The Role of Assessment in Mathematics Classrooms: A Review

Abstract

This paper tries to understand the role of assessment in bringing changes in students’ mathematics performance. Quality assessment is a key factor in improving the learning of mathematics. The relationship between learning and assessment is strong and robust. Students learn more in classes where assessment is an integral part of instruction than in those that are not, and brief frequent assessments that provide immediate feedback about learning progress that are more effective than one summative test. Therefore, mathematics teachers should be aware of the roles of assessment, different methods of assessing learners, and the effective assessment practices.

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International Journal of Advanced Research, Volume 5, Issue 1, 2022
Article DOI: https://doi.org/10.37284/ijar.5.1.887
156 | This work is licensed under a Creative Commons Attribution 4.0 International License
International Journal of Advanced Research
ijar.eanso.org
Volume 5, Issue 1, 2022
Print ISSN: 2707-7802 | Online ISSN: 2707-7810
Title DOI: https://doi.org/10.37284/2707-7810
EAST AFRICAN
NATURE &
SCIENCE
ORGANIZATION
Original Article
The Role of Assessment in Mathematics Classrooms: A Review
Dr. Mbuthia Ngunjiri, PhD1*
1 Laikipia University, P. O. Box 1100-20300 Nyahururu, Kenya
* Author for Correspondence ORCID ID: https://orcid.org/0000-0002-4047-0950; Email: mbuthiangunjiri@gmail.com.
Article DOI: https://doi.org/10.37284/ijar.5.1.887
Publication Date:
14 October 2022
Keywords:
Assessment,
Evaluation,
Measurements,
Test.
ABSTRACT
This paper tries to understand the role of assessment in bringing changes
in students’ mathematics performance. Quality assessment is a key factor
in improving the learning of mathematics. The relationship between
learning and assessment is strong and robust. Students learn more in
classes where assessment is an integral part of instruction than in those
that are not, and brief frequent assessments that provide immediate
feedback about learning progress that are more effective than one
summative test. Therefore, mathematics teachers should be aware of the
roles of assessment, different methods of assessing learners, and the
effective assessment practices.
APA CITATION
Ngunjiri, M. (2022). The Role of Assessment in Mathematics Classrooms: A Review. International Journal of Advanced
Research, 5(1), 156-160. https://doi.org/10.37284/ijar.5.1.887
CHICAGO CITATION
Ngunjiri, Mbuthia. 2022. “The Role of Assessment in Mathematics Classrooms: A Review.” International Journal of
Advanced Research 5 (1), 156-160. https://doi.org/10.37284/ijar.5.1.887.
HARVARD CITATION
Ngunjiri, M. (2022) “The Role of Assessment in Mathematics Classrooms: A Review.”, International Journal of Advanced
Research, 5(1), pp. 156-160. doi: 10.37284/ijar.5.1.887.
IEEE CITATION
M. Ngunjiri, “The Role of Assessment in Mathematics Classrooms: A Review.”, IJAR, vol. 5, no. 1, pp. 156-160, Oct.
2022.
MLA CITATION
Ngunjiri, Mbuthia. “The Role of Assessment in Mathematics Classrooms: A Review.”. International Journal of Advanced
Research, Vol. 5, no. 1, Oct. 2022, pp. 156-160, doi:10.37284/ijar.5.1.887.
INTRODUCTION
In the field of education, the terms of
measurement, assessment, and evaluation have
been used interchangeably, sometimes causing
confusion to many users of the terms. In this paper
the meaning of the terms is clearly explained.
First, measurement is the process of assigning
numerical values to objects and events according
to predetermined values (Kithuka, 2012). The
information required is in precise quantities, for
example in meters, kilogrammes, marks and so
on. Measuring is done using measuring
instruments, and a test is therefore an instrument

International Journal of Advanced Research, Volume 5, Issue 1, 2022
Article DOI: https://doi.org/10.37284/ijar.5.1.887
157 | This work is licensed under a Creative Commons Attribution 4.0 International License
for measuring students’ performance using a
percentage scale (Black & William, 2008).
Second, evaluation is the process of collecting
qualitative and/or quantitative information,
analysing the information, and presenting it in a
form that facilitates judgment or decision making
(Twoli et al., 2007). Third, assessment include all
the processes involved in making decisions about
students’ learning progress (Airasian, 2000). It
includes observations of students’ written work,
their answers to questions in class, and
performance in teacher made and standardized
tests. It also involves decisions such as re-teaching
a topic or assigning grades.
Two basic processes are involved in
assessment:(i) measurement (i.e., the process of
gathering information about learning), and(ii)
evaluation (i.e., the process of making decisions
on the basis of measurements). Assessment can
either be informal or formal assessment (MoEST,
2012). As a mathematical teacher, you constantly
carry out informal assessment. This could be
through listening to students’ explanations,
demonstrations, or deliberate questioning. The
characteristics of informal assessment is that it is;
(i) ongoing to support students learning, (ii)
diagnostic so that it highlights difficulties which a
teacher can address. In contrast, formal
assessment is; (i) timed, (ii) marked and graded,
(iii) emphasizes individual work, and (iv) has
internal and external invigilators (MoEST, 2012).
The following literature focuses on functions of
classroom mathematics assessment, different
methods of assessment and the effective
assessment practices
REVIEW OF LITERATURE
Assessment is an important part of mathematics
teaching and learning (Kiruhi et al., 2009). One
assumption is that assessment serves only a single
purpose: to help teachers make grading decisions.
But, assessment has much wider functions, at least
eight of which are considered briefly at this point.
First, assessment can be used to inform
mathematics learners of their attainment.
Knowledge of results is one of the cornerstones of
learning theory. Knowing whether one has
attained a goal, or by how much it has been missed
or exceeded has been shown to be an important
incentive in human performance, especially when
results of results quickly follow performance
(Ngunjiri, 2022; Pratt, 1980). Second, assessment
can be used to diagnose areas of strengths and
weaknesses in mathematics (Ngunjiri, 2022; Pratt,
1980). It is not enough for the mathematics
teacher to indicate that the student has “passed” or
“failed”. But both the mathematics teacher and the
learner must know areas of strengths and
weaknesses if remediation is to be effective.
Third, assessment can be used to guide decisions
about the student’s future (Ngunjiri, 2022; Pratt,
1980). Adequate academic and career guidance
must be based on sound data about the learners’
aptitudes, interests, and attainments. At some
point, decisions will be made to include some
aspirants, and to exclude others from certain
courses, programs, and careers especially those
that require mathematics as a prerequisite. Such
decisions are made by educators, students, or
other parties based on valid assessment of
achievement data.
Fourth, assessment can be used to inform
interested parties of student competence
(Ngunjiri, 2022; Pratt, 1980). Parents have a right
to know what their children have learnt at school
including in mathematics. Employers have to
know what capability potential employees have
acquired. Tax payers are entitled to know what
effects schools they are supporting are imparting
on students.
Fifth, assessment maybe used to provide feedback
to the instructional system (Nicol & Mcfarlane-
Dick, 2006). Any effective teaching of
mathematics can achieve its potential only if the
results of teaching and learning are monitored and
corrective and active actions by mathematics
teachers taken where necessary (Ngunjiri, 2022).
Sixth, assessment in mathematics can be used to
provide an operational target to the learner
(Ngunjiri, 2022; Pratt, 1980). In practice, students
set a target for themselves like wanting to get a
good grade in mathematics, and the target directs
the students’ effort in the subject. Seventh,
assessment can be used to license candidates for a
profession or occupation (Ngunjiri, 2022; Pratt,
1980). For example, engineers, accountants,
pilots, surveyors must pass professional
examinations to be allowed to practice. These
careers among others require a strong background
of mathematics.
Eighth, assessment in mathematics can help to
promote minimum educational equality (Ngunjiri,
2022; Pratt, 1980). Differences in mathematics

International Journal of Advanced Research, Volume 5, Issue 1, 2022
Article DOI: https://doi.org/10.37284/ijar.5.1.887
158 | This work is licensed under a Creative Commons Attribution 4.0 International License
performance will always exist in different schools
and different classrooms. In the absence of
achievement data, the extent of such differences
will not be recognized for securing equality of
minimal educational opportunities such as fair
provision of qualified teachers and other needed
resources for good performance in various
subjects including mathematics.
The purpose and level of assessment will
determine the type of assessment a mathematics
teacher will carry out. The various methods of
assessing learners include: (i) oral assessment, (ii)
observation of learners, (iii) written assessment,
(iv) projects. Oral assessment is when the teacher
asks questions and the students respond (Hattie &
Timperley, 2007). As each student responds to the
questions, the mathematics teacher may record
their score. This will give the total score of each
student in relation to their responses (KIE, 2010;
Mwangi, 2009). Oral questioning is directly
aimed at the processing of information or learning
processes, requiring understanding or completing
the tasks (Hattie & Timperley, 2007).
Assessment through observation occurs when the
mathematics teacher observes students as they
carry out given tasks (MoEST, 2012; Mwangi,
2009). The subject teacher can observe the learner
in various situations, note his/her attitudes,
feelings, interests, changes in behaviour patterns,
and relationship between classmates (Mwaka et
al., 2014). Written assessment include: (i)
assignments, (ii) subjective tests, (iii) objective
tests, and (iv) Projects (MoEST, 2012). The
assignment is an integral part of learning
mathematics (Nacico-Brown et al., 1994 ). The
way in which students complete their assignment
or homework is a measure of their attitude
towards the subject. The assignment is valuable
not only to the learner, but also the mathematics
teacher as it helps to evaluate a learner’s overall
behaviour (MoEST, 2012).
Subjective tests include essay tests. They require
the learner to read the question, think and organize
ideas (Nacico-Brown et al., 1994). This type of
test is used in measuring student’s ability to
organize, interpret, evaluate, and apply
knowledge. Items such as “prove that” or “show
that” in mathematics are examples of essay type
of testing
Objective tests are written tests with items which
require short answers. They fall into four main
categories, namely: (i) multiple choice questions,
(ii) true/false questions, (iii) Matching type
questions, and (iv) completion type questions
(Eggen & Kauchak, 2004; MoEST, 2012;
Mwangi 2009). Multiple choice format is a
measurement format that consists of a question or
statement called a stem and a series of answer
choices called distractors. The learner responds to
the items by choosing the correct or best answer
(Eggen & Kauchak, 2004). An example is: If 3x +
7= 13, then x equals: (a)10, (b)21, (c) 7, (d) 3.
True or false questions comprises a statement
which is true or false (Eggen & Kauchak, 2014;
Linn & Gronlund, 2000; Nacico-Brown et al.,
1994). They usually measure lower- order
outcomes (Linn & Grownland, 2000), and an
example is: The square root of 4900 = 70 (T/F).
Matching type questions comprise a statement
called a stem followed by a set of items to the left-
hand side and responses to the right-hand side,
both listed vertically. Students are required the
match the given items to the listed responses
(Eggen & Kauchak, 2014; MoEST, 2012; Nacico-
Brown et al., 1994. An example is: Match the
figures (i.e., pentagon, triangle, trapezium) listed
vertically on the left-hand side to their correct
number of sides (i.e., 4,5,30 listed vertically on the
right-hand side.
Completion type of questions consist of a
statement with a missing word or number ((Eggen
& Kauchak, 2014; MoEST, 2012; Nacico-Brown
et al., 1994). Students are required to complete the
statements by filling the missing word or number.
For example; The square root of 81 is____. In
mathematics, the subject teacher can also use
projects to assess learners (MoEST, 2012). The
teacher can give projects individually or in groups
and they can be short or long term. There are
projects which are carried out in the classroom,
and these include: (i) making learning aids or (ii)
investigating patterns and relationships. Out of
classroom projects include: (i) collecting and
analysing data, and (ii) collecting learning aids
from the environment (MoEST, 2012).
Lastly, experts in measurement and evaluation
recommend that teachers use four principles to
design effective assignment practices. These are:
(i) plan tests systematically using a table of
specification (Campbell & Evans, 2000). The
table demands that the teacher should assess
learning objectives (i.e., knowledge,
comprehension, application, analysis, synthesis,
and evaluation) against the content areas in the

International Journal of Advanced Research, Volume 5, Issue 1, 2022
Article DOI: https://doi.org/10.37284/ijar.5.1.887
159 | This work is licensed under a Creative Commons Attribution 4.0 International License
test, (ii) the teacher should prepare students for
assessments, for example, teaching test-taking
strategies (Eggen & Kauchak, 2014). They
include: (a) using test-time efficiently by pacing
oneself, (b) reading instruction carefully, (c)
identifying important information in questions,
(d) understanding the demands of different testing
formats, and (e) finding out how questions will be
scored. To be effective, these strategies should be
emphasized through the school years (Eggen &
Kauchak, 2014). (iii) The teacher should
administer tests and quizzes under optimal
conditions to maximize students’ performance.
For example, keeping students informed about the
amount of time remaining during a test, and (iv)
the teacher should analyse test results and give
immediate feedback. Research supports the
benefits of individual feedback on tests. Students
who receive positive comments or encouraging
words on test outcomes do better on subsequent
work (Page, 1992). Moreover, the effects of short
personalized comments (e.g., good, can do better)
justify extra efforts involved in future work in
mathematics.
CONCLUSION
It is important for students to know how they
doing as they learn. This is because knowledge of
current understanding gives students a source of
awareness of their achievement which may
motivate them to learn more. Thus, it is absolutely
essential for mathematics teachers to assess
students’ learning and give them immediate
feedback (Anderson, 1993). Furthermore,
assessment should be given to students as
frequently as possible using oral tests,
observation, written tests, and projects where
possible and feedback given accordingly (Gore,
2000). Mathematics teachers should also be aware
of the functions of assessment in the mathematics
classroom as seen in this paper. These are;
informing students of their attainment, diagnosing
areas of strengths and weaknesses, guiding the
student’s future, informing the interested parties
of student competence, providing feedback to
instruction, providing an operational target to the
learner, licensing candidates for a profession, and
provision of equal educational opportunities. In
all, effective assessments are congruent with goals
and instructions, and effective teachers
communicate what will be covered in
assessments, allow students to practice on items
similar to those that will be on tests, teach test-
making skills, and give positive comments for
student performance (Gore, 2000).
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Article DOI: https://doi.org/10.37284/ijar.5.1.887
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