1. ENHANCING ACADEMIC PERFORMANCE AND POSITIVE ATTITUDE OF
STUDENTS IN MATHEMATICS WITH ALTERNATIVE ASSESSMENT
By
Godfred, Kwame Abledu - Koforidua Polytechnic
godfredabledu@yahoo.com
Introduction
The purpose and scope of formal education have undergone various changes over
the years since the time of the Castle schools. Consequently, assessment has also
undergone a massive reform. This has led to a wider range of assessment now than there
was twenty-five years ago (Gipps, 1994). Evidence has shown that educational systems
have undergone assessment reforms, which are coincident with curriculum reforms
(Nitko, 1995). A number of assessment methods have been applied in the Ghanaian
educational system since the introduction of schooling in the country (MOE, 1987).
The educational reform in Ghana began with the hope that learning was to be
more practical and examinations should be based on practical oriented syllabus. What
had emerged was that the cost and difficulties involved in assessing students’ practical
work and the unreliability of teachers’ assessment had resulted in a return to the status
quo, that is pen and paper tests.
Currently, Ghanaian teachers tend to monitor students’ understanding through
pen-and-paper tests and exercises in class, and move through the syllabus and textbook
with little or no attempt to use new instructional strategies if students do not understand
the material. The use of pen-and-paper tests has been used almost exclusively by schools
to monitor students’ achievement. These tools have also dominated examination for the
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2. professional certification of teacher and college admission. These strategies of assessing
students have come under severe criticism by many educators (Wolf, 19891).
The perception that much of what gets tested is not relevant or has not been taught
to students has been a source of concern to many educators and parents. Such concerns
have made educators direct their attention to a new approach to testing variously
described as “performance assessment”, “authentic assessment”, portfolio assessment”,
and “alternative assessment” (Winzer, 1992).
The Curriculum and Evaluation Standards for School Mathematics (NCTM,
1989) call for significant change in the way mathematics is taught. In conjunction with
this demand for change in mathematics instruction, a change format for assessing
students is needed. To document these new expressions of teaching and learning,
alternative assessments have emerged as the vehicle by which students and teachers can
organise, manage and analyse life inside and outside the school.
One of the most exciting and liberating things about the current interest in
assessment is the recognition that numerous assessment tools are available to schools,
districts, and states that are developing new assessment systems. These tools range from
standardized fixed-response tests to alternatives such as performance assessment,
exhibitions, portfolios, and observation scales. However, in Ghana, alternative
assessment is relatively an unknown concept and only few researches have been
conducted in this area.
Each type of assessment brings with it different strengths and weaknesses to the
problem of fair and equitable assessment. Recognizing the complexity of understanding
performance or success for individuals, it is virtually impossible that any single tool will
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3. do the job of fairly assessing student performance. Instead, the National Center for
Research on Evaluation, Standards, and Student Testing (1996) suggests that an
assessment system made up of multiple assessments (including norm-referenced or
criterion-referenced assessments, alternative assessments, and classroom assessments)
can produce "comprehensive, credible, dependable information upon which important
decisions can be made about students, schools, districts, or states."
Since the influence of testing on curriculum and instruction is now widely
acknowledged, educators, policymakers, and others are turning to alternative assessment
methods as a tool for educational reform. The movement away from traditional, multiple-
choice tests to alternative assessments, variously called authentic assessment or
performance assessment, has included a wide variety of strategies such as open-ended
questions, exhibits, demonstrations, hands-on execution of experiments, computer
simulations, writing in many disciplines, and portfolios of student work over time.
These terms and assessment strategies have led the quest for more meaningful
assessments which better capture the significant outcomes we want students to achieve
and better match the kinds of tasks which they will need to accomplish in order to assure
their future success.
Billions of dollars are spent each year on education, yet there is widespread
dissatisfaction with our educational system among educators, parents, policymakers, and
the business community. Efforts to reform and restructure schools have focused attention
on the role of assessment in school improvement.
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4. After years of increases in the quantity of formalized testing and the consequences
of poor test scores, many educators have begun to strongly criticize the measures used to
monitor student performance and evaluate programs. They claim that traditional
measures fail to assess significant learning outcomes and thereby undermine curriculum,
instruction, and policy decisions.
The way in which students are assessed fundamentally affects their learning.
Good assessment practice is designed to ensure that, in order to pass the module or
programme, students have to demonstrate they have achieved the intended learning
outcomes. To test a wide range of intended learning outcomes, diversity of assessment
practice between and within different subjects is to be expected and welcomed, requiring
and enabling students to demonstrate their capabilities and achievements within each
module or programme.
The aim of this paper is to provide a guide to the range of alternative assessment
tools available, to discuss the potential benefits and difficulties in using the approach and
suggest a process for its use.
Alternative Assessment
Alternative assessment is a generic term referring to the new forms of assessment
(Winzer, 1992). It includes a variety of instruments that can be adapted to varying
situations. The teacher and the students can collaboratively decide which procedures are
to be used for assessment (Huerta - Macias 1995). Individual students are also often
given the responsibility of selecting specific products of their work on which they will be
assessed. It provides the students with the opportunity to reflect on his/her learning
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5. experience, pointing out what he/she understands, and the factors that contribute to
his/her lack of understanding.
The main goal of alternative assessment is to gather evidence about how students
are approaching, processing, and completing “real-life” tasks in a particular domain
(Garcia and Pearson, 1994). Alternative assessment may include interviews with
students, journal writing by students, developing portfolios of students’ work and writing
of reflections. Also, students are encouraged to engage in small co-operative group
learning and may be assessed individually and jointly.
Alternative assessment, most importantly, provides alternative to traditional
assessment in that it;
i. does not intrude on regular classroom activities;
ii. provides multiple indices that can be used to gauge students
progress; and
iii. provides information on the strengths and weaknesses of each
individual student (Huerta-Macias, 1995; p. 9)
One of the major advantages of alternative assessment as a tool for assessing
students is that it empowers students to become partners and decision makers in their
learning (Smolen et al 1995). Curran (1997) in his study with middle level educators
found that alternative assessment is most valuable for students’ involvement in meta-
cognitive learning. Vlaskamp (1995) found that alternative assessment processes engage
students to become active in learning. The processes offer them opportunities for
reflection and to be thoughtful respondents and judges of their own learning. Lee (1996)
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6. found that the real value of alternative assessment is an information source for teachers
and a learning tool for the students.
Alternative assessment includes a variety of instruments that can be adapted to
varying situations. These instruments include the use of checklist of students’ behaviour
or product, journals, reading log, videos of role plays, audio tape of discussions, self
evaluation, questionnaire, work samples and teacher observation of anecdotal records
(Huerta-Macias, 1995, p.12). According to her, the teacher or instructor and students can
collaboratively decide which procedures are to be used for assessment in a given class.
Individual students are also given the responsibility of selecting specific products of their
work on which they will be assessed.
Portfolio Assessment
The concept of portfolio assessment comes from the field of fine arts in which
portfolios are used to demonstrate the depth and breath of an artist’s talents and
capabilities. A portfolio is a systematic, well organised collection of evidence used to
monitor the growth of a student’s knowledge, skills and attitudes (Bonnestetter, 1994). It
is a purposeful collection of students work that exhibits to the students and others the
student’s efforts, progress or achievement in (a) given area(s) (Reckase 1995).
This collection according to them should include:
 Student participation in selection of portfolio contents
 The criteria for selection, and evidence of student self-reflection (p.12)
To fulfil the purpose of portfolio assessment as a methodology based on multiple
measures and high content validity, the portfolio is to be composed of materials that
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7. should be selected jointly by the student and the teacher to reflect the students' work over
the entire schooling period. All work are to be taken directly from the classroom
activities.
To help the students select materials for the portfolio, a set of guidelines should
be made available to the students. The guidelines include how the content of the
portfolio is to be selected and the criteria that would be used to assess the portfolios.
The contents of the students’ portfolios are to include the following:
i. individual assignments (homework and tests);
ii. group assignments;
iii. self reflection on each selected student or group work
iv. group reflection on group work.
The reflections are to indicate evidence of learning mathematics in the school,
what they know and can do. They are also to explain what they have understood and the
action that contributes to their understanding. They are to identify what they still do not
understand and explain the cause of their lack of understanding and what they can do to
change the situation.
Journal
A journal is a daily or weekly record of occurrences, experiences or observations
(Berenson and Carter, 1995). Journal writing by students can be used to record the daily
and weekly mathematics learning experiences and the attitude of students towards
mathematics. The journal can be used to keep track of the students’ progress in
mathematics and to gain insight into the understanding and misunderstanding of the
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8. student. The journal can also be used to document the student's attitudinal changes during
the project.
Students are asked to write three sets of journals in each semester (term). The
first one is to be written during the first week of the semester (term), the second in the
fourth week and the third journal in the last week of the semester (term).
At the beginning of the semester(term), the students should be asked to write
journals to indicate their previous and current feelings about mathematics. They are also
to assess their strengths and weaknesses in mathematics, pointing out the factors that
contributed to their failure or success and describe what they need to do.
During the fourth week of the semester, the students would be asked again to
write journals to identify ideas they understood easily during discussions with the teacher
or their colleagues, and then explain why it was easy for them to understand such ideas.
They are to identify ideas, which are still difficult for them to understand, and explain
why they thnk they are having such difficulties in comprehending these ideas. They are
to comment on a homework or class test they did, and explain why they thought they did
well or did not do well. They are to identify aspects of their work that needed
improvement. They are also to explain what they learned from doing homework or
taking a test and state what they would do differently if they are to do the homework or
take the test again.
During the last week of the semester(term), students are to write another journal.
They should be asked to express their feelings of the test, classwork, homework etc, and
their feeling about mathematics. They are to state whether there is any improvement in
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9. their learning or understanding of mathematics, and identify things, which contribute to
their understanding or lack of understanding.
Journal writing can be used as means of regularly focusing on course progress and
possible modifications. The journals are the first step in placing the responsibility for
learning with the students. Research had found that the journal was an important
diagnostic tool in three important ways.
First, as a writing sample, it provided information about students’ strengths and
weaknesses in mathematics. Second, the journals gave an indication of how the students
perceived themselves, and finally, the journals revealed students’ perceptions of the
mathematics learning process.
The journal the students write will help teachers to know early in the course how
students perceived themselves as mathematics learners and how they understood the
learning process entailed. Whenever their work was seen, evaluations were made which
either corroborated their assessment or highlighted their misconceptions. With this
information, the students will be helped to become better more efficient learners. When
misconceptions are discovered, students will be helped to establish realistic expectations
about what mathematics skills they need to achieve their goals. In fact, the first journal
they write is an important point of reference when working with individual students and
helping them to identify their objectives during the learning process.
Research findings show that journal writing provides the opportunities for the
students to reflect on the learning process, and to develop new learning skills. These
opportunities will help the students to identify differences between their school
experiences and those they are encountering at college.
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10. Challenges
Testing for accountability purpose is essentially large scale testing and for this
reason it relies on tests that are relatively cheap, brief, offer broad but shallow coverage,
are easy to score and reliable (Gipps, 1994). Alternative assessment by contrast is time-
consuming, tends to provide detailed multi- dimensional information about a particular
skill or area; (and because of time factor, depth may be exchanged for breadth), scoring is
generally complex and usually involves the classroom teacher Standardisation of the
performance is not possible and therefore reliability in the traditional sense is not high
(Mehrens, 1992).
However, alternative assessment in general, has become the cornerstone of
educational reform movement. The arguments for using these forms of assessment to
support instructional practice are that;
(i) they engage students in tasks that are more comprehensive and consistent with the
goals of a discipline or resonant with the desired outcomes of educational process;
(ii) they provide detailed evidence about student’s thinking that enables more specific
instructional decision making; and
(iii) they encourage students to take active role in their own assessment enabling a
sharing responsibility for learning (LeMahieu, et. al. 1995, p11)
Many educators are of the view that alternative assessment must be held to the
same stringent standard of reliability, validity and objectivity as those achieved by
standardised norm - referenced assessment, if it is to provide credible and legally
defensible measure of learning and performance (Linn and Burtin, 1994).
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11. Objections to alternative assessment are often voiced in terms of validity,
reliability and objectivity. Questions that focus around these issues are:
i. Does the instrument measure what it is supposed to measure?
ii. Is the instrument consistent in its measurement?
iii. Is the instrument unbiased? (Garcia and Pearson, 1994).
Alternative assessment represents the best of worlds in that it looks at actual
performance on real life tasks, such as writing, self-editing, reading, participation in
collaborative work, and doing a demonstration in front of a group. These procedures are
in themselves valid (Garcia and Pearson, 1994).
As regards reliability of alternative assessment, Huerta - Macias (1955), mentions
triangulation as a means of ensuring reliability in a qualitative research. In qualitative
research, triangulation refers to the combination of methodologies to strengthen a study
design. When applied to alternative assessment, triangulation refers to the collection of
data/information from three difference sources/perspectives - teacher, student, and parent.
On the question of objectivity of alternative assessment, research findings show
that, standardised tests merely represent agreement among a number of people on scoring
procedures, format or content. These individuals are not objective; they just collectively
shared the same biases. In this regard, Huerta - Marcias (1995) says that standardised test
is not more objective than an alternative assessment.
Other challenges of alternative assessment have to do with curriculum and
instructional practice. Torrance (1993) reviewed the impact alternative assessment has on
curricular and instructional practice in the context of the National Assessment in England
and Wales. Among the concerns raised were exorbitant demands on teachers, adding up
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12. to two to three hours of extra work daily. Teachers also reported dissatisfaction with
managing assessment interactions with small groups of students while trying to maintain
the focus of all students. Torrance (1993) concluded that teachers treated assessment as a
special activity set apart from teaching, and they felt obliged to do this by the instructions
they received, a vision at odds with the integrated assessment and instruction offered by
alternative assessment advocates.
The question of relative practicality of alternative and traditional assessment in
terms of time consumption has been raised by many authors (Linn, 1993; Gipps 1994).
Research results indicate that alternative assessment is not more time consuming than
traditional assessment on the part of the students. Research has shown that students can
cope with the time demands of the alternative assessment(Eshun & Abledu, 2000).
Educational Implications and Recommendations
The following educational implications and recommendations are made for
improving the academic performance and enhancing positive attitude of students in
mathematics:
i. Through alternative assessment processes, the teacher is given the opportunity to
know from the students’ journals and portfolios the positive and negative points
of his teaching process and work out strategies for his subsequent teaching.
ii. Alternative assessment processes offer a chance for the development of better
student- student and student-teacher relationship. During their group work and
discussions of their journals with the teacher a friendly climate is generated which
helps them to get to know one another better.
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13. iii. With alternative assessment the teacher is given a chance to break the everyday
monotonous teaching routine. Activities are organised for the students that create
a pleasant and motivating atmosphere in the classroom, which revives the interest
of the pupils for the subject.
iv. Alternative assessment processes lead to discovery learning and planning. Thus, it
is valuable for increasing and maintaining the efficiency of the skills and concepts
that the students learn. However, it makes heavy demands on the teacher to plan
activities for the students.
v. Students who have language problems will be unwilling to communicate in
writing with the teacher. Teachers who use alternative assessment processes
should rely more on oral interview than the writing of journal.
vi. The positive benefits of alternative assessment lie not only in its implementation
but also in the teachers’ ability to extend and enrich the curriculum through the
activities he/she arranges for the students. Thorough planning and understanding
of the skills students must develop are prerequisite to successful implementation
of alternative assessment processes. Teachers must be trained to live up to the
task. It is recommended therefore that pre-service teachers be introduced to the
alternative assessment processes. In-service and induction courses on alternative
assessment can be organised for teachers who are already teaching. This training
is worthwhile since teachers will have the means to bring about higher
achievement in mathematics and higher attitudinal changes in female pre-service
teachers towards mathematics.
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14. vii. Teachers need to provide many opportunities for students to explore and reflect
on mathematical concepts. Having students talk and write about mathematical
concepts and how these ideas are applied in various problems situation can
strengthen their understanding and provide valuable information to the teachers. It
is therefore recommended that mathematics concepts be presented to students
through the alternative assessment processes. This will then enhance the current
programme of promoting the interest of girls in Science, Technology and
Mathematics Education (STME).
viii. To evaluate our programmes and the progress students are making, me must look
beyond the current traditional assessment alone, and find better ways of assessing
students’ creativity, ability, and sensitivity in mathematics. The point is,
continuous assessment ought to provide a more comprehensive view of pupils’
all-round performance. The Ministry of Education (MOE), the Ghana Education
Service (GES) and other policy makers on education must adopt alternative
assessment to improve female students’ performance and attitudes in
mathematics.
Conclusion
Knowing mathematics is doing mathematics. We need to create situations where
students can be active, creative, and responsive to the physical world. I believe that to
learn mathematics, students must construct it for themselves. They can only do that by
exploring, justifying, representing, discussing, using, describing, investigating,
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15. predicting, in short by being active in the world. Alternative assessment is an ideal
activity for such processes.
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