MODULE 5

EVALUATING MATHEMATICS
ASSESSMENTS
 Lesson 1. The
Content Principle
 Applying the content principle to a
mathematics assessment means judging
how well it reflects the mathematics that is
most important for students to learn. The
judgments are similar to early notions of
content validity that were limited to asking
about the representativeness and
relevance of test content. The difference
lies in a greater concern today for the
quality of the mathematics reflected in the
assessment tasks and in the responses to
them.
New issues arise when the content
principle is applied:
The nature of the important
mathematics content leads to some
types of tasks that have not been
common in educational assessment.
New issues arise when the content
principle is applied:
The emphasis on thinking processes
leads to new forms of student
performance.
New issues arise when the content
principle is applied:
The characteristics of today's
important mathematics lead to a
broader view of curricular relevance.
 According to the Content Principle,
instructional materials should be
relevant, meaningful, and engaging to
learners. They should be designed in a
way that facilitates the acquisition and
retention of knowledge or skills.
Content should be organized logically,
presented clearly, and scaffolded
appropriately to support learners'
understanding and progression.
CONTENT OF TASKS
 Because mathematics has been
stereotyped as cut and dried, some
assessment designers have assumed
that creating high-quality
mathematics tasks is simple and
straightforward. That assumption is
false. Because mathematics relies on
precise reasoning, errors easily creep
into the words, figures, and symbols in
which assessment tasks are expressed.
The content of tasks encompasses various
elements, including:
Learning Objectives: Tasks should
align with the stated learning
objectives or outcomes. These
objectives specify what students
should be able to know or do after
completing the tasks.
The content of tasks encompasses various
elements, including:
Learning Objectives: Tasks should
align with the stated learning
objectives or outcomes. These
objectives specify what students
should be able to know or do after
completing the tasks.
The content of tasks encompasses various
elements, including:
Relevance: Tasks should be
relevant to the subject matter being
taught and meaningful to the
learners. When tasks are meaningful,
students are more likely to engage
with the content and retain what
they learn.
The content of tasks encompasses various
elements, including:
Complexity: Tasks should be
appropriately challenging for the
learners' skill level. They should offer
opportunities for students to apply
and extend their understanding of
the content.
The content of tasks encompasses various
elements, including:
Variety: Tasks should incorporate a
variety of formats and activities to
accommodate different learning
styles and preferences. This may
include readings, discussions,
hands-on activities, projects, etc.
The content of tasks encompasses various
elements, including:
Feedback: Tasks should provide
opportunities for feedback, allowing
students to assess their understanding
and receive guidance on areas for
improvement.
The content of tasks encompasses various
elements, including:
Authenticity: Whenever possible, tasks
should simulate real-world situations or
problems relevant to the subject matter.
This enhances the authenticity of the
learning experience and promotes
transfer of knowledge and skills to
practical contexts.
The content of tasks encompasses various
elements, including:
Progression: Tasks should be
sequenced in a logical order,
building upon prior knowledge and
skills. This ensures a coherent and
scaffolded learning experience.
 Lesson 2. The
Learning Principle
Understanding Learners:
Recognizing the diverse
backgrounds, experiences, and
learning styles of students is crucial.
Instructional materials should be
tailored to accommodate these
differences and promote inclusive
learning environments.
Active Engagement:
Encouraging active engagement in
the learning process is key to promoting
deeper understanding and retention of
information. Activities and tasks should
be designed to actively involve learners,
such as through discussions,
problem-solving exercises, and
hands-on activities.
Meaningful Learning:
Meaningful Learning: Facilitating
meaningful learning involves helping
students make connections between new
information and their existing knowledge
and experiences. Instructional materials
should be designed to promote conceptual
understanding rather than rote
memorization.
Feedback and Assessment:
Providing timely and constructive
feedback is essential for supporting
student learning and growth.
Assessment methods should align
with the learning objectives and
provide opportunities for students to
demonstrate their understanding.
Metacognition:
Promoting metacognitive skills,
such as self-monitoring and
self-regulation, can help students
become more effective learners.
Instructional materials should
encourage reflection on learning
processes and strategies.
Transfer of Learning:
Helping students transfer their
learning to new contexts and
situations is an important goal of
instruction. Instructional materials
should include opportunities for
students to apply their knowledge
and skills in different contexts.
IMPROVED LEARNING
Student engagement in assessment
tasks should be judged through
various types of evidence, including
teacher reports, student reports, and
observations.
EFFECTS ON THE
EDUCATIONAL
SYSTEM
 Recent proposals for assessment reform
and for some type of national examination
system contend that new forms of
assessment will promote improvements in
education. The report Raising Standards for
Education claims that high national
standards and a system of assessment are
needed because "in the absence of
well-defined and demanding standards,
education has gravitated toward de facto
national minimum expectations."
Systemic validity
Refers to the curricular and
instructional changes induced in the
educational system by an assessment.
Evaluating systemic effects thoroughly is
a massive undertaking, and there are
few extant examples in assessment
practice.
Curricular Effects
A comprehensive evaluation of the
consequences of any assessment
system would include evidence about
the impact of the assessments on the
curriculum. Influences on curriculum
include changes in the way instructional
time is allocated and in the nature of
the assignments given students.
Outside Effects
Assessments such as the Scholastic
Assessment Test (SAT) and the Advanced
Placement (AP) test are undergoing
fundamental change with widespread
impact. The use of calculators on the
calculus AP exam, for example, is having a
profound effect on many high school
teachers and way they use technology in
their classrooms.
QUESTION?