modified cell are indicated by the key below Figure 12.

Figure 13. Moving into the Future: Current Coverage of Topics Defining a New Literacy

Note. Orange cells indicate the number of countries that cover that topic at that grade level. The accompanying column indicates the number of
countries/jurisdictions that included that topic at any grade level; Blue cells indicate specific country/jurisdiction coverage. The absence of green
cells indicates the lack of coverage of those topics in TIMSS95.

Unclassified
 EDU/WKP(2022)6  47

Korea
Curriculum Standards
Index
 Page 1 portrays the composition of the country’s/ Figure 2. Degree of Emphasis for the Coverage of
jurisdiction’s curriculum standards. Four Types of Quantitative Reasoning
 Page 2 portrays the composition of a representative 8 th
grade mathematics textbook.
 Page 3 portrays the curriculum decision-making authority
within the educational system.
 Page 4 portrays the mathematics topic coverage of the
country’s/jurisdiction’s curriculum standards across
grades 1-8 in comparison to the 1995 TIMSS A+
benchmark curriculum.

Figure 1. Number of Topics to be Covered at each Grade

Figure 3. Degree of Emphasis for the Coverage of
Higher-Order Applications

Figure 4. Degree of Emphasis for the Coverage of 21st

Century Competencies/Skills

Notes for Figure 1:

 Light Grey bars show the range for the number of topics that each
of the 19 countries/jurisdictions intended to cover.
 Dark Grey bars show the Inter-Quartile Range (25th to 75th Notes for Figures 2-4:
Percentile) found within the broader range for the number of  The structure of these figures is the same as described in the note for Figure
topics that each of the 19 countries/jurisdictions intended to 1.
cover.  The variable represented in each of these figures is a measure of the
 The stars show the number of topics that the country/ intensity/emphasis that the curriculum standards for each of the
jurisdiction intended to cover at each of the grades. countries/jurisdictions placed on each of these three dimensions of
mathematics literacy.
 The measure is defined with 0 indicating no mention of the
dimension and 1-75 indicating the degree of emphasis (see
methods section of the introduction to the country/jurisdiction
reports).

Unclassified
48  EDU/WKP(2022)6

8th Grade Textbook Exercises

Textbook Exercise Composition Characteristics of Higher-Order Real-World
Application Textbook Exercises
Figure 5. Totals Over All Participants’ Figure 7. Types of Quantitative Reasoning
Textbooks

Figure 8. Types of 21st Century Competencies

Figure 6. Country/Jurisdiction Textbook

Notes for Figures 5 (total number of exercises across all countries/jurisdictions)

& 6 (country/jurisdiction specific):
 The Blue pie diagram shows the total number of different types of
exercises.
 The Grey pie diagram shows the number of standard word problems
(an expansion of the light-blue wedge).
 The Orange wedge represents the number of Higher-Order Math- Notes for Figures 7 & 8:
World applications.
 Light Grey bars show the range for the number of Higher-Order Real-World
 The Yellow wedge represents the number of Higher-Order Real-
application exercises of each type for each country/jurisdiction.
World applications.
 Dark Grey bars show the Inter-Quartile Range (25th to 75th percentile).
 For countries/jurisdictions that coded 2 textbooks, the average
 Special case: in cases where the majority of the country’s/jurisdiction’s
number of exercises of the two textbooks was used in Figures 5,
values were 0, the light grey bar encompasses the dark grey bar.
6, 7 and 8.
 The stars show the number of Higher-Order Real-World application
exercises of each type that are included.

Unclassified
 EDU/WKP(2022)6  49

Curriculum Decision Making

0 1 2 3

Decision No formal Advice & Constrain, veto or Final authority

Role: role recommendations modify or approval
recommendations

[\\\\\\] zz\\\\\] [\zzzzzz zzzzzzzz

Figure 9. Who Makes What Decisions?
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils
A By overall system completion
B For intermediate stages
[\\\\\\] [\zzzzzz [\zzzzzz [\zzzzzz [\zzzzzz
[\\\\\\] [\zzzzzz [\zzzzzz [\zzzzzz [\zzzzzz
C For differentiated programme types
[\\\\\\] [\zzzzzz zz\\\\\] zz\\\\\] zz\\\\\]
D To be reached in a given grade
[\\\\\\] [\zzzzzz [\zzzzzz [\zzzzzz [\zzzzzz
E To apply for a specific school
[\zzzzzz [\zzzzzz zzzzzzzz zz\\\\\] zz\\\\\]
Content of instruction
F Course (grade level) offerings
[\\\\\\] zz\\\\\] zz\\\\\] zz\\\\\] zz\\\\\]
G Student course assignment rules
[\zzzzzz [\zzzzzz zzzzzzzz zz\\\\\] zz\\\\\]
H Course content (syllabi)
zz\\\\\] zz\\\\\] zz\\\\\] zzzzzzzz zzzzzzzz
I Auxiliary content outside of syllabi
[\zzzzzz [\zzzzzz [\zzzzzz zzzzzzzz zzzzzzzz
Methods of instruction
J Textbook selection
[\\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
K Instructional methods/techniques
zz\\\\\] zz\\\\\] zz\\\\\] zzzzzzzz zzzzzzzz
Examinations
L Content of examinations
[\\\\\\] zz\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
M Examination performance standards
[\\\\\\] zz\\\\\] zz\\\\\] zz\\\\\] zz\\\\\]
N School Examination standards
zz\\\\\] zz\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
Figure 10. Country/Jurisd: Relative Importance for each of the Four Facets
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 13% 67% 67% 53% 53%
Content of instruction 42% 50% 58% 67% 67%
Methods (including textbooks) 17% 17% 67% 100% 100%
Examinations 11% 33% 78% 78% 78%
Note. The denominator for the percentages is the number of subcategories (as defined in Figure 9) within each category x 3.
The numerator (x) is the sum of the values assigned for each chosen subcategory; for example, for cell (1,1) the formula is x/15.
The facet Methods of Instruction includes textbook selection as well.
Figure 11. Relative Importance Averaged Across All 19 Countries/Jurisdictions
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 52% 24% 40% 29% 33%
Content of instruction 46% 19% 43% 42% 53%
Methods (including textbooks) 28% 18% 55% 50% 74%
Examinations 55% 16% 30% 40% 41%
Note for Figures 9, 10 & 11. In the above figures looking across rows tells who has what role while looking down the columns
especially in Figures 10 and 11, indicates over which facets each locus has the most influence.
We acknowledge David E. Wiley’s contribution to the study of curriculum decision making.

Unclassified
50  EDU/WKP(2022)6

Coverage of Mathematics Topics in the Standards

Figure 12. Comparing the Patterns of Coverage over 25 Years

Note. Green cells indicate coverage defined by TIMSS A+; Orange cells indicate coverage defined by at least a simple majority of the 19
countries/jurisdictions; Blue cells indicate specific country/jurisdiction coverage.

Figure 13. Moving into the Future: Current Coverage of Topics Defining a New
Literacy

Note. Orange cells indicate the number of countries that cover that topic at that grade level. The accompanying column indicates the number of
countries/jurisdictions that included that topic at any grade level; Blue cells indicate specific country/jurisdiction coverage. The absence of green
cells indicates the lack of coverage of those topics in TIMSS95.

Unclassified
 EDU/WKP(2022)6  51

Latvia
Curriculum Standards
Index
 Page 1 portrays the composition of the country’s/ Figure 2. Degree of Emphasis for the Coverage of
jurisdiction’s curriculum standards. Four Types of Quantitative Reasoning
 Page 2 portrays the composition of a representative 8 th
grade mathematics textbook.
 Page 3 portrays the curriculum decision-making authority
within the educational system.
 Page 4 portrays the mathematics topic coverage of the
country’s/jurisdiction’s curriculum standards across
grades 1-8 in comparison to the 1995 TIMSS A+
benchmark curriculum.

Figure 1. Number of Topics to be Covered at each Grade

Figure 3. Degree of Emphasis for the Coverage of
Higher-Order Applications

Figure 4. Degree of Emphasis for the Coverage of 21st

Century Competencies/Skills

Notes for Figure 1:

 Light Grey bars show the range for the number of topics that each
of the 19 countries/jurisdictions intended to cover.
 Dark Grey bars show the Inter-Quartile Range (25th to 75th Notes for Figures 2-4:
Percentile) found within the broader range for the number of  The structure of these figures is the same as described in the note for Figure
topics that each of the 19 countries/jurisdictions intended to 1.
cover.  The variable represented in each of these figures is a measure of the
 The stars show the number of topics that the country/ intensity/emphasis that the curriculum standards for each of the
jurisdiction intended to cover at each of the grades. countries/jurisdictions placed on each of these three dimensions of
mathematics literacy.
 The measure is defined with 0 indicating no mention of the
dimension and 1-75 indicating the degree of emphasis (see
methods section of the introduction to the country/jurisdiction
reports).

Unclassified
52  EDU/WKP(2022)6

8th Grade Textbook Exercises

Textbook Exercise Composition Characteristics of Higher-Order Real-World
Application Textbook Exercises
Figure 5. Totals Over All Participants’ Figure 7. Types of Quantitative Reasoning
Textbooks

Figure 8. Types of 21st Century Competencies

Figure 6. Country/Jurisdiction Textbook

Notes for Figures 5 (total number of exercises across all countries/jurisdictions)

& 6 (country/jurisdiction specific):
 The Blue pie diagram shows the total number of different types of
exercises.
 The Grey pie diagram shows the number of standard word problems
(an expansion of the light-blue wedge). Notes for Figures 7 & 8:
 The Orange wedge represents the number of Higher-Order Math-  Light Grey bars show the range for the number of Higher-Order Real-World
World applications. application exercises of each type for each country/jurisdiction.
 The Yellow wedge represents the number of Higher-Order Real-  Dark Grey bars show the Inter-Quartile Range (25th to 75th percentile).
World applications.
 Special case: in cases where the majority of the country’s/jurisdiction’s
 For countries/jurisdictions that coded 2 textbooks, the average
values were 0, the light grey bar encompasses the dark grey bar.
number of exercises of the two textbooks was used in Figures 5,
 The stars show the number of Higher-Order Real-World application
6, 7 and 8.
exercises of each type that are included.

Unclassified
 EDU/WKP(2022)6  53

Curriculum Decision Making

0 1 2 3
Constrain, veto or
Advice & Final authority or
No formal role modify
Decision recommendations
recommendations
approval

Role:
[\\\\\\] zz\\\\\] [\zzzzzz zzzzzzzz
Figure 9. Who Makes What Decisions?
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils
A By overall system completion
zzzzzzzz [\zzzzzz [\zzzzzz [\zzzzzz [\zzzzzz
B For intermediate stages
zzzzzzzz [\zzzzzz [\zzzzzz [\zzzzzz [\zzzzzz
C For differentiated programme types
zz\\\\\] [\zzzzzz zzzzzzzz [\zzzzzz [\zzzzzz
D To be reached in a given grade
zz\\\\\] [\zzzzzz zzzzzzzz [\zzzzzz [\zzzzzz
E To apply for a specific school
zz\\\\\] [\zzzzzz zzzzzzzz [\zzzzzz [\zzzzzz
Content of instruction
F Course (grade level) offerings
zz\\\\\] [\\\\\\] [\zzzzzz [\zzzzzz zzzzzzzz
G Student course assignment rules
zz\\\\\] [\\\\\\] [\zzzzzz [\zzzzzz zzzzzzzz
H Course content (syllabi)
zz\\\\\] [\\\\\\] [\zzzzzz [\zzzzzz zzzzzzzz
I Auxiliary content outside of syllabi
[\\\\\\] [\\\\\\] zzzzzzzz [\zzzzzz zzzzzzzz
Methods of instruction
J Textbook selection
zz\\\\\] [\\\\\\] zzzzzzzz [\zzzzzz [\zzzzzz
K Instructional methods/techniques
[\\\\\\] [\\\\\\] zz\\\\\] [\zzzzzz zzzzzzzz
Examinations
L Content of examinations
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
M Examination performance standards
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
N School Examination standards
zz\\\\\] [\\\\\\] zz\\\\\] zzzzzzzz zzzzzzzz
Figure 10. Country/Jurisdictions: Relative Importance for each of the Four Facets
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 60% 67% 87% 67% 67%
Content of instruction 25% 0% 75% 67% 100%
Methods (including textbooks) 17% 0% 67% 67% 83%
Examinations 78% 0% 11% 33% 33%
Notes The denominator for the percentages is the number of subcategories (as defined in Figure 9) within each category x 3.
The numerator (x) is the sum of the values assigned for each chosen subcategory; for example, for cell (1,1) the formula is
x/15.The facet Methods of Instruction includes textbook selection as well.
Figure 11. Relative Importance Averaged Across All 19 Countries/Jurisdictions
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 52% 24% 40% 29% 33%
Content of instruction 46% 19% 43% 42% 53%
Methods (including textbooks) 28% 18% 55% 50% 74%
Examinations 55% 16% 30% 40% 41%
Note for Figures 9, 10 & 11. In the above figures looking across rows tells who has what role while looking down the columns
especially in Figures 10 and 11, indicates over which facets each locus has the most influence. We acknowledge David E.
Wiley’s contribution to the study of curriculum decision making.

Unclassified
54  EDU/WKP(2022)6

Coverage of Mathematics Topics in the Standards

Figure 12. Comparing the Patterns of Coverage over 25 Years

Note. Green cells indicate coverage defined by TIMSS A+; Orange cells indicate coverage defined by at least a simple majority of the 19
countries/jurisdictions; Blue cells indicate specific country/jurisdiction coverage.

Figure 13. Moving into the Future: Current Coverage of Topics Defining a New Literacy

Note. Orange cells indicate the number of countries that cover that topic at that grade level. The accompanying column indicates the number
of countries/jurisdictions that included that topic at any grade level; Blue cells indicate specific country/jurisdiction coverage. The absence
of green cells indicates the lack of coverage of those topics in TIMSS95.

Unclassified
 EDU/WKP(2022)6  55

8th Grade Textbook Exercises: Book 1

Exercise Composition of Characteristics of Higher-
Textbooks Order Real- World Application
Textbook Exercises
Figure 5. Totals Over All
Participants’ Textbooks Figure 7. Type of Quantitative
Reasoning

Figure 8. Type of 21st Century

Figure 6. Country/Jurisdiction Competencies
Textbook

Notes for Figures 5 (total number of exercises across all

countries/jurisdictions) & 6 (country/jurisdiction specific): Notes for Figures 7 & 8:
 The Blue pie diagram shows the total number of different
types of exercises.  Light Grey bars show the range for the number of
 The Grey pie diagram shows the number of standard word Higher-Order Real-World application exercises of
problems (an expansion of the light-blue wedge). each type for each country/jurisdiction.
 The Orange wedge represents the number of Higher-  Dark Grey bars show the Inter-Quartile Range (25th
Order Math-World applications. to 75th percentile).
 The Yellow wedge represents the number of Higher-  Special case: in cases where the majority of the
Order Real-World applications. country’s/jurisdiction’s values were 0, the light grey
bar encompasses the dark grey bar.
 For countries/jurisdictions that coded 2 textbooks, the
average number of exercises of the two textbooks was  The stars show the number of Higher-Order Real-
used in Figures 5, 6, 7 and 8. World application exercises of each type that are
included.

Unclassified
56  EDU/WKP(2022)6

8th Grade Textbook Exercises: Book 2

Exercise Composition of Textbooks Characteristics of Higher-Order
Real- World Application Textbook
Figure 5. Totals Over All Participants’ Exercises
Textbooks
Figure 7. Type of Quantitative Reasoning

Figure 6. Country/Jurisdiction Textbook Figure 8. Type of 21st Century

Competencies

Notes for Figures 5 (total number of exercises across all countries/jurisdictions)

& 6 (country/jurisdiction specific):
 The Blue pie diagram shows the total number of different types of
exercises.
 The Grey pie diagram shows the number of standard word
problems (an expansion of the light-blue wedge). Notes for Figures 7 & 8:
 The Orange wedge represents the number of Higher-Order Math-  Light Grey bars show the range for the number of Higher-Order
World applications. Real-World application exercises of each type for each
 The Yellow wedge represents the number of Higher-Order Real- country/jurisdiction.
World applications.  Dark Grey bars show the Inter-Quartile Range (25th to 75th
 For countries/jurisdictions that coded 2 textbooks, the average percentile).
number of exercises of the two textbooks was used in Figures 5,  Special case: in cases where the majority of the
6, 7 and 8. country’s/jurisdiction’s values were 0, the light grey bar encompasses
the dark grey bar.
 The stars show the number of Higher-Order Real-World
application exercises of each type that are included.

Unclassified
 EDU/WKP(2022)6  57

Lithuania
Curriculum Standards
Index
 Page 1 portrays the composition of the country’s/ Figure 2. Degree of Emphasis for the Coverage of
jurisdiction’s curriculum standards. Four Types of Quantitative Reasoning
 Page 2 portrays the composition of a representative 8 th
grade mathematics textbook.
 Page 3 portrays the curriculum decision-making authority
within the educational system.
 Page 4 portrays the mathematics topic coverage of the
country’s/jurisdiction’s curriculum standards across
grades 1-8 in comparison to the 1995 TIMSS A+
benchmark curriculum.

Figure 1. Number of Topics to be Covered at each Grade

Figure 3. Degree of Emphasis for the Coverage of
Higher-Order Applications

Figure 4. Degree of Emphasis for the Coverage of 21st

Century Competencies/Skills

Notes for Figure 1:

 Light Grey bars show the range for the number of topics that each
of the 19 countries/jurisdictions intended to cover.
 Dark Grey bars show the Inter-Quartile Range (25th to 75th
Percentile) found within the broader range for the number of Notes for Figures 2-4:
topics that each of the 19 countries/jurisdictions intended to  The structure of these figures is the same as described in the note for Figure
cover. 1.
 The stars show the number of topics that the country/  The variable represented in each of these figures is a measure of the
jurisdiction intended to cover at each of the grades. intensity/emphasis that the curriculum standards for each of the
countries/jurisdictions placed on each of these three dimensions of
mathematics literacy.
 The measure is defined with 0 indicating no mention of the
dimension and 1-75 indicating the degree of emphasis (see
methods section of the introduction to the country/jurisdiction
reports).

Unclassified
58  EDU/WKP(2022)6

8th Grade Textbook Exercises

Textbook Exercise Composition Characteristics of Higher-Order Real-World
Application Textbook Exercises
Figure 5. Totals Over All Participants’ Figure 7. Types of Quantitative Reasoning
Textbooks

Figure 8. Types of 21st Century Competencies

Figure 6. Country/Jurisdiction Textbook

Notes for Figures 5 (total number of exercises across all countries/jurisdictions)

& 6 (country/jurisdiction specific):
 The Blue pie diagram shows the total number of different types of
exercises. Notes for Figures 7 & 8:
 The Grey pie diagram shows the number of standard word problems
(an expansion of the light-blue wedge).  Light Grey bars show the range for the number of Higher-Order Real-World
 The Orange wedge represents the number of Higher-Order Math- application exercises of each type for each country/jurisdiction.
World applications.  Dark Grey bars show the Inter-Quartile Range (25th to 75th percentile).
 The Yellow wedge represents the number of Higher-Order Real-  Special case: in cases where the majority of the country’s/jurisdiction’s
World applications. values were 0, the light grey bar encompasses the dark grey bar.
 For countries/jurisdictions that coded 2 textbooks, the average  The stars show the number of Higher-Order Real-World application
number of exercises of the two textbooks was used in Figures 5, exercises of each type that are included.
6, 7 and 8.

Unclassified
 EDU/WKP(2022)6  59

Curriculum Decision Making

0 1 2 3

No formal Advice & Constrain, veto or modify Final authority

Decision Role:
role recommendations recommendations or approval

[\\\\\\] zz\\\\\] [\zzzzzz zzzzzzzz

Figure 9. Who Makes What Decisions?
Teachers Teachers
National Regional School Collectively Individually
Goals for pupils
A By overall system completion
[\\\\\\] zz\\\\\] [\zzzzzz [\zzzzzz [\zzzzzz
B For intermediate stages
[\\\\\\] zz\\\\\] [\zzzzzz [\zzzzzz [\zzzzzz
C For differentiated programme types
[\\\\\\] zz\\\\\] [\zzzzzz [\zzzzzz [\zzzzzz
D To be reached in a given grade
[\\\\\\] zz\\\\\] [\zzzzzz [\zzzzzz [\zzzzzz
E To apply for a specific school
[\\\\\\] zz\\\\\] [\zzzzzz [\zzzzzz [\zzzzzz
Content of instruction
F Course (grade level) offerings
[\\\\\\] zz\\\\\] zz\\\\\] zz\\\\\] zz\\\\\]
G Student course assignment rules
[\\\\\\] zz\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
H Course content (syllabi)
zzzzzzzz zz\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
I Auxiliary content outside of syllabi
zz\\\\\] zz\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
Methods of instruction
J Textbook selection
[\zzzzzz zz\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
K Instructional methods/techniques
zz\\\\\] zz\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
Examinations
L Content of examinations
[\\\\\\] [\\\\\\] [\\\\\\] zz\\\\\] zz\\\\\]
M Examination performance standards
[\\\\\\] [\\\\\\] [\\\\\\] zz\\\\\] zz\\\\\]
N School Examination standards
zz\\\\\] zz\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
Figure 10. Country/Jurisdictions: Relative Importance for each of the Four Facets
National Regional School Teachers Collectively Teachers Individually
Goals for pupils 60% 67% 87% 67% 67%
Content of instruction 25% 0% 75% 67% 100%
Methods (including textbooks) 17% 0% 67% 67% 83%
Examinations 78% 0% 11% 33% 33%
Note. The denominator for the percentages is the number of subcategories (as defined in Figure 9) within each category x 3. The numerator (x) is the sum of the
values assigned for each chosen subcategory; for example, for cell (1,1) the formula is x/15. The facet Methods of Instruction includes textbook selection as well.
Figure 11. Relative Importance Averaged Across All 19 Countries/Jurisdictions
National Regional School Teachers Collectively Teachers Individually
Goals for pupils 52% 24% 40% 29% 33%
Content of instruction 46% 19% 43% 42% 53%
Methods (including textbooks) 28% 18% 55% 50% 74%
Examinations 55% 16% 30% 40% 41%
Note for Figures 9, 10 & 11. In the above figures looking across rows tells who has what role while looking down the columns especially in
Figures 10 and 11, indicates over which facets each locus has the most influence.We acknowledge David E. Wiley’s contribution to the study
of curriculum decision making.

Unclassified
60  EDU/WKP(2022)6

Coverage of Mathematics Topics in the Standards

Figure 12. Comparing the Patterns of Coverage over 25 Years

Note. Green cells indicate coverage defined by TIMSS A+; Orange cells indicate coverage defined by at least a simple majority of the 19
countries/jurisdictions; Blue cells indicate specific country/jurisdiction coverage.

Figure 13. Moving into the Future: Current Coverage of Topics Defining a New Literacy

Note. Orange cells indicate the number of countries that cover that topic at that grade level. The accompanying column indicates the number of
countries/jurisdictions that included that topic at any grade level; Blue cells indicate specific country/jurisdiction coverage. The absence of green
cells indicates the lack of coverage of those topics in TIMSS95.

Unclassified
 EDU/WKP(2022)6  61

Netherlands
Curriculum Standards
Index Figure 2. Degree of Emphasis for the Coverage of
 Page 1 portrays the composition of the country’s/ Four Types of Quantitative Reasoning
jurisdiction’s curriculum standards.
 Page 2 portrays the composition of a representative 8th
grade mathematics textbook.
 Page 3 portrays the curriculum decision making authority
within the educational system.
 Page 4 portrays the mathematics topic coverage of the
country’s/jurisdiction’s curriculum standards across
grades 1-8 in comparison to the 1995 TIMSS A+
benchmark curriculum.

Figure 1. Number of Topics to be Covered at each Grade Figure 3. Degree of Emphasis for the Coverage of
Higher-Order Applications

Figure 4. Degree of Emphasis for the Coverage of 21st

Century Competencies/Skills

Notes for Figure 1:

 Light Grey bars show the range for the number of topics that each
of the 19 countries/jurisdictions intended to cover. Notes for Figures 2-4:
 Dark Grey bars show the Inter-Quartile Range (25th to 75th  The structure of these figures is the same as described in the note for Figure
Percentile) found within the broader range for the number of 1.
topics that each of the 19 countries/jurisdictions intended to  The variable represented in each of these figures is a measure of the
cover. intensity/emphasis that the curriculum standards for each of the
 The stars show the number of topics that the country/ countries/jurisdictions placed on each of these three dimensions of
jurisdiction intended to cover at each of the grades. mathematics literacy.
 The measure is defined with 0 indicating no mention of the
dimension and 1-75 indicating the degree of emphasis (see
methods section of the introduction to the country/jurisdiction
reports).

Unclassified
62  EDU/WKP(2022)6

8th Grade Textbook Exercises

Textbook Exercise Composition Characteristics of Higher-Order Real-World
Application Textbook Exercises
Figure 5. Totals Over All Participants’
Textbooks Figure 7. Types of Quantitative Reasoning

Figure 8. Types of 21st Century Competencies

Figure 6. Country/Jurisdiction Textbook

Notes for Figures 5 (total number of exercises across all countries/jurisdictions)

& 6 (country/jurisdiction specific):
 The Blue pie diagram shows the total number of different types of
exercises.
Notes for Figures 7 & 8:
 The Grey pie diagram shows the number of standard word problems
(an expansion of the light-blue wedge).  Light Grey bars show the range for the number of Higher-Order Real-World
 The Orange wedge represents the number of Higher-Order Math- application exercises of each type for each country/jurisdiction.
World applications.  Dark Grey bars show the Inter-Quartile Range (25th to 75th percentile).
 The Yellow wedge represents the number of Higher-Order Real-  Special case: in cases where the majority of the country’s/jurisdiction’s
World applications. values were 0, the light grey bar encompasses the dark grey bar.
 For countries/jurisdictions that coded 2 textbooks, the average  The stars show the number of Higher-Order Real-World application
number of exercises of the two textbooks was used in Figures 5, exercises of each type that are included.
6, 7 and 8.

Unclassified
 EDU/WKP(2022)6  63

Curriculum Decision Making

0 1 2 3
Advice & Constrain, veto Final authority
No formal role recommendati or modify
Decision or approval
Role: ons recommendati
ons
[\\\\\\] zz\\\\\] [\zzzzzz zzzzzzzz
Figure 9. Who Makes What Decisions?
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils
A By overall system completion
zzzzzzzz [\\\\\\] [\\\\\\] zz\\\\\] [\\\\\\]
B For intermediate stages
[\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
C For differentiated programme types
[\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
D To be reached in a given grade
[\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
E To apply for a specific school
[\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
Content of instruction
F Course (grade level) offerings
[\\\\\\] [\\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz
G Student course assignment rules
[\\\\\\] [\\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz
H Course content (syllabi)
[\\\\\\] [\\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz
I Auxiliary content outside of syllabi
[\\\\\\] [\\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz
Methods of instruction
J Textbook selection
[\\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
K Instructional methods/techniques
[\\\\\\] [\\\\\\] zz\\\\\] [\\\\\\] zzzzzzzz
Examinations
L Content of examinations
zzzzzzzz [\\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz
M Examination performance standards
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
N School Examination standards
[\\\\\\] [\\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz
Figure 10. Country/Jurisdictions: Relative Importance for each of the Four Facets
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 20% 0% 0% 7% 0%
Content of instruction 0% 0% 0% 100% 100%
Methods (including textbooks) 0% 0% 67% 50% 100%
Examinations 67% 0% 0% 67% 67%
Note. The denominator for the percentages is the number of subcategories (as defined in Figure 9) within each category x 3.
The numerator (x) is the sum of the values assigned for each chosen subcategory; for example, for cell (1,1) the formula is
x/15.The facet Methods of Instruction includes textbook selection as well.
Figure 11. Relative Importance Averaged Across All 19 Countries/Jurisdictions
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 52% 24% 40% 29% 33%
Content of instruction 46% 19% 43% 42% 53%
Methods (including textbooks) 28% 18% 55% 50% 74%
Examinations 55% 16% 30% 40% 41%
Note for Figures 9, 10 & 11. In the above figures looking across rows tells who has what role while looking down the columns
especially in Figures 10 and 11, indicates over which facets each locus has the most influence. Given late edits to Figure 9,
Figure 11 does not include the Netherland’s revised data. We acknowledge David E. Wiley’s contribution to the study of
curriculum decision making.

Unclassified
64  EDU/WKP(2022)6

Coverage of Mathematics Topics in the Standards

Figure 12. Comparing the Patterns of Coverage over 25 Years

Note. Green cells indicate coverage defined by TIMSS A+; Orange cells indicate coverage defined by at least a simple majority of the 19
countries/jurisdictions; Blue cells indicate specific country/jurisdiction coverage.

Figure 13. Moving into the Future: Current Coverage of Topics Defining a New Literacy
No. of
No. of Countries/Jurisdictions
TIMSS95 covering topics at each grade level
Countries/ The Netherlands
Jurisdictions
covering
Mathematics Topic 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
Binary Arithmetic & Other Number Bases 0 0 0 0 0 0 0 0 0 0 0 1 2 2 2 2 3 0 0 0 0 0 0 0 0
Computational Thinking 0 0 0 0 0 0 0 0 2 2 2 2 1 1 2 2 3 0 0 0 0 0 0 0 0
Computer Coding 0 0 0 0 0 0 0 0 0 0 0 1 1 1 2 2 2 0 0 0 0 0 0 0 0
Vectors and Matrices 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 2 4 0 0 0 0 0 0 0 0
Geometric approx. for irregular shapes 0 0 0 0 0 0 0 0 0 0 0 1 1 2 2 3 3 0 0 0 0 0 1 1 1
Trigonometric equations and identities 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 4 4 0 0 0 0 0 0 1 1
Other Equations and Inequalities 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 10 10 0 0 0 0 0 0 1 1
Exponential Functions 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 2 0 0 0 0 0 0 1 1
Other non-Linear Functions 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 8 9 0 0 0 0 0 0 1 1
Linear, non-Linear, and Exponential 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 6 6 0 0 0 0 0 0 1 1
Definition of discrete probability 0 0 0 0 0 0 0 0 2 2 3 4 5 6 11 10 15 0 0 0 0 0 0 0 0
Conditional probability/Independent Events 0 0 0 0 0 0 0 0 0 0 0 1 0 1 3 4 4 0 0 0 0 0 0 0 0
Discrete & continuous random variables 0 0 0 0 0 0 0 0 0 0 0 1 1 1 2 2 2 0 0 0 0 0 0 0 0
Populations and their parameters 0 0 0 0 0 0 0 0 0 0 0 1 1 1 2 5 5 0 0 0 0 0 0 0 0
Random Sampling 0 0 0 0 0 0 0 0 1 1 1 1 1 1 3 5 6 0 0 0 0 0 0 0 0
Estimation of parameters 0 0 0 0 0 0 0 0 0 0 0 2 2 2 4 3 6 0 0 0 0 0 0 0 0
Definition of Correlation Coefficient 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0
Contingency Tables 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0
Regression 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0
Historical Perspectives 0 0 0 0 0 0 0 0 1 1 2 2 2 2 3 3 3 0 0 0 0 0 0 0 0
Sampling dist., Standard errors, Significance testing 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ANOVA: Relationship involving categorical variables 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Note. Orange cells indicate the number of countries that cover that topic at that grade level. The accompanying column indicates the number of
countries/jurisdictions that included that topic at any grade level; Blue cells indicate specific country/jurisdiction coverage. The absence of green
cells indicates the lack of coverage of those topics in TIMSS95.

Unclassified
 EDU/WKP(2022)6  65

New Zealand
Curriculum Standards
Index Figure 2. Degree of Emphasis for the Coverage of
 Page 1 portrays the composition of the country’s/ Four Types of Quantitative Reasoning
jurisdiction’s curriculum standards.
 Page 2 portrays the composition of a representative 9th
grade mathematics textbook (see below).
 Page 3 portrays the curriculum decision-making authority
within the educational system.
 Page 4 portrays the mathematics topic coverage of the
country’s/jurisdiction’s curriculum standards across
grades 1-9 in comparison to the 1995 TIMSS A+
benchmark curriculum.
Figure 3. Degree of Emphasis for the Coverage of
Figure 1. Number of Topics to be Covered at each Grade Higher-Order Applications

Figure 4. Degree of Emphasis for the Coverage of 21st

Century Competencies/Skills

Notes for Figure 1:

 Light Grey bars show the range for the number of topics that each
of the 19 countries/jurisdictions intended to cover.
 Dark Grey bars show the Inter-Quartile Range (25th to 75th
Percentile) found within the broader range for the number of
topics that each of the 19 countries/jurisdictions intended to
cover.
 The stars show the number of topics that the country/
Notes for Figures 2-4:
jurisdiction intended to cover at each of the grades.
 The structure of these figures is the same as described in the note for Figure
Notes for Country Level Grade Designations: 1.
 The variable represented in each of these figures is a measure of the
 The equivalent grade designations for New Zealand are 1-9 where 9 is intensity/emphasis that the curriculum standards for each of the
the equivalent of 8th grade. Accordingly, when interpreting New countries/jurisdictions placed on each of these three dimensions of
Zealand results, grades 1 and 2 are noted by grade 1 throughout mathematics literacy.
the report and grade 9 is equivalent to grade 8 internationally.  The measure is defined with 0 indicating no mention of the
Between international grades 2 and 7 are New Zealand Grades 3 dimension and 1-75 indicating the degree of emphasis (see
– 8. methods section of the introduction to the country/jurisdiction
reports).

Unclassified
66  EDU/WKP(2022)6

8th Grade Textbook Exercises

Textbook Exercise Composition Characteristics of Higher-Order Real-World

Application Textbook Exercises
Figure 5. Totals Over All Participants’
Textbooks Figure 7. Types of Quantitative Reasoning

Figure 8. Types of 21st Century Competencies

Figure 6. Country/Jurisdiction Textbook

Notes for Figures 5 (total number of exercises across all countries/jurisdictions)

& 6 (country/jurisdiction specific):
 The Blue pie diagram shows the total number of different types of
exercises.
 The Grey pie diagram shows the number of standard word problems
(an expansion of the light-blue wedge).
 The Orange wedge represents the number of Higher-Order Math- Notes for Figures 7 & 8:
World applications.  Light Greay bars show the range for the number of Higher-Order Real-World
 The Yellow wedge represents the number of Higher-Order Real- application exercises of each type for each country/jurisdiction.
World applications.  Dark Grey bars show the Inter-Quartile Range (25th to 75th percentile).
 For countries/jurisdictions that coded 2 textbooks, the average  Special case: in cases where the majority of the country’s/jurisdiction’s
number of exercises of the two textbooks was used in Figures 5, values were 0, the light grey bar encompasses the dark grey bar.
6, 7 and 8.
 The stars show the number of Higher-Order Real-World application
exercises of each type that are included.

Unclassified
 EDU/WKP(2022)6  67

Curriculum Decision Making

0 1 2 3
Advice & Constrain, veto Final authority
No formal role recommendatio or modify
Decision or approval
Role: ns recommendatio
ns
[\\\\\\] zz\\\\\] [\zzzzzz zzzzzzzz
Figure 9. Who Makes What Decisions?
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils
A By overall system completion
zzzzzzzz [\\\\\\] [\zzzzzz [\zzzzzz [\zzzzzz
B For intermediate stages
zzzzzzzz [\\\\\\] [\zzzzzz [\zzzzzz [\zzzzzz
C For differentiated programme types
zz\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
D To be reached in a given grade
zz\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
E To apply for a specific school
zz\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
Content of instruction
F Course (grade level) offerings
zz\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
G Student course assignment rules
zz\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
H Course content (syllabi)
[\\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
i Auxiliary content outside of syllabi
zz\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
Methods of instruction
J Textbook selection
[\\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
K Instructional methods/techniques
[\\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
Examinations
L Content of examinations
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
M Examination performance standards
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
N School Examination standards
zzzzzzzz [\\\\\\] [\zzzzzz [\zzzzzz [\zzzzzz
Figure 10. Country/Jurisdictions: Relative Importance for each of the Four Facets
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 60% 0% 87% 87% 87%
Content of instruction 25% 0% 100% 100% 100%
Methods (including textbooks) 0% 0% 100% 100% 100%
Examinations 100% 0% 22% 22% 22%
Note. The denominator for the percentages is the number of subcategories (as defined in Figure 9) within each category x 3.
The numerator (x) is the sum of the values assigned for each chosen subcategory; for example, for cell (1,1) the formula is x/15.
Note. The facet Methods of Instruction includes textbook selection as well.
Figure 11. Relative Importance Averaged Across All 19 Countries/Jurisdictions
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 52% 24% 40% 29% 33%
Content of instruction 46% 19% 43% 42% 53%
Methods (including textbooks) 28% 18% 55% 50% 74%
Examinations 55% 16% 30% 40% 41%

Note for Figures 9, 10 & 11. In the above figures looking across rows tells who has what role while looking down the columns
especially in Figures 10 and 11, indicates over which facets each locus has the most influence. We acknowledge David E.
Wiley’s contribution to the study of curriculum decision making.

Unclassified
68  EDU/WKP(2022)6

Coverage of Mathematics Topics in the Standards

Figure 12. Comparing the Patterns of Coverage over 25 Years

Note. Green cells indicate coverage defined by TIMSS A+; Orange cells indicate coverage defined by at least a simple majority of the 19
countries/jurisdictions; Blue cells indicate specific country/jurisdiction coverage.

Figure 13. Moving into the Future: Current Coverage of Topics Defining a New Literacy

Note. Orange cells indicate the number of countries that cover that topic at that grade level. The accompanying column indicates the number of
countries/jurisdictions that included that topic at any grade level; Blue cells indicate specific country/jurisdiction coverage. The absence of green
cells indicates the lack of coverage of those topics in TIMSS95.

Unclassified
 EDU/WKP(2022)6  69

Norway
Curriculum Standards
Index Figure 2. Degree of Emphasis for the Coverage of
 Page 1 portrays the composition of the country’s/ Four Types of Quantitative Reasoning
jurisdiction’s curriculum standards.
 Page 2 portrays the composition of a representative 9th
grade mathematics textbook (see below).
 Page 3 portrays the curriculum decision-making authority
within the educational system.
 Page 4 portrays the mathematics topic coverage of the
country’s/jurisdiction’s curriculum standards across
grades 1-9 in comparison to the 1995 TIMSS A+
benchmark curriculum.

Figure 1. Number of Topics to be Covered at each Grade Figure 3. Degree of Emphasis for the Coverage of
Higher-Order Applications

Figure 4. Degree of Emphasis for the Coverage of 21st

Century Competencies/Skills

Notes for Figure 1:

 Light Grey bars show the range for the number of topics that each
of the 19 countries/jurisdictions intended to cover.
 Dark Grey bars show the Inter-Quartile Range (25th to 75th
Percentile) found within the broader range for the number of
topics that each of the 19 countries/jurisdictions intended to
cover.
 The stars show the number of topics that the country/
jurisdiction intended to cover at each of the grades.

Notes for Figures 2-4:

Notes for Country Level Grade Designations:  The structure of these figures is the same as described in the note for Figure
1.
 The equivalent grade designations for Norway are 1-9 where 9 is
 The variable represented in each of these figures is a measure of the
the equivalent of 8th grade. Accordingly, when interpreting
intensity/emphasis that the curriculum standards for each of the
Norwegian results, grades 1 and 2 are noted by grade 1
countries/jurisdictions placed on each of these three dimensions of
throughout the report and grade 9 is equivalent to grade 8
mathematics literacy.
internationally. Between international grades 2 and 7 are Norway
 The measure is defined with 0 indicating no mention of the
Grades 3 – 8.
dimension and 1-75 indicating the degree of emphasis (see
 Norway refers to the above curriculum as LK06.
methods section of the introduction to the country/jurisdiction
reports).

Unclassified
70  EDU/WKP(2022)6

8th Grade Textbook Exercises

Textbook Exercise Composition Characteristics of Higher-Order Real-World
Application Textbook Exercises
Figure 5. Totals Over All Participants’ Figure 7. Types of Quantitative Reasoning
Textbooks

Figure 8. Types of 21st Century Competencies

Figure 6. Country/Jurisdiction Textbook

Notes for Figures 5 (total number of exercises across all countries/jurisdictions)

& 6 (country/jurisdiction specific):
 The Blue pie diagram shows the total number of different types of
exercises.
Notes for Figures 7 & 8:
 The Grey pie diagram shows the number of standard word problems
(an expansion of the light-blue wedge).  Light Grey bars show the range for the number of Higher-Order Real-World
 The Orange wedge represents the number of Higher-Order Math- application exercises of each type for each country/jurisdiction.
World applications.  Dark Grey bars show the Inter-Quartile Range (25th to 75th percentile).
 The Yellow wedge represents the number of Higher-Order Real-  Special case: in cases where the majority of the country’s/jurisdiction’s
World applications. values were 0, the light grey bar encompasses the dark grey bar.
 For countries/jurisdictions that coded 2 textbooks, the average  The stars show the number of Higher-Order Real-World application
number of exercises of the two textbooks was used in Figures 5, exercises of each type that are included.
6, 7 and 8.

Unclassified
 EDU/WKP(2022)6  71

Curriculum Decision Making

0 1 2 3
Advice & Constrain, veto Final
No formal role recommendati or modify authority or
Decision
Role: ons recommendati approval
ons
[\\\\\\] zz\\\\\] [\zzzzzz zzzzzzzz
Figure 9. Who Makes What Decisions?
Teachers Teachers
National Regional School
Collectively Individually
Goals for pupils
A By overall system completion
zzzzzzzz zz\\\\\] zz\\\\\] zz\\\\\] zz\\\\\]
B For intermediate stages
zzzzzzzz zz\\\\\] zz\\\\\] zz\\\\\] zz\\\\\]
C For differentiated programme types
zzzzzzzz zz\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
D To be reached in a given grade
zzzzzzzz zz\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
E To apply for a specific school
[\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
Content of instruction
F Course (grade level) offerings
zzzzzzzz zz\\\\\] zz\\\\\] zz\\\\\] zz\\\\\]
G Student course assignment rules
[\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
H Course content (syllabi)
zzzzzzzz zz\\\\\] zz\\\\\] zz\\\\\] zz\\\\\]
I Auxiliary content outside of syllabi
zzzzzzzz zz\\\\\] zz\\\\\] zz\\\\\] zz\\\\\]
Methods of instruction
J Textbook selection
zz\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz zzzzzzzz
K Instructional methods/techniques
Examinations
[\\\\\\] [\\\\\\] zz\\\\\] zz\\\\\] zzzzzzzz
L Content of examinations
zzzzzzzz zz\\\\\] zz\\\\\] zzzzzzzz zz\\\\\]
M Examination performance standards
zzzzzzzz zz\\\\\] zz\\\\\] zz\\\\\] zz\\\\\]
N School Examination standards
zzzzzzzz zz\\\\\] zz\\\\\] zzzzzzzz zzzzzzzz
Figure 10. Country/Jurisdictions: Relative Importance for each of the Four Facets
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 80% 27% 13% 13% 13%
Content of instruction 75% 25% 25% 25% 25%
Methods (including textbooks) 17% 50% 67% 67% 100%
Examinations 100% 33% 33% 78% 56%
Note. The denominator for the percentages is the number of subcategories (as defined in Figure 9) within each category x 3.
The numerator (x) is the sum of the values assigned for each chosen subcategory; for example, for cell (1,1) the formula is x/15.
The facet Methods of Instruction includes textbook selection as well.
Figure 11. Relative Importance Averaged Across All 19 Countries/Jurisdictions
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 52% 24% 40% 29% 33%
Content of instruction 46% 19% 43% 42% 53%
Methods (including textbooks) 28% 18% 55% 50% 74%
Examinations 55% 16% 30% 40% 41%
Note for Figures 9, 10 & 11. In the above figures looking across rows tells who has what role while looking down the columns
especially in Figures 10 and 11, indicates over which facets each locus has the most influence.
We acknowledge David E. Wiley’s contribution to the study of curriculum decision making.

Unclassified
72  EDU/WKP(2022)6

Coverage of Mathematics Topics in the Standards

Figure 12. Comparing the Patterns of Coverage over 25 Years

Note. Green cells indicate coverage defined by TIMSS A+; Orange cells indicate coverage defined by at least a simple majority of the 19
countries/jurisdictions; Blue cells indicate specific country/jurisdiction coverage.

Figure 13. Moving into the Future: Current Coverage of Topics Defining a New Literacy

Note. Orange cells indicate the number of countries that cover that topic at that grade level. The accompanying column indicates the number of
countries/jurisdictions that included that topic at any grade level; Blue cells indicate specific country/jurisdiction coverage. The absence of green
cells indicates the lack of coverage of those topics in TIMSS95.

Unclassified
 EDU/WKP(2022)6  73

Norway
Revised Curriculum Standards*
Index
 Page 1 portrays the composition of the country’s/ Figure 2. Degree of Emphasis for the Coverage of
jurisdiction’s curriculum standards. Four Types of Quantitative Reasoning
 Page 2 portrays the composition of a representative 9th
grade mathematics textbook (see below).
 Page 3 portrays the curriculum decision-making authority
within the educational system.
 Page 4 portrays the mathematics topic coverage of the
country’s/jurisdiction’s curriculum standards across
grades 1-9 in comparison to the 1995 TIMSS A+
benchmark curriculum.

Figure 1. Number of Topics to be Covered at each Grade Figure 3. Degree of Emphasis for the Coverage of
Higher-Order Applications

Figure 4. Degree of Emphasis for the Coverage of 21st

Century Competencies/Skills

Notes for Figure 1:

 Light Grey bars show the range for the number of topics that each
of the 19 countries/jurisdictions intended to cover.
 Dark Grey bars show the Inter-Quartile Range (25th to 75th
Percentile) found within the broader range for the number of
topics that each of the 19 countries/jurisdictions intended to
cover.
 The stars show the number of topics that the country/
jurisdiction intended to cover at each of the grades.
Notes for Figures 2-4:
 The structure of these figures is the same as described in the note for Figure
1.
Notes for Country Level Grade Designations:
 The variable represented in each of these figures is a measure of the
 The equivalent grade designations for Norway are 1-9 where 9 is intensity/emphasis that the curriculum standards for each of the
the equivalent of 8th grade. Accordingly, when interpreting countries/jurisdictions placed on each of these three dimensions of
Norwegian results, grades 1 and 2 are noted by grade 1 mathematics literacy.
throughout the report and grade 9 is equivalent to grade 8  The measure is defined with 0 indicating no mention of the
internationally. Between international grades 2 and 7 are Norway dimension and 1-75 indicating the degree of emphasis (see
Grades 3 – 8. methods section of the introduction to the country/jurisdiction
 *Norway refers to the revised curriculum as LK20. reports).

Unclassified
74  EDU/WKP(2022)6

8th Grade Textbook Exercises

Textbook Exercise Composition Characteristics of Higher-Order Real-World
Application Textbook Exercises
Figure 5. Totals Over All Participants’
Textbooks Figure 7. Types of Quantitative Reasoning
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Algorithmic

Geometric 49

Mathematics

Statistical
81
i
10
Number of Excercises

Figure 6. Country/Jurisdiction Textbook Figure 8. Types of 21st Century Competencies

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Communica-
tion 71
Creativity

Critical
49
Thinking
Information 49
Use

Reflection 49
Persistence
/Resilience 62
Systems
Thinking
i
i
10
Number of Excercises
Notes for Figures 5 (total number of exercises across all countries/jurisdictions) 100
& 6 (country/jurisdiction specific):
 The Blue pie diagram shows the total number of different types of
exercises. Notes for Figures 7 & 8:
 The Grey pie diagram shows the number of standard word problems  Light Grey bars show the range for the number of Higher-Order Real-World
(an expansion of the light-blue wedge). application exercises of each type for each country/jurisdiction.
 The Orange wedge represents the number of Higher-Order Math-  Dark Grey bars show the Inter-Quartile Range (25th to 75th percentile).
World applications.  Special case: in cases where the majority of the country’s/jurisdiction’s
 The Yellow wedge represents the number of Higher-Order Real- values were 0, the light grey bar encompasses the dark grey bar.
World applications.  The stars show the number of Higher-Order Real-World application
 For countries/jurisdictions that coded 2 textbooks, the average exercises of each type that are included.
number of exercises of the two textbooks was used in Figures 5,  In Figures 7 and 8, because the number of exercises reported was so
6, 7 and 8. large and were often outside the range they are reported as actual
numbers. If the number was within the scale it is represented by a
Notes for Textbook Data: star. The Ranges and Inter-Quartile Ranges were not altered.
 The data reported in the figures on this page were based on a  The large number of exercises identified as Higher-Order Real-
Norwegian textbook that was coded very late in the process at World by Norway have not been verified, as such the numbers in
Norway’s special request – so as to have characteristics of a Figures 7 and 8 have not been validated.
textbook written for the revised standards.
 The number of Higher-Order Real-World Application Exercises
found in Figure 6 has not been verified. All the remaining
numbers have been verified and are accurate.
 Figure 5 does not include the data from this textbook.

Unclassified
 EDU/WKP(2022)6  75

Curriculum Decision Making

0 1 2 3

Decision Advice & Constrain, veto Final

No formal role or modify authority or
Role: recommendations
recommendati approval
ons zzzzzzzz
[\\\\\\] zz\\\\\] [\zzzzzz
Figure 9. Who Makes What Decisions?
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils
A By overall system completion
zzzzzzzz zz\\\\\] zz\\\\\] zz\\\\\] zz\\\\\]
B For intermediate stages
zzzzzzzz zz\\\\\] zz\\\\\] zz\\\\\] zz\\\\\]
C For differentiated programme types
zzzzzzzz zz\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
D To be reached in a given grade
zzzzzzzz zz\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
E To apply for a specific school
[\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
Content of instruction
F Course (grade level) offerings
zzzzzzzz zz\\\\\] zz\\\\\] zz\\\\\] zz\\\\\]
G Student course assignment rules)
[\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
H Course content (syllabi)
I Auxiliary content outside of syllabi
zzzzzzzz zz\\\\\] zz\\\\\] zz\\\\\] zz\\\\\]
zzzzzzzz zz\\\\\] zz\\\\\] zz\\\\\] zz\\\\\]
Methods of instruction
J Textbook selection
zz\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz zzzzzzzz
K Instructional methods/techniques
[\\\\\\] [\\\\\\] zz\\\\\] zz\\\\\] zzzzzzzz
Examinations
L Content of examinations
zzzzzzzz zz\\\\\] zz\\\\\] zzzzzzzz zz\\\\\]
M Examination performance standards standards
zzzzzzzz zz\\\\\] zz\\\\\] zz\\\\\] zz\\\\\]
N School Examination
zzzzzzzz zz\\\\\] zz\\\\\] zzzzzzzz zzzzzzzz
Figure 10. Country/Jurisd: Relative Importance for each of the Four Facets
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 80% 27% 13% 13% 13%
Content of instruction 75% 25% 25% 25% 25%
Methods (including textbooks) 17% 50% 67% 67% 100%
Examinations 100% 33% 33% 78% 56%
Note. The denominator for the percentages is the number of subcategories (as defined in Figure 9) within each category x 3.
The numerator (x) is the sum of the values assigned for each chosen subcategory; for example, for cell (1,1) the formula is x/15.
Note. The facet Methods of Instruction includes textbook selection as well.
Figure 11. Relative Importance Averaged Across All 19 Countries/Jurisdictions

National Regional School Teachers Teachers

Collectively Individually
Goals for pupils 52% 24% 40% 29% 33%
Content of instruction 46% 19% 43% 42% 53%
Methods (including textbooks) 28% 18% 55% 50% 74%
Examinations 55% 16% 30% 40% 41%
Note for Figures 9, 10 & 11. In the above figures looking across rows tells who has what role while looking down the columns
especially in Figures 10 and 11, indicates over which facets each locus has the most influence. We acknowledge David E.
Wiley’s contribution to the study of curriculum decision making.

Unclassified
76  EDU/WKP(2022)6

Coverage of Mathematics Topics in the Standards

Figure 12. Comparing the Patterns of Coverage over 25 Years

Note. Green cells indicate coverage defined by TIMSS A+; Orange cells indicate coverage defined by at least a simple majority of the 19 `
countries/jurisdictions; Blue cells indicate specific country/jurisdiction coverage.

Figure 13. Moving into the Future: Current Coverage of Topics Defining a New Literacy

Note. Orange cells indicate the number of countries that cover that topic at that grade level. The accompanying column indicates the number of
countries/jurisdictions that included that topic at any grade level; Blue cells indicate specific country/jurisdiction coverage. The absence of green
cells indicates the lack of coverage of those topics in TIMSS95.

Unclassified
 EDU/WKP(2022)6  77

Portugal
Curriculum Standards
Index Figure 2. Degree of Emphasis for the Coverage
 Page 1 portrays the composition of the country’s/ of Four Types of Quantitative Reasoning
jurisdiction’s curriculum standards.
 Page 2 portrays the composition of a representative 8 th
grade mathematics textbook.
 Page 3 portrays the curriculum decision-making authority
within the educational system.
 Page 4 portrays the mathematics topic coverage of the
country’s/jurisdiction’s curriculum standards across
grades 1-8 in comparison to the 1995 TIMSS A+
benchmark curriculum.

Figure 1. Number of Topics to be Covered at each Grade Figure 3. Degree of Emphasis for the Coverage of
Higher-Order Applications

Figure 4. Degree of Emphasis for the Coverage of 21st

Century Competencies/Skills

Notes for Figure 1:

 Light Grey bars show the range for the number of topics that each
of the 19 countries/jurisdictions intended to cover.
 Dark Grey bars show the Inter-Quartile Range (25th to 75th
Percentile) found within the broader range for the number of
topics that each of the 19 countries/jurisdictions intended to
cover.
 The stars show the number of topics that the country/ Notes for Figures 2-4:
jurisdiction intended to cover at each of the grades.  The structure of these figures is the same as described in the note for Figure
1.
 The variable represented in each of these figures is a measure of the
intensity/emphasis that the curriculum standards for each of the
Note:
countries/jurisdictions placed on each of these three dimensions of
 In 2021 Portugal adopted a new set of mathematics standards for mathematics literacy.
grades 1-9 that will be implemented in 2022/23. Several new  The measure is defined with 0 indicating no mention of the
literacy topics (found in Figure 13) were added to the new dimension and 1-75 indicating the degree of emphasis (see
curriculum. methods section of the introduction to the country/jurisdiction
reports).

Unclassified
78  EDU/WKP(2022)6

8th Grade Textbook Exercises

Textbook Exercise Composition Characteristics of Higher-Order Real-World
Application Textbook Exercises

Figure 5. Totals Over All Participants’ Figure 7. Types of Quantitative Reasoning

Textbooks

Figure 8. Types of 21st Century Competencies

Figure 6. Country/Jurisdiction Textbook

Notes for Figures 5 (total number of exercises across all countries/jurisdictions)

& 6 (country/jurisdiction specific):
 The Blue pie diagram shows the total number of different types of
exercises.
 The Grey pie diagram shows the number of standard word problems
(an expansion of the light-blue wedge).
 The Orange wedge represents the number of Higher-Order Math-
Notes for Figures 7 & 8:
World applications.
 The Yellow wedge represents the number of Higher-Order Real-  Light Grey bars show the range for the number of Higher-Order Real-World
World applications. application exercises of each type for each country/jurisdiction.
 For countries/jurisdictions that coded 2 textbooks, the average  Dark Grey bars show the Inter-Quartile Range (25th to 75th percentile).
number of exercises of the two textbooks was used in Figures 5,  Special case: in cases where the majority of the country’s/jurisdiction’s
6, 7 and 8. values were 0, the light grey bar encompasses the dark grey bar.
 The stars show the number of Higher-Order Real-World application
exercises of each type that are included.

Unclassified
 EDU/WKP(2022)6  79

Curriculum Decision Making

0 1 2 3
Advice & Constrain, veto Final authority
No formal role recommendati or modify
Decision or approval
Role: ons recommendati
ons
[\\\\\\] zz\\\\\] [\zzzzzz zzzzzzzz
Figure 9. Who Makes What Decisions?
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils
A By overall system completion
zzzzzzzz [\\\\\\] [\zzzzzz [\\\\\\] [\\\\\\]
B For intermediate stages
zzzzzzzz [\\\\\\] [\zzzzzz [\\\\\\] [\\\\\\]
C For differentiated programme types
zz\\\\\] [\\\\\\] zzzzzzzz zz\\\\\] zz\\\\\]
D To be reached in a given grade
zzzzzzzz [\\\\\\] [\zzzzzz [\\\\\\] [\\\\\\]
E To apply for a specific school
zzzzzzzz [\\\\\\] [\zzzzzz zz\\\\\] zz\\\\\]
Content of instruction
F Course (grade level) offerings
zzzzzzzz [\\\\\\] zz\\\\\] [\\\\\\] [\\\\\\]
G Student course assignment rules)
zzzzzzzz [\\\\\\] zzzzzzzz zz\\\\\] [\\\\\\]
H Course content (syllabi)
zzzzzzzz [\\\\\\] [\zzzzzz zz\\\\\] zz\\\\\]
I Auxiliary content outside of syllabi
zz\\\\\] [\\\\\\] zzzzzzzz zz\\\\\] zz\\\\\]
Methods of instruction
J Textbook selection
zz\\\\\] [\\\\\\] zzzzzzzz zz\\\\\] zz\\\\\]
K Instructional methods/techniques
zz\\\\\] [\\\\\\] zz\\\\\] zz\\\\\] zzzzzzzz
Examinations
L Content of examinations
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
M Examination performance standards
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
N School Examination standards
zz\\\\\] [\\\\\\] zzzzzzzz zz\\\\\] [\\\\\\]
Figure 10. Country/Jurisdictions: Relative Importance for each of the Four Facets
Teachers Teachers
National Regional School
Collectively Individually
Goals for pupils 87% 0% 73% 13% 13%
Content of instruction 83% 0% 75% 25% 17%
Methods (including textbooks) 33% 0% 67% 33% 67%
Examinations 78% 0% 33% 11% 0%
Note. The denominator for the percentages is the number of subcategories (as defined in Figure 9) within each category x 3.
The numerator (x) is the sum of the values assigned for each chosen subcategory; for example, for cell (1,1) the formula is x/15.
The facet Methods of Instruction includes textbook selection as well.
Figure 11. Relative Importance Averaged Across All 19 Countries/Jurisdictions
Teachers Teachers
National Regional School
Collectively Individually
Goals for pupils 52% 24% 40% 29% 33%
Content of instruction 46% 19% 43% 42% 53%
Methods (including textbooks) 28% 18% 55% 50% 74%
Examinations 55% 16% 30% 40% 41%

Note for Figures 9, 10 & 11. In the above figures looking across rows tells who has what role while looking down the columns
especially in Figures 10 and 11, indicates over which facets each locus has the most influence.
We acknowledge David E. Wiley’s contribution to the study of curriculum decision making.

Unclassified
80  EDU/WKP(2022)6

Coverage of Mathematics Topics in the Standards

Figure 12. Comparing the Patterns of Coverage over 25 Years

Note. Green cells indicate coverage defined by TIMSS A+; Orange cells indicate coverage defined by at least a simple majority of the 19
countries/jurisdictions; Blue cells indicate specific country/jurisdiction coverage.

Figure 13. Moving into the Future: Current Coverage of Topics Defining a New Literacy
No. of
No. of Countries/Jurisdictions
TIMSS95 covering topics at each grade level
Countries/ Portugal
Jurisdictions
covering
Mathematics Topic 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
Binary Arithmetic & Other Number Bases 0 0 0 0 0 0 0 0 0 0 0 1 2 2 2 2 3 0 0 0 0 0 0 0 0
Computational Thinking 0 0 0 0 0 0 0 0 2 2 2 2 1 1 2 2 3 0 0 0 0 0 0 0 0
Computer Coding 0 0 0 0 0 0 0 0 0 0 0 1 1 1 2 2 2 0 0 0 0 0 0 0 0
Vectors and Matrices 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 2 4 0 0 0 0 0 0 0 0
Geometric approx. for irregular shapes 0 0 0 0 0 0 0 0 0 0 0 1 1 2 2 3 3 0 0 0 0 0 0 0 0
Trigonometric equations and identities 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 4 4 0 0 0 0 0 0 0 0
Other Equations and Inequalities 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 10 10 0 0 0 0 0 0 0 1
Exponential Functions 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 2 0 0 0 0 0 0 0 0
Other non-Linear Functions 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 8 9 0 0 0 0 0 0 0 0
Linear, non-Linear, and Exponential 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 6 6 0 0 0 0 0 0 0 0
Definition of discrete probability 0 0 0 0 0 0 0 0 2 2 3 4 5 6 11 10 15 0 0 0 0 0 0 0 0
Conditional probability/Independent Events 0 0 0 0 0 0 0 0 0 0 0 1 0 1 3 4 4 0 0 0 0 0 0 0 0
Discrete & continuous random variables 0 0 0 0 0 0 0 0 0 0 0 1 1 1 2 2 2 0 0 0 0 0 0 0 0
Populations and their parameters 0 0 0 0 0 0 0 0 0 0 0 1 1 1 2 5 5 0 0 0 0 0 0 0 1
Random Sampling 0 0 0 0 0 0 0 0 1 1 1 1 1 1 3 5 6 0 0 0 0 0 0 0 1
Estimation of parameters 0 0 0 0 0 0 0 0 0 0 0 2 2 2 4 3 6 0 0 0 0 0 0 0 0
Definition of Correlation Coefficient 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0
Contingency Tables 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0
Regression 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0
Historical Perspectives 0 0 0 0 0 0 0 0 1 1 2 2 2 2 3 3 3 0 0 0 0 0 0 0 0
Sampling dist., Standard errors, Significance testing 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ANOVA: Relationship involving categorical variables 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Note. Orange cells indicate the number of countries that cover that topic at that grade level. The accompanying column indicates the number of
countries/jurisdictions that included that topic at any grade level; Blue cells indicate specific country/jurisdiction coverage. The absence of green
cells indicates the lack of coverage of those topics in TIMSS95.

Unclassified
 EDU/WKP(2022)6  81

Sweden
Curriculum Standards
Index Figure 2. Degree of Emphasis for the Coverage of
 Page 1 portrays the composition of the country’s/ Four Types of Quantitative Reasoning
jurisdiction’s curriculum standards.
 Page 2 portrays the composition of a representative 8 th
grade mathematics textbook.
 Page 3 portrays the curriculum decision-making authority
within the educational system.
 Page 4 portrays the mathematics topic coverage of the
country’s/jurisdiction’s curriculum standards across
grades 1-8 in comparison to the 1995 TIMSS A+
benchmark curriculum.
Figure 3. Degree of Emphasis for the Coverage of
Figure 1. Number of Topics to be Covered at each Grade Higher-Order Applications

Figure 4. Degree of Emphasis for the Coverage of 21st

Century Competencies/Skills

Notes for Figure 1:

 Light Grey bars show the range for the number of topics that each
of the 19 countries/jurisdictions intended to cover.
 Dark Grey bars show the Inter-Quartile Range (25th to 75th
Percentile) found within the broader range for the number of Notes for Figures 2-4:
topics that each of the 19 countries/jurisdictions intended to  The structure of these figures is the same as described in the note for Figure
cover. 1.
 The stars show the number of topics that the country/  The variable represented in each of these figures is a measure of the
jurisdiction intended to cover at each of the grades. intensity/emphasis that the curriculum standards for each of the
countries/jurisdictions placed on each of these three dimensions of
mathematics literacy.
 The measure is defined with 0 indicating no mention of the
Note:
dimension and 1-75 indicating the degree of emphasis (see
 Sweden will have a new revised curriculum starting in July 2022. methods section of the introduction to the country/jurisdiction
reports).

Unclassified
82  EDU/WKP(2022)6

8th Grade Textbook Exercises

Textbook Exercise Composition
Characteristics of Higher-Order Real-World
Figure 5. Totals Over All Participants’ Application Textbook Exercises
Textbooks Figure 7. Types of Quantitative Reasoning

Figure 6. Country/Jurisdiction Textbook Figure 8. Types of 21st Century Competencies

Notes for Figures 5 (total number of exercises across all countries/jurisdictions)

& 6 (country/jurisdiction specific):
 The Blue pie diagram shows the total number of different types of
exercises.
 The Grey pie diagram shows the number of standard word problems
(an expansion of the light-blue wedge).
 The Orange wedge represents the number of Higher-Order Math-
World applications.
 The Yellow wedge represents the number of Higher-Order Real-
Notes for Figures 7 & 8:
World applications.
 For countries/jurisdictions that coded 2 textbooks, the average  Light Grey bars show the range for the number of Higher-Order Real-World
number of exercises of the two textbooks was used in Figures 5, application exercises of each type for each country/jurisdiction.
6, 7 and 8.  Dark Grey bars show the Inter-Quartile Range (25th to 75th percentile).
 Special case: in cases where the majority of the country’s/jurisdiction’s
values were 0, the light grey bar encompasses the dark grey bar.
 The stars show the number of Higher-Order Real-World application
exercises of each type that are included.

Unclassified
 EDU/WKP(2022)6  83

Curriculum Decision Making

0 1 2 3
Advice & Constrain, veto Final authority
No formal role recommendatio or modify
Decision or approval
Role: ns recommendatio
ns
[\\\\\\] zz\\\\\] [\zzzzzz zzzzzzzz
Figure 9. Who Makes What Decisions?
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils
A By overall system completion
zzzzzzzz zz\\\\\] [\\\\\\] zz\\\\\] [\\\\\\]
Bb For intermediate stages
zzzzzzzz zz\\\\\] [\\\\\\] zz\\\\\] [\\\\\\]
Cc For differentiated programme types
[\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
D To be reached in a given grade
zzzzzzzz zz\\\\\] zz\\\\\] zz\\\\\] zz\\\\\]
E To apply for a specific school
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
Content of instruction
FI Course (grade level) offerings
[\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
G Student course assignment rules)
[\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\] zzzzzzzz
H Course content (syllabi
zzzzzzzz zz\\\\\] [\\\\\\] zz\\\\\] [\\\\\\]
I Auxiliary content outside of syllabi
zz\\\\\] [\\\\\\] [\\\\\\] [\\\\\\] zzzzzzzz
Methods of instruction
J Textbook selection
[\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\] zzzzzzzz
k Instructional methods/techniques
Examinations
zz\\\\\] [\\\\\\] [\\\\\\] [\\\\\\] zzzzzzzz
L Content of examinations
[\zzzzzz [\\\\\\] [\\\\\\] [\\\\\\] zzzzzzzz
M Examination performance standards
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
N School Examination standards
[\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\] zzzzzzzz
Figure 10. Country/Jurisdictions: Relative Importance for each of the Four Facets
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 80% 20% 7% 20% 7%
Content of instruction 33% 8% 0% 8% 50%
Methods (including textbooks) 17% 0% 0% 0% 100%
Examinations 56% 0% 0% 0% 67%
Note. The denominator for the percentages is the number of subcategories (as defined in Figure 9) within each category x 3.
The numerator (x) is the sum of the values assigned for each chosen subcategory; for example, for cell (1,1) the formula is x/15.
The facet Methods of Instruction includes textbook selection as well.
Figure 11. Relative Importance Averaged Across All 19 Countries/Jurisdictions
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 52% 24% 40% 29% 33%
Content of instruction 46% 19% 43% 42% 53%
Methods (including textbooks) 28% 18% 55% 50% 74%
Examinations 55% 16% 30% 40% 41%

Note for Figures 9, 10 & 11. In the above figures looking across rows tells who has what role while looking down the columns
especially in Figures 10 and 11, indicates over which facets each locus has the most influence.
We acknowledge David E. Wiley’s contribution to the study of curriculum decision making.

Unclassified
84  EDU/WKP(2022)6

Coverage of Mathematics Topics in the Standards

Figure 12. Comparing the Patterns of Coverage over 25 Years

Note. Green cells indicate coverage defined by TIMSS A+; Orange cells indicate coverage defined by at least a simple majority of the 19
countries/jurisdictions; Blue cells indicate specific country/jurisdiction coverage.

Figure 13. Moving into the Future: Current Coverage of Topics Defining a New Literacy

Note. Orange cells indicate the number of countries that cover that topic at that grade level. The accompanying column indicates the number of
countries/jurisdictions that included that topic at any grade level; Blue cells indicate specific country/jurisdiction coverage. The absence of green
cells indicates the lack of coverage of those topics in TIMSS95.

Unclassified
 EDU/WKP(2022)6  85

United States
Curriculum Standards
Figure 2. Degree of Emphasis for the Coverage of
Index Four Types of Quantitative Reasoning
 Page 1 portrays the composition of the country’s/
jurisdiction’s curriculum standards.
 Page 2 portrays the composition of a representative 8 th
grade mathematics textbook.
 Page 3 portrays the curriculum decision-making authority
within the educational system.
 Page 4 portrays the mathematics topic coverage of the
country’s/jurisdiction’s curriculum standards across
grades 1-8 in comparison to the 1995 TIMSS A+
benchmark curriculum.
Figure 3. Degree of Emphasis for the Coverage of
Figure 1. Number of Topics to be Covered at each Grade Higher-Order Applications

Figure 4. Degree of Emphasis for the Coverage of 21st

Century Competencies/Skills

Notes for Figure 1:

 Light Grey bars show the range for the number of topics that each
of the 19 countries/jurisdictions intended to cover.
 Dark Grey bars show the Inter-Quartile Range (25th to 75th
Percentile) found within the broader range for the number of
topics that each of the 19 countries/jurisdictions intended to
cover.
 The stars show the number of topics that the country/ Notes for Figures 2-4:
jurisdiction intended to cover at each of the grades.  The structure of these figures is the same as described in the note for Figure
1.
 The variable represented in each of these figures is a measure of the
intensity/emphasis that the curriculum standards for each of the
countries/jurisdictions placed on each of these three dimensions of
mathematics literacy.
 The measure is defined with 0 indicating no mention of the
dimension and 1-75 indicating the degree of emphasis (see
methods section of the introduction to the country/jurisdiction
reports).

Unclassified
86  EDU/WKP(2022)6

8th Grade Textbook Exercises

Textbook Exercise Composition Characteristics of Higher-Order Real-World
Application Textbook Exercises

Figure 5. Totals Over All Participants’ Figure 7. Types of Quantitative Reasoning

Textbooks

Figure 8. Types of 21st Century Competencies

Figure 6. Country/Jurisdiction Textbook

Notes for Figures 5 (total number of exercises across all countries/jurisdictions)

Notes for Figures 7 & 8:
& 6 (country/jurisdiction specific):
 The Blue pie diagram shows the total number of different types of  Light Grey bars show the range for the number of Higher-Order Real-World
exercises. application exercises of each type for each country/jurisdiction.
 The Grey pie diagram shows the number of standard word problems  Dark Grey bars show the Inter-Quartile Range (25th to 75th percentile).
(an expansion of the light-blue wedge).  Special case: in cases where the majority of the country’s/jurisdiction’s
 The Orange wedge represents the number of Higher-Order Math- values were 0, the light grey bar encompasses the dark grey bar.
World applications.  The stars show the number of Higher-Order Real-World application
 The Yellow wedge represents the number of Higher-Order Real- exercises of each type that are included.
World applications.
 For countries/jurisdictions that coded 2 textbooks, the average
number of exercises of the two textbooks was used in Figures 5,
6, 7 and 8.

Unclassified
 EDU/WKP(2022)6  87

Curriculum Decision Making

0 1 2 3
Constrain, veto
Decision No formal Advice & or modify Final authority
Role: role recommendations recommendati or approval
ons
[\\\\\\] zz\\\\\] [\zzzzzz zzzzzzzz
Figure 9. Who Makes What Decisions?
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils
A By overall system completion
[\\\\\\] zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\]
B For intermediate stages
[\\\\\\] zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\]
C For differentiated programme types
[\\\\\\] zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\]
D To be reached in a given grade
[\\\\\\] zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\]
E To apply for a specific school
[\\\\\\] zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\]
Content of instruction
F Course (grade level) offerings
[\\\\\\] zzzzzzzz zzzzzzzz [\\\\\\] [\\\\\\]
G Student course assignment rules
[\\\\\\] zz\\\\\] zzzzzzzz [\zzzzzz [\\\\\\]
H Course content (syllabi)
[\\\\\\] zzzzzzzz [\zzzzzz [\zzzzzz [\zzzzzz
I Auxiliary content outside of syllabi
[\\\\\\] [\\\\\\] [\zzzzzz [\zzzzzz zzzzzzzz
Methods of instruction
J Textbook selection
[\\\\\\] [\\\\\\] zzzzzzzz [\zzzzzz [\\\\\\]
K Instructional methods/techniques
[\\\\\\] zz\\\\\] zz\\\\\] [\\\\\\] zzzzzzzz
Examinations
L Content of examinations
zzzzzzzz zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\]
M Examination performance standards
[\\\\\\] zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\]
N School Examination standards
zz\\\\\] zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\]
Figure 10. Country/Jurisdictions: Relative Importance for each of the Four Facets
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 0% 100% 0% 0% 0%
Content of instruction 0% 58% 83% 50% 42%
Methods (including textbooks) 0% 17% 67% 33% 50%
Examinations 44% 100% 0% 0% 0%
Notes The denominator for the percentages is the number of subcategories (as defined in Figure 9) within each category x 3.
The numerator (x) is the sum of the values assigned for each chosen subcategory; for example, for cell (1,1) the formula is x/15.
Note. The facet Methods of Instruction includes textbook selection as well.
Figure 11. Relative Importance Averaged Across All 19 Countries/Jurisdictions
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 52% 24% 40% 29% 33%
Content of instruction 46% 19% 43% 42% 53%
Methods (including textbooks) 28% 18% 55% 50% 74%
Examinations 55% 16% 30% 40% 41%
Note for Figures 9, 10 & 11. In the above figures looking across rows tells who has what role while looking down the columns
especially in Figures 10 and 11, indicates over which facets each locus has the most influence.
We acknowledge David E. Wiley’s contribution to the study of curriculum decision making.

Unclassified
88  EDU/WKP(2022)6

Coverage of Mathematics Topics in the Standards

Figure 12. Comparing the Patterns of Coverage over 25 Years

` Note. Green cells indicate coverage defined by TIMSS A+; Orange cells indicate coverage defined by at least a simple majority of the 19
countries/jurisdictions; Blue cells indicate specific country/jurisdiction coverage.

Figure 13. Moving into the Future: Current Coverage of Topics Defining a New Literacy

Note. Orange cells indicate the number of countries that cover that topic at that grade level. The accompanying column indicates the number of
countries/jurisdictions that included that topic at any grade level; Blue cells indicate specific country/jurisdiction coverage. The absence of green
cells indicates the lack of coverage of those topics in TIMSS95.

Unclassified
 EDU/WKP(2022)6  89

8th Grade Textbook Exercises: Book 1

Exercise Composition of Textbooks Characteristics of Higher-Order
Real- World Application
Figure 5. Totals Over All Participants’ Textbook Exercises
Textbooks
Figure 7. Type of Quantitative
Reasoning

Figure 8. Type of 21st Century

Figure 6. Country/Jurisdiction Textbook Competencies

Notes for Figures 5 (total number of exercises across all

countries/jurisdictions) & 6 (country/jurisdiction specific):
 The Blue pie diagram shows the total number of different types
of exercises.
 The Grey pie diagram shows the number of standard word
problems (an expansion of the light-blue wedge).
 The Orange wedge represents the number of Higher-Order Notes for Figures 7 & 8:
Math-World applications.  Light Grey bars show the range for the number of Higher-Order Real-
 The Yellow wedge represents the number of Higher-Order World application exercises of each type for each country/jurisdiction.
Real-World applications.  Dark Grey bars show the Inter-Quartile Range (25th to 75th
 For countries/jurisdictions that coded 2 textbooks, the average percentile).
number of exercises of the two textbooks was used in  Special case: in cases where the majority of the country’s/jurisdiction’s
Figures 5, 6, 7 and 8. values were 0, the light grey bar encompasses the dark grey bar.
 The stars show the number of Higher-Order Real-World application
exercises of each type that are included.

Unclassified
90  EDU/WKP(2022)6

8th Grade Textbook Exercises: Book 2

Characteristics of Higher-Order Real-
Exercise Composition of Textbooks World Application Textbook Exercises
Figure 7. Type of Quantitative Reasoning
Figure 5. Totals Over All Participants’
Textbooks

Figure 8. Type of 21st Century

Competencies

Figure 6. Country/Jurisdiction Textbook

Notes for Figures 5 (total number of exercises across all countries/jurisdictions)

& 6 (country/jurisdiction specific):

 The Blue pie diagram shows the total number of different types of exercises.
 The Grey pie diagram shows the number of standard word problems (an Notes for Figures 7 & 8:
expansion of the light-blue wedge).  Light Grey bars show the range for the number of Higher-Order Real-World
 The Orange wedge represents the number of Higher-Order Math-World application exercises of each type for each country/jurisdiction.
applications.  Dark Grey bars show the Inter-Quartile Range (25th to 75th percentile).
 The Yellow wedge represents the number of Higher-Order Real-World  Special case: in cases where the majority of the country’s/jurisdiction’s values
applications. were 0, the light grey bar encompasses the dark grey bar.
 For countries/jurisdictions that coded 2 textbooks, the average number of  The stars show the number of Higher-Order Real-World application exercises of
exercises of the two textbooks was used in Figures 5, 6, 7 and 8. each type that are included.

Unclassified
 EDU/WKP(2022)6  91

Argentina
Curriculum Standards
Index
 Page 1 portrays the composition of the country’s/ Figure 2. Degree of Emphasis for the Coverage of
jurisdiction’s curriculum standards. Four Types of Quantitative Reasoning
 Page 2 portrays the composition of a representative 8 th
grade mathematics textbook.
 Page 3 portrays the curriculum decision-making authority
within the educational system.
 Page 4 portrays the mathematics topic coverage of the
country’s/jurisdiction’s curriculum standards across
grades 1-8 in comparison to the 1995 TIMSS A+
benchmark curriculum.

Figure 1. Number of Topics to be Covered at each Grade Figure 3. Degree of Emphasis for the Coverage of
Higher-Order Applications

Figure 4. Degree of Emphasis for the Coverage of 21st

Century Competencies/Skills

Notes for Figure 1:

 Light Grey bars show the range for the number of topics that each
of the 19 countries/jurisdictions intended to cover.
 Dark Grey bars show the Inter-Quartile Range (25th to 75th
Percentile) found within the broader range for the number of
topics that each of the 19 countries/jurisdictions intended to
cover.
 The stars show the number of topics that the country/
jurisdiction intended to cover at each of the grades.

Notes for Figures 2-4:

 The structure of these figures is the same as described in the note for Figure
1.
 The variable represented in each of these figures is a measure of the
intensity/emphasis that the curriculum standards for each of the
countries/jurisdictions placed on each of these three dimensions of
mathematics literacy.
 The measure is defined with 0 indicating no mention of the
dimension and 1-75 indicating the degree of emphasis (see
methods section of the introduction to the country/jurisdiction
reports).

Unclassified
92  EDU/WKP(2022)6

8th Grade Textbook Exercises

Textbook Exercise Composition Characteristics of Higher-Order Real-
World Application Textbook Exercises
Figure 5. Totals Over All Participants’ Figure 7. Types of Quantitative Reasoning
Textbooks

Figure 6. Country/Jurisdiction Textbook Figure 8. Types of 21st Century Competencies

Notes for Figures 5 (total number of exercises across all

countries/jurisdictions) & 6 (country/jurisdiction specific):
 The Blue pie diagram shows the total number of different types
of exercises.
 The Grey pie diagram shows the number of standard word
problems (an expansion of the light-blue wedge).
 The Orange wedge represents the number of Higher-Order
Math-World applications.
 The Yellow wedge represents the number of Higher-Order Notes for Figures 7 & 8:
Real-World applications.
 Light Grey bars show the range for the number of Higher-Order Real-
 For countries/jurisdictions that coded 2 textbooks, the average
World application exercises of each type for each country/jurisdiction.
number of exercises of the two textbooks was used in
 Dark Grey bars show the Inter-Quartile Range (25th to 75th
Figures 5, 6, 7 and 8.
percentile).
 Special case: in cases where the majority of the country’s/jurisdiction’s
values were 0, the light grey bar encompasses the dark grey bar.
 The stars show the number of Higher-Order Real-World application
exercises of each type that are included.

Unclassified
 EDU/WKP(2022)6  93

Curriculum Decision Making

0 1 2 3
Constrain, veto or
Advice & Final authority or
No formal role modify
Decision recommendations
recommendations
approval
Role:
[\\\\\\] zz\\\\\] [\zzzzzz zzzzzzzz
Figure 9. Who Makes What Decisions?
Teachers Teachers
National Regional School
Collectively Individually
Goals for pupils

A By overall system completion [\\\\\\] zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\]

B For intermediate stages [\\\\\\] zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\]

C For differentiated programme types [\\\\\\] zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\]

D To be reached in a given grade [\\\\\\] zzzzzzzz [\\\\\\] [\\\\\\] [\zzzzzz

E To apply for a specific school [\\\\\\] zz\\\\\] zzzzzzzz zz\\\\\] [\\\\\\]

Content of instruction

F Course (grade level) offerings [\\\\\\] zzzzzzzz [\\\\\\] [\\\\\\] [\zzzzzz

G Student course assignment rules [\\\\\\] [\\\\\\] zzzzzzzz [\zzzzzz [\\\\\\]

H Course content (syllabi) [\\\\\\] zz\\\\\] zzzzzzzz zz\\\\\] zzzzzzzz

I Auxiliary content outside of syllabi [\\\\\\] zz\\\\\] zzzzzzzz [\zzzzzz zzzzzzzz

Methods of instruction

J Textbook selection zz\\\\\] zz\\\\\] zz\\\\\] zz\\\\\] zzzzzzzz

k methods/techniques Instructional zz\\\\\] [\zzzzzz zz\\\\\] zz\\\\\] zzzzzzzz

Examinations
L Content of examinations zzzzzzzz [\zzzzzz [\\\\\\] [\\\\\\] [\\\\\\]

M Examination performance zzzzzzzz [\zzzzzz [\\\\\\] [\\\\\\] [\\\\\\]

N Examination standards School [\\\\\\] [\\\\\\] zz\\\\\] [\zzzzzz zzzzzzzz

Figure 10. Country/Jurisdictions: Relative Importance for each of the Four Facets
National Regional School Teachers Collectively Teachers Individually

Goals for pupils 0% 87% 20% 7% 13%

Content of instruction 0% 42% 75% 42% 67%
Methods (including textbooks) 33% 50% 33% 33% 100%
Examinations 67% 44% 11% 22% 33%
Note. The denominator for the percentages is the number of subcategories (as defined in Figure 9) within each category x 3. The numerator (x) is the sum of
the values assigned for each chosen subcategory; for example, for cell (1,1) the formula is x/15. The facet Methods of Instruction includes textbook selection as
well.
Figure 11. Relative Importance Averaged Across All 19 Countries/Jurisdictions
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 52% 24% 40% 29% 33%
Content of instruction 46% 19% 43% 42% 53%
Methods (including textbooks) 28% 18% 55% 50% 74%
Examinations 55% 16% 30% 40% 41%

Note for Figures 9, 10 & 11. In the above figures looking across rows tells who has what role while looking down the columns especially in
Figures 10 and 11, indicates over which facets each locus has the most influence. We acknowledge David E. Wiley’s contribution to the
study of curriculum decision making

Unclassified
94  EDU/WKP(2022)6

Coverage of Mathematics Topics in the Standards

Figure 12. Comparing the Patterns of Coverage over 25 Years

Note. Green cells indicate coverage defined by TIMSS A+; Orange cells indicate coverage defined by at least a simple majority of the 19
countries/jurisdictions; Blue cells indicate specific country/jurisdiction coverage.

Figure 13. Moving into the Future: Current Coverage of Topics Defining a New Literacy

Note. Orange cells indicate the number of countries that cover that topic at that grade level. The accompanying column indicates the number of
countries/jurisdictions that included that topic at any grade level; Blue cells indicate specific country/jurisdiction coverage. The absence of
green cells indicates the lack of coverage of those topics in TIMSS95.

Unclassified
 EDU/WKP(2022)6  95

Chinese Taipei
Curriculum Standards

Figure 2. Degree of Emphasis for the Coverage of

Index Four Types of Quantitative Reasoning
 Page 1 portrays the composition of the country’s/
jurisdiction’s curriculum standards.
 Page 2 portrays the composition of a representative 8th
grade mathematics textbook.
 Page 3 portrays the curriculum decision-making authority
within the educational system.
 Page 4 portrays the mathematics topic coverage of the
country’s/jurisdiction’s curriculum standards across
grades 1-8 in comparison to the 1995 TIMSS A+
benchmark curriculum. Figure 3. Degree of Emphasis for the Coverage of
Higher-Order Applications
Figure 1. Number of Topics to be Covered at each Grade

Figure 4. Degree of Emphasis for the Coverage of 21st

Century Competencies/Skills

Notes for Figures 2-4:

Notes for Figure 1:  The structure of these figures is the same as described in the note for Figure
 Light Grey bars show the range for the number of topics that each 1.
of the 19 countries/jurisdictions intended to cover.  The variable represented in each of these figures is a measure of the
 Dark Grey bars show the Inter-Quartile Range (25th to 75th intensity/emphasis that the curriculum standards for each of the
Percentile) found within the broader range for the number of countries/jurisdictions placed on each of these three dimensions of
topics that each of the 19 countries/jurisdictions intended to mathematics literacy.
cover.  The measure is defined with 0 indicating no mention of the
 The stars show the number of topics that the country/ dimension and 1-75 indicating the degree of emphasis (see
jurisdiction intended to cover at each of the grades. methods section of the introduction to the country/jurisdiction
reports).

Unclassified
96  EDU/WKP(2022)6

8th Grade Textbook Exercises

Textbook Exercise Composition Characteristics of Higher-Order Real-World
Figure 5. Totals Over All Participants’ Application Textbook Exercises
Textbooks
Figure 7. Types of Quantitative Reasoning

Figure 6. Country/Jurisdiction Textbook Figure 8. Types of 21st Century Competencies

Notes for Figures 5 (total number of exercises across all countries/jurisdictions)

& 6 (country/jurisdiction specific):
 The Blue pie diagram shows the total number of different types of
exercises.
 The Grey pie diagram shows the number of standard word problems Notes for Figures 7 & 8:
(an expansion of the light-blue wedge).  Light Grey bars show the range for the number of Higher-Order Real-World
 The Orange wedge represents the number of Higher-Order Math- application exercises of each type for each country/jurisdiction.
World applications.  Dark Grey bars show the Inter-Quartile Range (25th to 75th percentile).
 The Yellow wedge represents the number of Higher-Order Real-  Special case: in cases where the majority of the country’s/jurisdiction’s
World applications. values were 0, the light grey bar encompasses the dark grey bar.
 For countries/jurisdictions that coded 2 textbooks, the average  The stars show the number of Higher-Order Real-World application
number of exercises of the two textbooks was used in Figures 5, exercises of each type that are included.
6, 7 and 8.

Unclassified
 EDU/WKP(2022)6  97

Curriculum Decision Making

0 1 2 3

Constrain, veto or
No formal Advice & Final authority
modify
Decision role recommendations or approval
recommendations
Role:

[\\\\\\] zz\\\\\] [\zzzzzz zzzzzzzz

Figure 9. Who Makes What Decisions?
National Regional School Teachers Teachers
Collectively Individually
Goals for Pupils
A By overall system completion zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
B For intermediate stages zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
C For differentiated programme types [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
D To be reached in a given grade zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
E To apply for a specific school zzzzzzzz [\\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz
Content of Instruction
F Course (grade level) offerings zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
G Student course assignment rules zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
H Course content (syllabi) [\\\\\\] [\\\\\\] [\\\\\\] [\zzzzzz [\zzzzzz
I Auxiliary content outside of syllabi [\\\\\\] [\\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz
Methods of instruction
J Textbook selection [\\\\\\] [\\\\\\] [\\\\\\] zzzzzzzz [\\\\\\]
K Instructional methods/techniques [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\] zzzzzzzz
Examinations
L Content of examinations zzzzzzzz [\\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz
M School Examination performance standards zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
N Examination standards [\\\\\\] [\\\\\\] zzzzzzzz zzzzzzzz zzzzzzzz
Figure 10. Country/Jurisdictions: Relative Importance for each of the Four Facets
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 80% 0% 0% 20% 20%
Content of instruction 50% 0% 0% 42% 42%
Methods (including textbooks) 0% 0% 0% 50% 50%
Examinations 67% 0% 33% 67% 67%
Note. The denominator for the percentages is the number of subcategories (as defined in Figure 9) within each category x 3. The numerator (x) is the sum of the
values assigned for each chosen subcategory; for example, for cell (1,1) the formula is x/15. The facet Methods of Instruction includes textbook selection as well.
Figure 11. Relative Importance Averaged Across All 19 Countries/Jurisdictions
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 52% 24% 40% 29% 33%
Content of instruction 46% 19% 43% 42% 53%
Methods (including textbooks) 28% 18% 55% 50% 74%
Examinations 55% 16% 30% 40% 41%
Note for Figures 9, 10 & 11. In the above figures looking across rows tells who has what role while looking down the columns especially in Figures 10 and 11,
indicates over which facets each locus has the most influence. We acknowledge David E. Wiley’s contribution to the study of curriculum decision making.

Unclassified
98  EDU/WKP(2022)6

Coverage of Mathematics Topics in the Standards

Figure 12. Comparing the Patterns of Coverage over 25 Years

Note. Green cells indicate coverage defined by TIMSS A+; Orange cells indicate coverage defined by at least a simple majority of the 19
countries/jurisdictions; Blue cells indicate specific country/jurisdiction coverage.
Figure 13. Moving into the Future: Current Coverage of Topics Defining a New Literacy

Note. Orange cells indicate the number of countries that cover that topic at that grade level. The accompanying column indicates the number of
countries/jurisdictions that included that topic at any grade level; Blue cells indicate specific country/jurisdiction coverage. The absence of green cells
indicates the lack of coverage of those topics in TIMSS95.

Unclassified
 EDU/WKP(2022)6  99

8th Grade Textbook Exercises: Book 1

Characteristics of Higher-Order Real-
Textbook Exercise Composition World Application Textbook Exercises
Figure 5. Totals Over All Participants’ Figure 7. Type of Quantitative Reasoning
Textbooks

Figure 8. Type of 21st Century Competencies

Figure 6. Country/Jurisdiction Textbook

Notes for Figures 5 (total number of exercises across all countries/jurisdictions) & 6
(country/jurisdiction specific):
 The Blue pie diagram shows the total number of different types of exercises.
 The Grey pie diagram shows the number of standard word problems (an
expansion of the light-blue wedge).

 The Orange wedge represents the number of Higher-Order Math-World

applications.
 The Yellow wedge represents the number of Higher-Order Real-World
applications. Notes for Figures 7 & 8:
 For countries/jurisdictions that coded 2 textbooks, the average number of  Light Grey bars show the range for the number of Higher-Order Real-
exercises of the two textbooks was used in Figures 5, 6, 7 and 8. World application exercises of each type for each country/jurisdiction.
 Dark Grey bars show the Inter-Quartile Range (25th to 75th percentile).
 Special case: in cases where the majority of the country’s/jurisdiction’s
values were 0, the light grey bar encompasses the dark grey bar.
 The stars show the number of Higher-Order Real-World application
exercises of each type that are included.

Unclassified
100  EDU/WKP(2022)6

8th Grade Textbook Exercises: Book 2

Textbook Exercise Composition Characteristics of Higher-Order Real-
World Application Textbook Exercises
Figure 5. Totals Over All Participants’
Textbooks Figure 7. Type of Quantitative Reasoning

Figure 6. Country/Jurisdiction Textbook Figure 8. Type of 21st Century

Competencies

Notes for Figures 5 (total number of exercises across all

countries/jurisdictions) & 6 (country/jurisdiction specific):
 The Blue pie diagram shows the total number of different types of
exercises.
 The Grey pie diagram shows the number of standard word problems (an Notes for Figures 7 & 8:
expansion of the light-blue wedge).
 The Orange wedge represents the number of Higher-Order Math-World
applications.  Light Grey bars show the range for the number of Higher-Order
 The Yellow wedge represents the number of Higher-Order Real-World Real-World application exercises of each type for each
applications. country/jurisdiction.
 For countries/jurisdictions that coded 2 textbooks, the average number of  Dark Grey bars show the Inter-Quartile Range (25th to 75th
exercises of the two textbooks was used in Figures 5, 6, 7 and 8. percentile).
 Special case: in cases where the majority of the
country’s/jurisdiction’s values were 0, the light grey bar encompasses
the dark grey bar.
 The stars show the number of Higher-Order Real-World application
exercises of each type that are included.

Unclassified
 EDU/WKP(2022)6  101

Hong Kong (China)

Curriculum Standards
Index
 Page 1 portrays the composition of the country’s/ Figure 2. Degree of Emphasis for the Coverage of
jurisdiction’s curriculum standards. Four Types of Quantitative Reasoning
 Page 2 portrays the composition of a representative 8 th
grade mathematics textbook.
 Page 3 portrays the curriculum decision-making authority
within the educational system.
 Page 4 portrays the mathematics topic coverage of the
country’s/jurisdiction’s curriculum standards across
grades 1-8 in comparison to the 1995 TIMSS A+
benchmark curriculum.

Figure 1. Number of Topics to be Covered at each Grade Figure 3. Degree of Emphasis for the Coverage of
Higher-Order Applications

Figure 4. Degree of Emphasis for the Coverage of 21st

Century Competencies/Skills

Notes for Figure 1:

 Light Grey bars show the range for the number of topics that each
of the 19 countries/jurisdictions intended to cover.
 Dark Grey bars show the Inter-Quartile Range (25th to 75th
Percentile) found within the broader range for the number of
topics that each of the 19 countries/jurisdictions intended to
cover.
 The stars show the number of topics that the country/
jurisdiction intended to cover at each of the grades.
Notes for Figures 2-4:
 The structure of these figures is the same as described in the note for Figure
Note: 1.
 The Hong Kong curriculum at grades 7 to 9 is organised as a whole  The variable represented in each of these figures is a measure of the
(called Key Stage 3), and teachers have some liberty to organise their intensity/emphasis that the curriculum standards for each of the
course sequencing logically amongst all of the 32 topics that are included countries/jurisdictions placed on each of these three dimensions of
in this Key Stage. It was not clear how to divide the 32 topics into 3 mathematics literacy.
partitions for grades 7 to 9. Hong Kong decided to essentially divide the  The measure is defined with 0 indicating no mention of the
32 topics evenly across the three grades (11, 11, 11). dimension and 1-75 indicating the degree of emphasis (see
methods section of the introduction to the country/jurisdiction
reports).

Unclassified
102  EDU/WKP(2022)6

8th Grade Textbook Exercises

Textbook Exercise Composition Characteristics of Higher-Order Real-World
Application Textbook Exercises
Figure 5. Totals Over All Participants’
Textbooks Figure 7. Types of Quantitative Reasoning

Figure 8. Types of 21st Century Competencies

Figure 6. Country/Jurisdiction Textbook

Notes for Figures 5 (total number of exercises across all countries/jurisdictions)

& 6 (country/jurisdiction specific): Notes for Figures 7 & 8:
 The Blue pie diagram shows the total number of different types of  Light Grey bars show the range for the number of Higher-Order Real-World
exercises. application exercises of each type for each country/jurisdiction.
 The Grey pie diagram shows the number of standard word problems  Dark Grey bars show the Inter-Quartile Range (25th to 75th percentile).
(an expansion of the light-blue wedge).  Special case: in cases where the majority of the country’s/jurisdiction’s
 The Orange wedge represents the number of Higher-Order Math- values were 0, the light grey bar encompasses the dark grey bar.
World applications.  The stars show the number of Higher-Order Real-World application
 The Yellow wedge represents the number of Higher-Order Real- exercises of each type that are included.
World applications.
 For countries/jurisdictions that coded 2 textbooks, the average
number of exercises of the two textbooks was used in Figures 5,
6, 7 and 8.

Unclassified
 EDU/WKP(2022)6  103

Curriculum Decision Making

0 1 2 3

Constrain, veto or
Advice &
No formal role modify Final authority or approval
Decision recommendations
recommendations
Role:
[\\\\\\] zz\\\\\] [\zzzzzz zzzzzzzz
Figure 9. Who Makes What Decisions?
National Regional School Teachers Collectively Teachers Individually

Goals for pupils

A By overall system completion
[\\\\\\] zzzzzzzz [\zzzzzz zz\\\\\] zz\\\\\]
B For intermediate stages
[\\\\\\] zzzzzzzz [\zzzzzz zz\\\\\] zz\\\\\]
C For differentiated programme types
[\\\\\\] zzzzzzzz [\zzzzzz zz\\\\\] zz\\\\\]
D To be reached in a given grade
[\\\\\\] zzzzzzzz [\zzzzzz zz\\\\\] zz\\\\\]
E To apply for a specific school
[\\\\\\] zzzzzzzz [\zzzzzz zz\\\\\] zz\\\\\]
Content of instruction
F Course (grade level) offerings
[\\\\\\] zzzzzzzz [\zzzzzz zz\\\\\] zz\\\\\]
G Student course assignment rules
[\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
H Course content (syllabi)
[\\\\\\] zzzzzzzz [\zzzzzz [\zzzzzz [\zzzzzz
I Auxiliary content outside of syllabi
[\\\\\\] zzzzzzzz [\zzzzzz [\zzzzzz [\zzzzzz
Methods of instruction
J Textbook selection
[\\\\\\] zzzzzzzz [\zzzzzz [\zzzzzz zz\\\\\]
K Instructional methods/techniques
[\\\\\\] zz\\\\\] [\zzzzzz [\zzzzzz [\zzzzzz
Examinations
L Content of examination
[\\\\\\] zzzzzzzz zz\\\\\] zz\\\\\] zz\\\\\]
M Examination performance standards
[\\\\\\] zzzzzzzz zz\\\\\] zz\\\\\] zz\\\\\]
N Examination standards
[\\\\\\] zz\\\\\] zzzzzzzz zz\\\\\] zz\\\\\]
Figure 10. Country/Jurisdictions: Relative Importance for each of the Four Facets
National Regional School Teachers Collectively Teachers Individually
Goals for pupils 0% 100% 67% 33% 33%
Content of instruction 0% 75% 50% 42% 42%
Methods (including textbooks) 0% 67% 67% 67% 50%
Examinations 0% 78% 56% 33% 33%
Note. The denominator for the percentages is the number of subcategories (as defined in Figure 9) within each category x 3. The numerator (x) is the sum of the
values assigned for each chosen subcategory; for example, for cell (1,1) the formula is x/15.Note. The facet Methods of Instruction includes textbook selection as
well.
Figure 11. Relative Importance Averaged Across All 19 Countries/Jurisdictions
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 52% 24% 40% 29% 33%
Content of instruction 46% 19% 43% 42% 53%
Methods (including textbooks) 28% 18% 55% 50% 74%
Examinations 55% 16% 30% 40% 41%
Note for Figures 9, 10 & 11. In the above figures looking across rows tells who has what role while looking down the columns especially in Figures 10 and 11,
indicates over which facets each locus has the most influence. We acknowledge David E. Wiley’s contribution to the study of curriculum decision making.

Unclassified
104  EDU/WKP(2022)6

Coverage of Mathematics Topics in the Standards

Figure 12. Comparing the Patterns of Coverage over 25 Years

Note. Green cells indicate coverage defined by TIMSS A+; Orange cells indicate coverage defined by at least a simple majority of the 19
countries/jurisdictions; Blue cells indicate specific country/jurisdiction coverage.
Figure 13. Moving into the Future: Current Coverage of Topics Defining a New Literacy

Note. Orange cells indicate the number of countries that cover that topic at that grade level. The accompanying column indicates the number of
countries/jurisdictions that included that topic at any grade level; Blue cells indicate specific country/jurisdiction coverage. The absence of Green cells
indicates the lack of coverage of those topics in TIMSS95

Unclassified
 EDU/WKP(2022)6  105

8th Grade Textbook Exercises: Book 1

Textbook Exercise Composition Characteristics of Higher-Order
Real- World Application Textbook
Figure 5. Totals Over All Participants’
Exercises
Textbooks
Figure 7. Type of Quantitative Reasoning

Figure 8. Type of 21st Century

Figure 6. Country/Jurisdiction Textbook Competencies

Notes for Figures 5 (total number of exercises across all countries/jurisdictions)

& 6 (country/jurisdiction specific):
 The Blue pie diagram shows the total number of different types of
exercises.
 The Gray pie diagram shows the number of standard word Notes for Figures 7 & 8:
problems (an expansion of the light-blue wedge).  Light Gray bars show the range for the number of Higher-Order Real-
 The Orange wedge represents the number of Higher-Order Math- World application exercises of each type for each country/jurisdiction.
World applications.  Dark Gray bars show the Inter-Quartile Range (25th to 75th percentile).
 The Yellow wedge represents the number of Higher-Order Real-
 Special case: in cases where the majority of the country’s/jurisdiction’s
World applications.
values were 0, the light gray bar encompasses the dark gray bar.
 For countries/jurisdictions that coded 2 textbooks, the average
 The stars show the number of Higher-Order Real-World application
number of exercises of the two textbooks was used in Figures 5,
exercises of each type that are included.
6, 7 and 8.

Unclassified
106  EDU/WKP(2022)6

8th Grade Textbook Exercises: Book 2

Characteristics of Higher-Order Real-
Textbook Exercise Composition
World Application Textbook Exercises
Figure 5. Totals Over All Participants’ Figure 7. Type of Quantitative Reasoning
Textbooks

Figure 8. Type of 21st Century Competencies

Figure 6. Country/Jurisdiction Textbook

Notes for Figures 7 & 8:

Notes for Figures 5 (total number of exercises across all countries/jurisdictions)
& 6 (country/jurisdiction specific):  Light grey bars show the range for the number of Higher-Order Real-World
 The blue pie diagram shows the total number of different types of exercises. application exercises of each type for each country/jurisdiction.
 The grey pie diagram shows the number of standard word problems (an  Dark grey bars show the Inter-Quartile Range (25th to 75th percentile).
expansion of the light-blue wedge).  Special case: in cases where the majority of the country’s/jurisdiction’s values
 The Orange wedge represents the number of Higher-Order Math-World were 0, the light grey bar encompasses the dark gray bar.
applications.  The stars show the number of Higher-Order Real-World application exercises of
 The Yellow wedge represents the number of Higher-Order Real-World each type that are included.
applications.
 For countries/jurisdictions that coded 2 textbooks, the average number of
exercises of the two textbooks was used in Figures 5, 6, 7 and 8.

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Kazakhstan
Curriculum Standards
Index Figure 2. Degree of Emphasis for the Coverage of
 Page 1 portrays the composition of the country’s/ Four Types of Quantitative Reasoning
jurisdiction’s curriculum standards.
 Page 2 portrays the composition of a representative 8 th
grade mathematics textbook.
 Page 3 portrays the curriculum decision-making authority
within the educational system.
 Page 4 portrays the mathematics topic coverage of the
country’s/jurisdiction’s curriculum standards across
grades 1-8 in comparison to the 1995 TIMSS A+
benchmark curriculum.

Figure 1. Number of Topics to be Covered at each Grade Figure 3. Degree of Emphasis for the Coverage of
Higher-Order Applications

Figure 4. Degree of Emphasis for the Coverage of 21st

Century Competencies/Skills

Notes for Figure 1:

 Light Grey bars show the range for the number of topics that each
of the 19 countries/jurisdictions intended to cover. Notes for Figures 2-4:
 Dark Grey bars show the Inter-Quartile Range (25th to 75th  The structure of these figures is the same as described in the note for Figure
Percentile) found within the broader range for the number of 1.
topics that each of the 19 countries/jurisdictions intended to  The variable represented in each of these figures is a measure of the
cover. intensity/emphasis that the curriculum standards for each of the
 The stars show the number of topics that the country/ countries/jurisdictions placed on each of these three dimensions of
jurisdiction intended to cover at each of the grades. mathematics literacy.
 The measure is defined with 0 indicating no mention of the
dimension and 1-75 indicating the degree of emphasis (see
methods section of the introduction to the country/jurisdiction
reports).

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8th Grade Textbook Exercises

Textbook Exercise Composition Characteristics of Higher-Order Real-World
Application Textbook Exercises
Figure 5. Totals Over All Participants’ Figure 7. Types of Quantitative Reasoning
Textbooks

Figure 8. Types of 21st Century Competencies

Figure 6. Country/Jurisdiction Textbook

Notes for Figures 5 (total number of exercises across all countries/jurisdictions)

& 6 (country/jurisdiction specific):
 The Blue pie diagram shows the total number of different types of
exercises. Notes for Figures 7 & 8:
 The Grey pie diagram shows the number of standard word problems  Light Grey bars show the range for the number of Higher-Order Real-World
(an expansion of the light-blue wedge). application exercises of each type for each country/jurisdiction.
 The Orange wedge represents the number of Higher-Order Math-  Dark Grey bars show the Inter-Quartile Range (25th to 75th percentile).
World applications.  Special case: in cases where the majority of the country’s/jurisdiction’s
 The Yellow wedge represents the number of Higher-Order Real- values were 0, the light grey bar encompasses the dark grey bar.
World applications.  The stars show the number of Higher-Order Real-World application
 For countries/jurisdictions that coded 2 textbooks, the average exercises of each type that are included.
number of exercises of the two textbooks was used in Figures 5,
6, 7 and 8.

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Curriculum Decision Making

0 1 2 3
Advice & Constrain, veto Final authority
No formal role recommendati or modify
Decision or approval
Role: ons recommendati
ons
[\\\\\\] zz\\\\\] [\zzzzzz zzzzzzzz
Figure 9. Who Makes What Decisions?
Teachers Teachers
National Regional School
Collectively Individually
Goals for pupils
A By overall system completion
zzzzzzzz [\\\\\\] [\\\\\\] zz\\\\\] zz\\\\\]
B For intermediate stages
zzzzzzzz [\\\\\\] [\\\\\\] zz\\\\\] zz\\\\\]
C For differentiated programme types
zzzzzzzz [\\\\\\] [\\\\\\] zz\\\\\] zz\\\\\]
D To be reached in a given grade
zzzzzzzz [\\\\\\] [\\\\\\] zz\\\\\] zz\\\\\]
E To apply for a specific school
zzzzzzzz [\\\\\\] [\\\\\\] zz\\\\\] zz\\\\\]
Content of instruction
F Course (grade level) offerings
zzzzzzzz [\\\\\\] [\\\\\\] zz\\\\\] zz\\\\\]
H Student course assignment rules
zzzzzzzz [\\\\\\] [\\\\\\] zz\\\\\] zz\\\\\]
I Course content (syllabi)
zzzzzzzz [\\\\\\] [\\\\\\] zz\\\\\] zz\\\\\]
J Auxiliary content outside of syllabi
zzzzzzzz [\\\\\\] zz\\\\\] zz\\\\\] zz\\\\\]
Methods of instruction
J Textbook selection
zzzzzzzz zz\\\\\] zzzzzzzz zz\\\\\] zz\\\\\]
K Instructional methods/techniques
zzzzzzzz zz\\\\\] [\zzzzzz zz\\\\\] zz\\\\\]
Examinations
L Content of examinations
zzzzzzzz [\\\\\\] [\\\\\\] zz\\\\\] zz\\\\\]
M Examination performance standards
zzzzzzzz [\\\\\\] [\\\\\\] [\\\\\\] [\\\\\\]
N School Examination standards
zz\\\\\] zz\\\\\] zz\\\\\] [\zzzzzz [\zzzzzz
Figure 10. Country/Jurisdictions: Relative Importance for each of the Four Facets
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 100% 0% 0% 33% 33%
Content of instruction 100% 0% 8% 33% 33%
Methods (including textbooks) 100% 33% 83% 33% 33%
Examinations 78% 11% 11% 33% 33%
Note. The denominator for the percentages is the number of subcategories (as defined in Figure 9) within each category x 3.
The numerator (x) is the sum of the values assigned for each chosen subcategory; for example, for cell (1,1) the formula is x/15.
The facet Methods of Instruction includes textbook selection as well.
Figure 11. Relative Importance Averaged Across All 19 Countries/Jurisdictions
National Regional School Teachers Teachers
Collectively Individually
Goals for pupils 52% 24% 40% 29% 33%
Content of instruction 46% 19% 43% 42% 53%
Methods (including textbooks) 28% 18% 55% 50% 74%
Examinations 55% 16% 30% 40% 41%
Note for Figures 9, 10 & 11. In the above figures looking across rows tells who has what role while looking down the columns
especially in Figures 10 and 11, indicates over which facets each locus has the most influence. We acknowledge David E.
Wiley’s contribution to the study of curriculum decision making.

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Coverage of Mathematics Topics in the Standards

Figure 12. Comparing the Patterns of Coverage over 25 Years

Note. Green cells indicate coverage defined by TIMSS A+; Orange cells indicate coverage defined by at least a simple majority of the 19
countries/jurisdictions; Blue cells indicate specific country/jurisdiction coverage.

Figure 13. Moving into the Future: Current Coverage of Topics Defining a New Literacy

Note. Orange cells indicate the number of countries that cover that topic at that grade level. The accompanying column indicates the number of
countries/jurisdictions that included that topic at any grade level; Blue cells indicate specific country/jurisdiction coverage. The absence of green
cells indicates the lack of coverage of those topics in TIMSS95.

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6. Discussion

We designed this report so that all of each country/jurisdiction’s results from the various analyses
described in the previous section would be combined in an individual country/jurisdiction report thus
creating a more complete characterisation of the issues related to that country’s/jurisdiction’s
curriculum. This we felt to be a more important format for country/jurisdiction use rather than to
have the results for the countries listed in a rank-ordered table. Each country/jurisdiction report
includes: how curriculum decisions are made; what the national curriculum standards specify to be
covered; a comparison to the A+ curriculum from 25 years ago; and a characterisation of at least one
8th grade mathematics textbook.
All the results within a country/jurisdiction report are anchored within the distribution of all 19
countries/jurisdictions providing them with an overall comparison but not specifically to any
individual country/jurisdiction. If any country/jurisdiction desires such a one-on-one comparison to
another country/jurisdiction, it will have to find the section containing the data for the other
country/jurisdiction and draw the comparison themselves.
Three research questions pertain to the coverage of formal mathematics content as well as to the three
dimensions related to mathematics literacy as found in the MCDA mathematics content framework.
The comparison of the formal mathematics topics – both those known to have been covered 25 years
ago as well as a set of new topics entering the curriculum of some countries early in the 21st century
– were compared to those of 25 years ago as reflected in the TIMSS-95 study. A third question
pertained directly to the coverage of the three aspects of the mathematics framework related to the
development of mathematics literacy.
Pertaining to the formal mathematics topics the main finding was that for a majority of the 19
countries/jurisdictions, the overall pattern of coverage was very similar to that found for the A+
countries in TIMSS-95. Most formal topics undergirding K-8 school mathematics were included in
most countries’/jurisdictions’ national standards – not always in the same order or at the same grades,
but they were covered. The more recently appearing formal topics were in general not covered by
most participants as might be expected. The data showed the occurrence of more statistics topics
being covered, but only a few countries/jurisdictions going into the more formal aspects of statistical
inference. The other topics such as algorithmic reasoning and non-linear statistical models were
rarely included.
We found, but to varying degrees of emphasis, that all three dimensions of mathematics literacy have
become the norm in the national curriculum standards of all 19 countries/jurisdictions. The
country/jurisdiction standards bring to the fore, not only formal mathematics related to K-8
schooling, but the dimensions of quantitative reasoning, real-world applications, and 21st century
competencies. There are major differences among countries as to the degree of emphasis placed on
each of these three dimensions. Within a country/jurisdiction the degree of emphasis also varies
across the three dimensions.
Some countries/jurisdictions mention any one of the three dimensions but only once. Others mention
two or three of the dimensions but, again, only once. Still others include one or more of the three
dimensions at each grade level. While still others achieve the greatest degree of emphasis by
including references to one or more of the three dimensions in association with specific topics at
specific grades. The repeated and/or specific references to topic/grade combinations for these three
dimensions, we hypothesise, indicate to the teachers the importance of covering them. As such,
teachers are told to teach not only the formal and fundamental aspects of K-8 mathematics but also
to include the aspects related to the development of mathematics literacy.
Opportunities to learn in mathematics are clearly related to the types of exercises provided in student
textbooks. Teachers are generally not expected to develop their own exercises but to rely on the
textbook. Studies indicate that most do as was the case in these 19 countries/jurisdictions. The

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following quote by education psychologists is relevant here as it talks about engaging students in
building connections within a domain of knowledge by “…providing opportunities for students to
engage repeatedly in this process over time as they deepen and extend their domain knowledge
[mathematics literacy]” (Fries et al., 2020[16]).
Textbook data related to the availability of higher-order real-world application exercises in
country/jurisdiction textbooks paint a dismal picture at best. From the point-of-view of the students,
such opportunities to learn and develop mathematics literacy are so few so as to be almost non-
existent averaging less than six exercises per 8th grade textbook. The analysis shows what is given to
them in the form of word problems (averaging around 15% per book) are really nothing more than
computational problems surrounded by words and as such provide weak opportunities to develop
mathematics literacy. Pollack, some 40 years ago, looked at the issue of how to teach the application
of mathematics to the real-world. What he recommended, essentially, is the use of what we have
defined as higher-order real-world applications. He noted that word problems are “silly, redundant
and even stupid” (Pollak, 1969[17]). Pollack also indicated that many times the applications around
which the exercises are developed make assumptions that are incorrect and inconsistent with the
reality that the item tries to represent.
It is here where the gap between policy and practice occurs as we found very few higher-order real-
world application exercises in any of the countries/jurisdiction textbooks. They occurred in such
small numbers that the average country/jurisdiction would run out of such exercises in one and a half
months even if they only included one such exercise per week. The results of this study indicate that
the countries’/jurisdictions’ education policy makers have “talked the talk” in terms of the
importance of providing opportunities to all students in order to develop mathematics literacy that
enables them to reason mathematically toward finding solutions to the problems that arise in their
current lives and certainly almost daily in their future lives as citizens.
Unfortunately, the analysis of the 23 textbooks that provide opportunities to learn to ostensibly
become mathematically literate in these 19 countries/jurisdictions, amount to less than one percent
of all the exercises contained in those 23 textbooks. Clearly, the textbooks fail to deliver the relevant
opportunities to learn. Recent research studies related to OECD Programme for International
Students Assessemnt (PISA) 2012 that contained a measure of mathematics opportunities to learn
(OTL) indicated the consistent and strong relationship of OTL to PISA performance with large
estimated effect sizes. The effect sizes varied across countries/jurisdictions but one thing that did not
vary is both the practical and statistical significance of mathematics OTL to PISA assessment
performance (Cogan, Schmidt and Guo, 2019[18]; Schmidt and Burroughs, 2016[19]; Schmidt et al.,
2015[20]; Schmidt, Guo and Houang, 2021[21]).
This leaves us with the serious predicament of a rather large gap between policy and practice.
Unfortunately, we do not have data pertaining to what the teachers actually taught in each
country/jurisdiction, but previous research indicates the strikingly large correlation (.9) between
teacher content coverage and textbook content coverage. Assuming this to be true, unfortunately, this
leaves countries/jurisdictions with strong policy but weak implementation.
Countries/jurisdictions do not publish textbooks but rely on the private sector for their development,
however, this does not imply that the policy makers have no influence over the content of the
textbooks. Perhaps newly developed policies could impact the content of mathematics textbooks.
Without such, one can only imagine the difficulties of reaching the important goal of providing all
children, no matter their socio-economic status the opportunity to acquire the second most important
literacy – mathematics. Without this, we are depriving many students of the opportunity to develop
the mathematics knowledge and quantitative reasoning necessary to, as a society, address the serious
problems facing the world including climate change, raging pandemics, and even the very survival
of democracy.

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References
American Psychological Association (2017), The Road to Resilience, http://www.apa.org/helpcenter/road- [14]
reslience.aspx.

Cogan, L., W. Schmidt and S. Guo (2019), “The role that mathematics plays in college- and career-readiness: [18]
Evidence from PISA”, Journal of Curriculum Studies, Vol. 51/4, pp. 530-553.

Eszterhazy Karoly University (2018), Matematika 8, Eszterhazy Karoly University. [6]

Facione, P., C. Giancarlo and N. Facione (1995), “The disposition toward critical thinking”, Journal of General [12]
Education, Vol. 44/1, pp. 1-25.

France, I., G. Lace and E. and Slokenberga (2017), Matematika 8. Klasei, Lielvārds. [7]

Fries, L. et al. (2020), “Practicing connections: A framework to guide instructional design for developing [16]
understanding in complex domains”, Educational Psychology Review, http://dx.doi.org/10.1007/s10648-020-
09561-x.

Great Minds (2015), Eureka Math! Grade 8 Modules 1 & 2 (Student Edition), Great Minds. [8]

Great Minds (2015), Eureka Math! Grade 8 Modules 3,4,&5 (Student Edition), Great Minds. [9]

Liu, O., L. Frankel and K. Roohr (2014), Assessing critical thinking in higher education: Current state and directions [13]
for next generation assessment.

Mumford, M., K. Medeiros and P. Partlow (2012), “Creative thinking: Processes, strategies, and knowledge”, The [10]
Journal of Creative Behaviour, Vol. 46/1, pp. 30-47.

OECD (2016), Education 2030: Preliminary reflections and research by experts on knowledge, skills, attitudes, and [11]
values towards 2030, http://www.oecd.org/education/2030.

Pearson Australia (2014), Pearson Mathematics 8 Student Book (1st ed.), Pearson. [5]

Pollak, H. (1969), “How Can We Teach Applications of Mathematics?”, Educational Studies in Mathematics, [17]
Vol. 2/3, pp. 393-404.

Schmidt, W. and N. Burroughs (2016), “The trade-off between excellence and equality: What international [19]
assessments tell us”, Georgetown Journal of International Affairs, Vol. 17/1, pp. 103-109.

Schmidt, W. et al. (2015), “The role of schooling in perpetuating educational inequality: An international [20]
perspective”, Educational Researcher, Vol. 44/7, pp. 371-386, http://dx.doi.org/10.3102/0013189x15603982.

Schmidt, W., S. Guo and R. Houang (2021), “The role of opportunity to learn in ethnic inequality in mathematics”, [21]
Journal of Curriculum Studies, Vol. 53/5, pp. 579-600, http://dx.doi.org/10.1080/00220272.2020.1863475.

Schmidt, W. et al. (2001), Why schools matter: A cross-national comparison of curriculum and learning, Jossey- [1]
Bass.

Schmidt, W. et al. (1997), Many visions, many aims: A cross-national investigation of curricular intentions in school [2]
mathematics, Kluwer Academic.

Schmidt, W., H. Wang and C. McKnight (2005), “Curriculum coherence: An examination of US mathematics and [3]
science content standards from an international perspective”, Journal of Curriculum Studies, Vol. 37/5, pp. 525-
559, http://dx.doi.org/10.1080/0022027042000294682.

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Sterman, J. (2000), Business dynamics: Systems thinking and modelling for acomplex world. [15]

Valverde, G. et al. (2002), According to the book: Using TIMSS to investigate the translation of pollicy into practice [4]
through the world of textbooks, Kluwer Academic.

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Annex A. Mathematics Curriculum Document Analysis (MCDA) Framework

Content
Quantity
Whole number
 Meaning (place value, ordering, comparison)
 Operations (meaning and computations)
 Properties of operations (order of operation, relationship among operations)
Fractions & decimals
 Common fractions
 Decimal fractions & percentages
 Properties and relationships of common & decimal fractions
Number sense & estimation
 Measurement units, estimation & errors
 Rounding & significant figures
 Estimating computations
 Exponents & orders of magnitude
Number systems
 Integers, negative numbers & their properties
 Rational numbers & their properties
 Real numbers, their subsets & properties
 Complex numbers
Other number concepts
 Simple number patterns and sequences
 Binary arithmetic &/or other number bases
 Roots, radicals and complex numbers
 Combinatorics (permutations and combinations)
 Computational thinking: Algorithmic mathematics & computer simulations
 Computer coding (including both formal and informal (pseudocode) syntax)
Space and shape
Position, visualisation & shape
 2-D Geometry: Basics (points, lines, segments, rays, angles)
 2-D Geometry: Polygons & circles (formulas, properties, perimeter, area)
 3-D Geometry (shapes, volume, surfaces, cross-sections)

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 Co-ordinate geometry (analytical geometry)

 Trigonometry of right-angled triangles including the Pythagorean Theorem
 Vectors and matrices
 Geometric approximation for irregular shapes
Symmetry, congruence & similarity
 Symmetry
 Transformations (including geometric patterns)
 Congruence & similarity
Change and relationships
Algebra foundations
 Rates and ratios
 Proportionality
Beginning algebra
 Algebraic sequences and patterns
 Expressions
 Simple linear equations
 Slope and intercept
Algebra
 Linear equations and inequalities
 Trigonometric equations and identities
 Other equations and inequalities (quadratics, polynomials, including factorization and
expansion)
 Linear functions
 Exponential functions
 Other non-linear functions
Change
 Infinite processes (e.g. sequence, series, limits and convergence)
 Calculus and analysis
 Linear, non-linear, and exponential for modelling growth and change
Statistics, probability and data
Descriptive statistics
 Mean, mode, median, variance, etc.
 Displays of distributions
Probability distributions
 Definition of discrete probability and related theorems

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 Conditional probability and independent events

 Bayes Theorem
 Discrete and continuous random variables and their distributions
Statistical inference
 Populations and their parameters
 Sampling from the population/random sampling
 Estimation of parameters (e.g. mean, variance)
 Sampling distributions (standard errors, bias)
 Confidence intervals
 Hypothesis testing
 Definition of correlation coefficient
 Relationship among categorical variables (contingency tables)
 Relationship involving continuous variables (regression)
 Relationship involving categorical and continuous variables (ANOVA)
 History of Mathematics as a Human Activity
Quantitative reasoning
 Mathematics
 Algorithmic
 Geometric
 Statistical
st
21 century skills/competencies relevant to mathematics
 Critical thinking
 Creativity
 Information use
 Systems thinking
 Communication
 Reflection
 Resistance/resilience

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Annex B. Contributors list

National experts for Mathematics Curriculum Document Analysis (MCDA) planning and
coding workshops

Australia: Hilary Dixon (Australian Curriculum, Assessment and Reporting Authority (ACARA)),
Patrick Donaldson (Permanent Delegation of Australia to the OECD), Patrick Kelly (ACARA),
Rainer Mittelbach (ACARA), Rachael Whitney-Smith (ACARA)
Estonia: Kädi Alanurm (Education Agency Foundation), Imbi Henno (Ministry of Education and
Research), Joosep Norma (Noored Kooli SA)
Greece: Dionysios Lamprinidis (Ministry of Education), Konstantinos Stouraitis (Institute of
Educational Policy), Petros Verykios (Honorary school advisor)
Hungary: Csaba Csapodi (Eszterházy Károly University), Ödön Vancsó (Eszterházy Károly
University), Gergely Wintsche (Eszterházy Károly University)
Israel: Genady Aranovich (Ministry of Education), Yafit Avital (Ministry of Education), Rachel
Gabai (Ministry of Education), Nerit Katz (Ministry of Education), Gilmor Keshet-Maor (Ministry
of Education), Yossy Machluf (Ministry of Education), Dorit Neria (Ministry of Education)
Korea: Inseon Choi (Korea Institute for Curriculum and Evaluation)
Latvia: Mark Giterman (consultant), Ilze France (University of Latvia), Marta Mikite (National
Centre for Education), Laura Treimane (Permanent Delegation of the Republic of Latvia to the
OECD and UNESCO), Janis Vilcins (National Centre for Education)
Lithuania: Jolita Dudaitė (Mykolas Romeris University), Rimas Norvaiša (Vilnius University)
Netherlands: Marc van Zanten (Netherlands Institute for Curriculum Development)
New Zealand: Christine Dew (Ministry of Education), Darryn Grey (Ministry of Education), Vince
Wright (Consultant to Ministry of Education)
Norway: Ole Christian Norum (Norwegian Directorate for Education and Training)
Portugal: Leonor Santos (University of Lisbon), Jaime Carvalho Silva (University of Coimbra)
Sweden: Johan Börjesson (Swedish National Agency for Education), Marica Dahlstedt (Swedish
National Agency for Education), Jenny Lindblom (Swedish National Agency for Education)
Argentina: Hugo Labate (Ministry of Education, Culture, Science and Technology)
Hong Kong (China): Vincent Siu-chuen Chan (The Education Bureau), Chun-yue Lee (The
Education Bureau), Kit-ying Leung (The Education Bureau)
Kazakhstan: Gulnara Apeyeva (AEO “Nazarbayev Intellectual Schools”), Talgat Bainazarov (AEO
“Nazarbayev Intellectual Schools”), Narken Burkenov (AEO “Nazarbayev Intellectual Schools”),
Dina Shaikhina (AEO “Nazarbayev Intellectual Schools”), Zhanat Zhuldassov (AEO “Nazarbayev
Intellectual Schools”)

National experts for MCDA planning workshops

Canada: Marie Macauley (Council of Ministers of Education, Canada), Federico Vargas (Council
of Ministers of Education, Canada)

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China (People’s Republic of): Ma Yunpeng (Northeast Normal University), Cao Yi Ming (Beijing
Normal University), Wang Shan Shan (Ministry of Education)
Russian Federation: Ivan Yashchenko (National Research University Higher School of
Economics), Andrei Trepalin (National Research University Higher School of Economics)
Turkey: Ayse Gunay Gokben (Ministry of National Education)

Researchers/experts for MCDA coding workshops

Yoshinori Shimizu (University of Tsukuba, Japan)

William Schmidt (Michigan State University, United States)
Leland Cogan (Michigan State University, United States)
Richard Houang (Michigan State University, United States)
William Sullivan (Michigan State University (Graduate Student), United States)
Feng-Jui Hsieh (National Taiwan Normal University, Chinese Taipei)
Ting-Ying Wang (National Taiwan Normal University, Chinese Taipei)

Researchers/experts for MCDA planning workshops

Ellen Weavers (Cambridge Assessment, United Kingdom)

Professionals in fields using mathematics who contributed to MCDA planning workshops

Finance: Albert Ferreiro Castilla (ALCO Portfolio Manager, Banco Sabadell, Spain)
Health: Wouter Kroese (Founder, Pacmed, Netherlands)
Manufacturing: Renan Devillieres (CEO, OPEO Studio, France)
Marketing and communication: Doug Harrison (Former President, US and current consultant,
YouGov, United States)

OECD Secretariat
Miho Taguma, Project Manager, Senior Policy Analyst
Kevin Gillespie, Project Assistant
Cassandra Morley, Project Assistant
OECD consultants
Florence Gabriel (Consultant, Australia)
Meow Hwee Lim (Consultant, Singapore)
Kelly Makowiecki (Consultant, United States)

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