Presented at the DLSU Research Congress 2015
De La Salle University, Manila, Philippines
March 2-4, 2015
Assessing the Mathematics Performance of Grade 8 Students
as Basis for Enhancing Instruction and Aligning with K to
12 Curriculum
Romee Nicker A. Capate* and Minie Rose C. Lapinid, PhD
De La Salle University, Manila
* romee_capate@dlsu.edu.ph
Abstract: This study sought to determine the performance and the difficulties of the
Grade 8 students during the first conduct of the new K to 12 Mathematics. Results of
this study served as basis for enhancing instruction and aligning the Grade 8
Mathematics competencies to Instruction and Assessment. Students’ scores in the
Formative Tests (FT) and the Mathematics Achievement Test (MAT) measured their
mathematics performance while interpretation of their mistakes in the leastmastered
contents of the new K to 12 Mathematics identified their difficulties. Results indicate
that most of the Grade 8 students were in the Beginning level of achievement only.
Moreover, half of the tested contents were least-mastered. Incorrectly applying the
formulas, properties, theorems, and/or laws and incompletely solving the problem
despite correctly doing the initial procedure are their common difficulties. The general
recommendation to align the Grade 8 Mathematics Competencies to Instruction and
Assessment was to include the missed instructional objectives during the past
instruction in the next Curriculum Planning. The recommended strategies to improve
instruction included needs assessment, more practice for automation, conduct review
classes for mastery and retention, explicit instruction, and peer-assisted mathematics
instruction.
Key Words: mathematics performance; instructional enhancement; curriculum
alignment; K to 12 Mathematics Curriculum
Institute for Developmental Studies, 2012). More so,
there is a need to highlight the competence of students
in subjects that prepares them for the world, including
1. INTRODUCTION Mathematics.
Mathematics is one subject that pervades life
Education plays an important role to every at any age and in any circumstance. Thus, its value
individual because it equips him/her with the goes beyond the classroom and the school.
necessary knowledge and skills needed to become a Mathematics as a school subject, therefore, must be
functional member of the society. According to the learned comprehensively and with much depth
World Bank, education can also be one of the strongest (Department of Education, 2013).
instruments for reducing poverty, thereupon The achievement scores, whether in local or
improving the well-being of the people. However, to international examinations, are means to measure
establish and maintain a high-quality education comprehension on different subject areas and
system, proper investments must be made (Philippine highlight students’ over-all academic performance.
LLI-II-020 1
Proceedings of the DLSU Research Congress Vol. 3 2015
Presented at the DLSU Research Congress 2015
De La Salle University, Manila, Philippines
March 2-4, 2015
The National Achievement Test (NAT) results for
grade 6 in SY 2009-2010 showed only a 69.21% passing
rate while the NAT results for high school is at a low
46.38%. Moreover, in international test results such as
the 2003 TIMSS (Trends in International
Mathematics and Science Study), the Philippines
ranked 34th out of 38 countries in HS II Math and
ranked 43rd out of 46 countries in HS II Science; for
grade 4, the Philippines ranked 23rd out of 25
participating countries in both Math and Science. In
2008, even with only the science high schools
participating in the Advanced Mathematics category,
the Philippines ranked lowest (Department of
Education, 2010). Figure 1. The principle of alignment
As part of the efforts of the government to
respond to the perceived needs of the education sector,
the Department of Education (DepEd) had pushed for Thus, this research would address the need of
the change in the basic education curriculum—the identifying of the level of success of the
implementation of the “Enhanced K to 12 Basic implementation of the Enhanced K to 12 Basic
Education Program”. Education Program through the assessment of Grade
Truly, in the Philippine context, education 8 students’ performance in K to 12 Mathematics.
remains a top priority. However, in implementing
academic curricular changes specifically in
Mathematics, many factors need to be considered. For
one, there is a need for carefully planned programs of 2. METHODS
exchange in the curriculum. Also, there must be an
examination of the place of formative process and The descriptive design was used in this study
summative evaluation of curriculum programs and of to determine the mathematics performance of the
the practical materials for the actual process of Grade 8 students. This design is the most appropriate
installing new curricula in schools (Andres and since this study deals with recording and tabulating
Francisco, 2008). data to come up with factual results.
As presented by Biggs (2003), the
A research and development study was also
implementation of the curriculum should follow the
utilized because of the recommendations that were
Principle of Alignment. It describes teaching as a
proposed and developed after finding out the
balanced system in which all components support each
leastmastered and most-mastered competencies of the
other, as they do in any ecosystem. To work properly,
Grade 8 students in MAT.
the three components, namely Objectives, Instruction,
The respondents of the study were one of the
and Assessment, must be aligned with each other.
pioneer batches of K to 12 in the Philippines—the two
In aligned teaching, there is maximum
hundred seventy-nine (279) Grade 8 students of Don
consistency throughout the system. The objectives
Bosco Technical Institute – Makati (DBTI). This study
must be clearly stated in a manner that the level of
used total enumeration so that below average,
understanding is properly defined and not simply a list
average, and above average students are
of topics to be covered. The instruction or the teaching
wellrepresented.
and learning tasks chosen must be those that are
Two research instruments were used in this
likely to realize the stated objectives. Finally, the
study—the Formative Tests (FT)
assessment tasks must address the objectives so that
one can identify if the students have learned what was and the Mathematics Achievement
intended for them to learn. Test (MAT). Both instruments have the same
Imbalance in the system will lead to poor competencies being tested. However, their difference
teaching and surface learning. Non-alignment is is only in test type.
signified by inconsistencies, unmet expectations, and FTs were mostly given in open-ended form—
practices that contradict what we preach. Problem Solving. Although there were still some type
of tests such as True or False, Multiple Choice,
LLI-II-020 2
Proceedings of the DLSU Research Congress Vol. 3 2015
Presented at the DLSU Research Congress 2015
De La Salle University, Manila, Philippines
March 2-4, 2015
Identification, and Fill-in the Blank. The MAT, on the curriculum, as prescribed by DepEd Order No. 31, s.
other hand, were all given in Multiple Choice type. 2012 was adopted—Beginning level (74.99% and
The FTs being described in this study were all below); Developing level (75.00% - 79.99%);
designed by the two Grade 8 Mathematics teachers Approaching Proficiency level (80.00% - 84.99%);
and validated by the Mathematics Coordinator of Don Proficient level (85.00% - 89.99%); and Advanced level
Bosco Technical Institute– Makati. They are experts (90.00% and above).
in the field of Mathematics Teaching and are in the To determine the least-mastered and
business for more than 15 years. mostmastered contents of the students according to
On the other hand, the Mathematics MAT, this research adopted the parameters used in
Achievement Test (MAT) was designed by the Grade determining the level of difficulty of an item as
8 Mathematics Area teachers of Salesian Philippines recommended by Gabuyo (2012).
North Province, wherein the researcher is a member. The students have mastered a specific content
the least if only less than sixty percent (60%) of them
A round-table discussion was organized to
got an item correctly. On the other hand, the students
consolidate the constructed multiple choice test items
have mastered a specific content the most if sixty
for MAT. The distractors in these questions were
percent (60%) of them or more got an item correctly.
based on the students’ common mistakes in their
In order to determine the students’
problem solving.
misconception in a specific content in MAT, the
The first draft of MAT was then validated by
researchers analyzed the test items’ distractors which
the other grade/year level Mathematics Area Teachers
were answered more than the correct answer. The
and the Mathematics Area Heads of Salesian
analysis of the misconception was validated by the
Philippines North Province using Face Validation and
other experts in the field of mathematics. This
Content Validation. They ensured that the items were
procedure was only done in the least-mastered
based on the competencies required by the
contents. For contents with more than one competency
Department of Education (2013) for Grade 8. From
being tested, the average percentage of correct
their evaluation, test items which were out of scope
responses was obtained.
were deleted or revised. Furthermore, some items
which were completely deleted had been replaced by
those in their Item Bank. These processes completed
the final draft of the MAT. 3. RESULTS AND DISCUSSIONS
Consequently, the reliability of the final test
draft was established using Internal Consistency Table 1 shows the mean score, standard
Method. This was the most appropriate method to use deviation, and level ofachievement of the Grade 8
since the test consists of dichotomously scored items— students in the Formative Tests (FT).
the examinee either passes or fails in an item. The Among the three areas, Patterns and Algebra
computed reliability of the instrument was 0.84 using turned out to be the more mastered content area
Cronbach Alpha, indicating that the instrument has a (77.45%). Meanwhile, both Geometry and Statistics
good internal consistency (George & Mallery, 2003). and Probability are below the passing 75% mark by
The MAT required students to answer 70 just a significant value, which could mean that
multiple choice questions. It was limited to the students had difficulty grasping content of these areas
competencies for Grade 8—Patterns and Algebra, during discussions.
Geometry, and Probability and Statistics. Summarizing the level of achievement of the
The students’ responses to MAT were scored Grade 8 students in the overall FT, they are placed at
as one (1) point for correct answer and no point for the Developing level of achievement (75.72%). It
incorrect answer. This gives seventy (70) points as the means that in general, students have minimum
highest possible score and zero (0) as the lowest knowledge and skills and core understandings in
possible score. After utilizing the 70-item during the conduct of the FTs.
Mathematics Achievement Test (MAT), the
descriptive method was applied using mean, standard Table 1. Mean score, standard deviation, and level of achievement of
deviation, frequency, percentage distribution, and the Grade 8 students in th e FTs
normalized gain. FT FT Level of
To interpret qualitatively the formative test Content Area Mean Standard Achievement
Score Deviation
scores and the mathematics achievement test score of
Patterns and Algebra 77.45% 8.30 Developing
the students, the grading system in the K to 12
LLI-II-020 3
Proceedings of the DLSU Research Congress Vol. 3 2015
Presented at the DLSU Research Congress 2015
De La Salle University, Manila, Philippines
March 2-4, 2015
Geometry 74.59% 8.22 Beginning present. If this premise is to be held true, we could
Statistics and Probability 74.56% 7.30 Beginning therefore say that Patterns and Algebra is easier for
students, since results on formative tests are higher.
Overall 75.72% 7.71 Developing However, since it garnered the lowest score in the
summative test, it may be attributed to another factor
Table 2 probes on the which is retention of information (Nickson, 2004).
Mathematics Achievement Test (MAT) scores of the Calculating the Average Normalized Gain in
the students’ score to determine whether there is a
students. Mean scores were determined to facilitate
gain or loss in students’ scores in MAT from FT, it
the performance evaluation.
showed that there was no gain in scores (-0.12) since
Contrary to the results of the formative tests, the result was negative.
Geometry has been determined as highest in the MAT Based from the result of the Average
(78.92%). It could be assumed that this area has been Normalized Gain, it can be concluded that students
more mastered by the students. Meanwhile, Patterns really lack retention of the skills learned before
and Algebra was lowest (72.73%). This could be the instruction. The lack of retention of the skills learned
least mastered. However, it is a fact that the turnout by the students should therefore be addressed as their
of the examination was low, the level of achievement performance to the next assessments may yield a low
only being in the Beginning and score again.
Developing stages. These figures signify that there is Looking into the least-mastered contents of
difficulty among students on mastering the content the Grade 8 students according to the results of their
areas because they differ slightly from each other. MAT in Figure 2, the number of least-mastered and
Summarizing the level of achievement of the most-mastered contents for the three areas was of
Grade 8 students in the overall MAT, they are only at equal degree. Overall, 50% of the contents were
the Beginning level of achievement (74.08%). This mostmastered (got a 60% and above correct response)
means that students struggle with their while the remaining 50% were least-mastered (got
understanding; pre-requisite and fundamental lower than 60% correct response). When analyzed per
knowledge and/or skills have not been acquired or area, Patterns and Algebra has the most number of
developed adequately to aid understanding. least-mastered contents, with 11 out of 17 (64.71%)
contents falling below the mastery level. Geometry
Table 2. Mean score, standard deviation, and level of achievement of
the Grade 8 students in the MAT (𝑵=𝟐𝟕𝟗)
meanwhile got the least, with only 2 out of 9 (22.22%)
MAT MAT Level of
content considered as least-mastered. Number of
Content Area Mean Standard Achievement least-mastered and most-mastered content areas for
Score Deviation the Statistics and Probability is on a 50:50 ratio.
Patterns and Algebra 72.73% 7.73 Beginning Noteworthy to mention, the extremities of the
Geometry 78.92% 8.50 Developing result appear that the most mastered content is the
Statistics and Probability 75.38% 9.77 Developing “Rectangular Coordinate System” (91.04%) under the
umbrella of the Patterns and Algebra area. On the
Overall 74.08% 7.29 Beginning other hand, the content “Quadrilaterals that are
Parallelograms” of the Geometry area was
When results for both FTs and MAT are leastmastered of all (21.15%).
compared, it is clear that results during regular The results were quite alarming because of
classroom works and quizzes (FTs) may not be the low results in students’ achievement and
reciprocal with that of the the summative test (MAT). mastery. As Biggs (1996) presented in his Principle of
As shown in Table 1, Patterns and Algebra was Alignment, if expectations were unmet, there might
highest. However, when the result of the MAT is be misalignment among Objectives,
investigated, it was ranked lowest. The remaining two Instruction, and Assessment.
content areas—Geometry and Statistics and
Probability—both yielded below passing results in the
formative tests but turned out positive in the
summative.
Formative tests are, in nature, easier than
summative tests simply because lessons are still fresh
from students’ memories and teacher’s guidance is
LLI-II-020 4
Proceedings of the DLSU Research Congress Vol. 3 2015
Presented at the DLSU Research Congress 2015
De La Salle University, Manila, Philippines
March 2-4, 2015
Figure 2. Percentage of correct responses in each of the tested contents
The planned curriculum objectives discussed least-mastered contents, Quadrilaterals
(Objectives) and the instructional objectives that are Parallelograms became leastmastered of all.
(Instruction) were compared. The basis of the planned The misconception and/or difficulty of the
curriculum objectives are the objectives stated in the students in answering some questions in the
Curriculum Guide prepared by the Grade 8 Mathematics Achievement Test (MAT) were also
Mathematics Teachers during the start of the School probed. The teachers’ previous encounter of students'
Year. On the other hand, the instructional objectives common mistakes in their problem solving was the
are based on the objectives stated in the Instructional basis for the construction of the distractors. Thus, the
Plans drafted by the Grade 8 Mathematics Teachers misconceptions and/or difficulties were already
and are implemented weekly. preempted by the teachers. The analysis of the
Upon comparing Objectives to the misconceptions was also validated by two experts in
Instruction, there were discrepancies between them the field of Mathematics Teaching.
on the seven contents namely, Rational Algebraic When the incorrect responses of the students
Expressions; Slope of a Line; (Solving Systems of in some of the least-mastered contents were examined,
Linear Inequalities; Properties of Parallelograms and it could be noted that misconceptions and difficulties
their Special Type; Quadrilaterals that are vary in many forms. In most cases, especially in the
Parallelograms; Measures of Variation; and items for Patterns and Algebra and Geometry, what is
Experimental/Theoretical Probability. common is that they were just missing to completely
If there were discrepancies in any of the three solve the problem but they were correctly doing the
components, there will be imbalance in the system. procedure. This shows that the expected students’
This had been evident in the results of the attitude of rechecking their answer to the problems is
Mathematics Achievement Test (MAT). The 7 contents not evident.
which were said to have discrepancies between the In some other cases for Patterns and Algebra
Objectives and the Instruction were also part of the 15 and Statistics and Probability, students were
least-mastered contents of the MAT. incorrectly applying the formulas, properties,
Noteworthy to mention, the 3 contents, theorems, and/or laws. This is evident in the items
namely, Solving Systems of Linear Inequalities; about Integral Exponents, Rational Algebraic
Quadrilaterals that are Parallelograms; and Expressions, Equation of a Line, and Experimental
Experimental/Theoretical Probability, had completely and Theoretical Probability.
dissimilar planned curriculum objectives and In terms of the nature of assessment, test
instructional objectives. Looking into the previously
LLI-II-020 5
Proceedings of the DLSU Research Congress Vol. 3 2015
Presented at the DLSU Research Congress 2015
De La Salle University, Manila, Philippines
March 2-4, 2015
items’ distractor which was answered more than the objectives. Finally, the assessment tasks must address
correct answer shows only that these are good the objectives so that one can identify if the students
distractors. However, many students were answering have learned what was intended for them to learn.
an incorrect distractor. It only reflects that they are To sum up, whatever objective is stated, it
not critical problem solvers. It could really be should be realized during instruction. Consequently,
reiterated that the root cause of misconceptions is the assessment method should be according to how a
retention of skills learned during instruction as the specific mathematical problem is taught and should be
Objectives and the Instruction are misaligned. according to the stated objective. Teachers must not
change the Planned Curriculum Objectives as this will
be the basis for assessment.
Thus, as a general action in the next school
4. CONCLUSIONS years, the following are recommended:
1. Don Bosco Technical Institute – Makati should
Based on the findings of the study, the already include the misses in the past instruction
researcher derived the following conclusions: 1. The to the next Curriculum Planning, on the following
results of the formative tests and the Mathematics contents, Rational Algebraic Expressions; Slope of
Achievement Test (MAT) showed that students’ a Line; Solving Systems of Linear Inequalities;
achievement is in the Beginning and in the Properties of Parallelograms and their Special
Developing level for the three content areas of the Type; Quadrilaterals that are Parallelograms;
Grade 8 Mathematics curriculum. These imply that Measures of Variation; and
they struggle with their understanding or possess Experimental/Theoretical Probability.
only the minimum knowledge and skills and core 2. The Subject Coordinator should ensure the
understandings; pre-requisite and fundamental alignment among the K to 12 Mathematics
knowledge and/or skills have not been acquired or Competencies provided by DepEd to the stated
developed adequately to aid understanding. instructional objectives of the teachers in their
2. Most of the least-mastered contents of the Instructional Plan and to the constructed
Mathematics Achievement Test were because of assessment tool being administered to the
the non-alignment between the Objectives and students.
the Instruction. There was an imbalance in the
system that led to poor surface learning. The The following strategies are also
non-alignment signified inconsistencies, unmet recommended according to stating learning objectives,
expectations, and practices that contradict what developing teaching and learning activities, and
is preached. constructing assessment methods (Entwistle & Tait,
3. In terms of the nature of assessment, test items’ 1990; Trigwell & Prosser, 1991; De Winstanley &
distractor which was answered more than the Bjork, 2002; Lizzio et al., 2002; Newmaster, et al.,
correct answer shows only that these are good 2006; Weiman, 2007; Kember, et.al., 2008; Revell &
distractors. However, many students were Wainwright, 2009).
answering an incorrect distractor. It only reflects
that they are not critical problem solvers to be Stating Objectives Developing Constructing
able discern the correct answer. Furthermore, Instruction Assessment
the root cause of misconceptions is retention of
skills learned during instruction.
5. RECOMMENDED ACTIONS
In order to address the low performance of the
Grade 8 students in K to 12 Mathematics, firstly, the
objectives must be clearly stated in a manner that the
level of understanding is properly defined and not
simply a list of topics to be covered. Secondly, the
instruction or the teaching and learning tasks chosen
must be those that are likely to realize the stated
LLI-II-020 6
Proceedings of the DLSU Research Congress Vol. 3 2015
Presented at the DLSU Research Congress 2015
De La Salle University, Manila, Philippines
March 2-4, 2015
• Establish and • Conduct review • Provide
communicate clear classes for opportunities to Department of Education. (2012). Retrieved June 12,
learning objectives mastery and receive frequent
throughout the retention Provide feedback and to 2014, from Official Gazette: http://www.gov.ph/k-
course opportunities for scaffold learning 12/#about
• Establish and peer interaction • Identify the
communicate clear and discussion prior knowledge
standards for • Repeat and space of the students Department of Education. (2013). K to 12 Curriculum
performance (e.g. key information before learning Guide (Mathematics). Pasig City: Department of
rubrics and within and the new concept
grading between lectures through Education.
guidelines) • Vary and diagnostic
• Provide structure teaching
opportunities for learning • Use the Entwistle, N., & Tait, H. (1990). Approaches to
independence and activities to focus information on learning, evaluations of teaching, and
choice in learning attention students’
preferences for contrasting academic
content and • Model each step formative
process in the process of mathematics environments. Higher Education, 19, 169-194.
reaching the performance to
solution to a identify what
George, D., & Mallery, P. (2003). SPSS for Windows
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strategies they teaching should
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problem solving whether to importance of establishing relevance in
Discuss the proceed to the
common next lesson motivating student learning. Active Learning in
misconceptions of Higher Education, 9 (3), 249-263.
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when solving a
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students’ perceptions of the learning
environment and academic outcomes:
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Presented at the DLSU Research Congress 2015
De La Salle University, Manila, Philippines
March 2-4, 2015
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