ABSTRACT
The study sought to identify the relationship between the
perception of mathematics teachers about assessment and their assessment
practices. Descriptive survey was adopted as a design for the study.
Questionnaires were administered to a sample of 63 teachers in the Binduri
District after which their lessons were observed to gather data for the study.
A multi-stage sampling technique was used to get the sample for the study. Data
was analysed based on the research questions and hypotheses that guided the
study. The descriptive statistics and inferential statistics were used to
present results for the study. From the study, although the perception of
teachers about assessment in mathematics is not generally in line with the
current thinking of assessment, teachers generally had positive perceptions
about what should be assessed, how it should be assessed and the feedback to
give to students. This implies that teachers generally have inadequate training
in assessment. It was also found that, teachers generally perceive and profess
positive assessment practices but their practice is not generally positive. It
was also found that, there was a significant difference between the professed
assessment practices of teachers and their actual assessment practices. It is
therefore recommended the Ghana Education Service should organise In-Service
Training and Education course on current trends in assessment in mathematics.
It is further recommended that heads of schools should conduct regular needs
assessment and provide adequate support to enable teachers practice what they professed.
CHAPTER ONE
INTRODUCTION
Background to the Study
Education is perceived across the world as perhaps the most
vital public service of all. As Asare (2011) succinctly puts it, “A sound
education structure leads to an enlightened society and manpower development,
which is able to lead a crusade for social transformation and economic
progress” (p. 43). To indicate the importance of education, Tefera (2014) also
asserted that the main objective of education is to cultivate the individual
capacity for problem-solving and adaptability to the environment by developing
the necessary knowledge, ability and attitude. The implication of these
statements is that, education is at the forefront as far as the development of
a nation is concerned. This probably accounts for nations and parents worldwide
investing huge sums of money and other resources into the education of its
citizenry and wards respectively.
One important discipline in education is undoubtedly
mathematics. Mathematics is a household name to many students and other
stakeholders in education and nation building. It manifests itself in our
immediate and remote environment. To Mereku (2000), mathematics is a science of
patterns that involve problem solving, search for relationships, imaginings,
creativity, and critical and logical thinking. This explains the usefulness of
mathematics to our everyday living as it is seen as a problem solving tool. Mathematics
forms the basis of all subjects and possibly all professions. As a vital tool
for the understanding and application of science and technology,
mathematics serves as a precursor to the much needed technological development
which is the pursuit of every nation including Ghana. Mathematics has had an
influence on man’s life that it has now become everyman’s everyday concern. The
importance of mathematics is so immeasurable that it is a prerequisite subject
in most levels of Ghanaian education.
The importance of mathematics to every nation is so glaring
that Legner (2013) argues that, it is very hard to come up with an area of
mathematics which has no application in life. Legner argues that we regularly
use mathematics in our everyday life: from measuring distances and weights to
reading timetables, estimating how much money we spent while shopping and
interpreting percentages in newspapers. Many of these skills are taught at the
basic school level including Ghana. Mefor, (2014) cited in Sa’ad, Adamu
Sadiq (2014) summarized it all by saying that mathematics
relates to everything in the universe from the smallest to the largest. Sa’ad,
Adamu & Sadiq (2014) further asserted that mathematics is intimately
connected to daily
life and everybody’s life-long planning. Therefore,
mathematics is a subject that education and human life cannot function
effectively without it. This justifies the compulsion of the study of the
subject by all students who go through basic and secondary education in most
countries including Ghana. Mathematics undoubtedly plays a vital role in the
development of individuals and nations.
Indeed, the potential success in the world today and in the
future can be realized if mathematics education is effective and is well
understood by its learners. It is no wonder that a strong foundation in
mathematics is a prerequisite for professions and careers in today’s changing
world. This claim is supported by a report by the Ministry of Education (2001)
which claimed that, strong Mathematical competencies development at the Junior
High School level is a necessary requirement for study in Mathematics, Science,
Commerce, Industry and a variety of other professions and vocations.
In Plato’s view (2000), mathematics has a philosophical
importance. Mathematics is a tool that helps and trains the mind to think. This
process of thinking will then help the mind to understand and acquire the idea
of good, which is the ultimate aim of philosophy. Plato did not deny the
important applications of mathematics in people’s daily life. But, to Plato,
the philosophical importance of mathematics is more important and more
rewarding as it may affect one’s understanding of his being.
Mathematics is also linked with power. Since mathematics is
behind most of society’s inventions, it tends to give those who succeed in it
access to wealth and power. It thus acts as a gatekeeper studies around the
world of which a large part of the world’s population is denied access to its
‘power’ (Ernest, Greer, & Sriraman, 2009; Secada, 1995). While power and
wealth may not seem to be of immediate concern to pupils at the basic level,
the foundations of mathematical proficiency are established during these years.
Umameh (2011) in Tshabalala and Ncube, (2013) was of the view
that mathematics is the bedrock and an indispensable tool for scientific,
technological and economic advancement of any nation. Adetunde (2009) also asserted
that, Mathematics is a tool for science and technology. The rich and more
advanced countries of the world have attained their affluence through the
advancement which they made in mathematics which links sciences and technology. This implies that mathematics education is a very
important input in the scientific and technological development of any society.
It is therefore not out of place if more efforts are put in place by interest
groups including researchers to make mathematics teaching and learning easier
and more meaningful.
In addition, Davies and Hersh, (2012) see mathematics as an
important subject not only from the point of view of getting an academic
qualification at school or college, but also is a subject that prepares the
students for the future irrespective of which work of life they choose to be a
part of. This explains that, mathematics gives its learner(s) not only job
opportunities but also fine-tune their skills in order to succeed in other
areas of work. In Ghana, Mathematics has become one of the prerequisite
subjects for students to pass to progress from one stage of the academic ladder
to the next. To a greater extent, failure in mathematics results in failure to
get access to a tertiary institution which prepares the individual to the world
of work. Competencies in mathematics also expose the individual child to myriad
and varied job opportunities including becoming teachers, engineers and
statisticians.
Having established the fact that mathematics plays a key role
in the development of the learner and a nation at large, it stand to reason
that a country that does not attach importance to educating most of its
citizenry in mathematics risks lagging behind as far as development is
concerned. Rightly so in Ghana, mathematics has been given the premium it
deserves in education. Mathematics like other subjects contributes partly to
the realization of our national aspirations and goals. The main rationale for
the mathematics curriculum in Ghana is focused on attaining one crucial goal:
to enable all
Ghanaian young people acquire the mathematical skills,
insights, attitudes and values that they will need to be successful in their
chosen careers and daily lives (Ministry of Education, Science and Sport,
2007). At the basic level in Ghana, mathematics aims at developing the numeracy
skills of the students. It is as a result of this aim that the mathematics
syllabus is based on the notion that an appropriate mathematics curriculum
results from a series of critical decisions about three inseparable linked
components: content, instruction and assessment. This means that the content,
instruction and assessment work in tandem to ensure the desired outcome. If one
fails to work properly, then the entire system will be faulty and the
aspirations of the nation in terms of mathematics will suffer. It is assessment
that determines whether the aims of mathematics is been achieved or not. Invariably,
assessment tells whether the content was properly taught and learnt or not. To
Tefera (2014), just as education and development never separate from each
other, quality education also go in line with assessment.
Assessment is very vital in helping the learners and teachers
become effective and efficient. Assessment denotes the collection of different
information to produce effective and competent teachers and learners. Without
assessment it is difficult to identify the students’ achievements or their
failure to achieve their learning. To this end, Airasian (2001) sees assessment
as a process of collecting, interpreting and synthesizing information to help
teachers understand their students, plan and monitor instructions and establish
a conducive classroom atmosphere. In effect, assessment is essential to allow
individuals to get the educational support they need to succeed, to see the
effectiveness of different educational methods, and to ensure that education budgets are being spent effectively. Inevitably, assessment
mirrors the successes and failures of teachers, learners, the institutions and
educational policies or programmes.
Classroom assessment has been found to be a critical factor
in promoting quality education and as such has become the pivot of various
educational improvement efforts (Oduro, 2015). This is because assessment
results provide information on pupils’ achievement, identify learning problems,
and indicate the remedial actions that need to be taken (Black, Harrison, Lee,
Marshall, and Wiliam, 2004). To ensure that the national aims of mathematics
are achieved, the syllabus provides an assessment procedure through which what
is taught and learnt can be determined and the appropriate action taken to
remedy any unrealized aim. It is expected that if these procedures are followed
to the latter, then it should reflect in the performance of students even in
standardized examinations and the general application of mathematical ideas in
the daily activities of the basic school graduate. As to whether these
procedures of assessment are being followed by teachers is an issue that needs
further studies.
It is worthy to note that, assessment score in itself is not
enough to validate the performance of a pupil in mathematics but the assessment
procedure adopted by assessor also counts. Teachers adopt several assessment
practices that can positively or negatively affect the performance of pupils.
Some assessment methods are sometimes more emphasized than others. These
practices if appropriate will help validate the performance of pupils otherwise
we cannot interpret any performance as the actual performance of the said
pupil. However, since mathematics is crucial to the development of the country, the need to provide a valid picture of progress of
pupils is necessary and the assessment practices of classroom teachers plays a
key role in this respect. After all, it is the assessment of these
instructional goals that contributes to the appropriate assessment of the
ultimate aim of the mathematics curriculum and by extension the effectiveness
of the entire educational system.
Assessment practices denote what teachers do to monitor and
improve teaching and learning in the classroom. Several studies on teachers’
assessment practices in the classroom have been carried in different parts of
the globe with divergent findings. Zhang and Burry-Stock (2003) reported that
teachers differ in their assessment practices due to the nature of classroom
assessment delineated by teaching levels. While secondary teachers rely mostly
on paper-pencil tests and were concerned about the quality of assessment,
elementary teachers often use performance assessment as an alternative.
Suurtamm, Koch and Arden (2010) also found that Canadian mathematics teachers
use variety forms of assessment to improve student learning with emphasis on
the use of test, homework and classroom exercise to elicit pupils understanding
as well as journals, observation, questioning, self-assessment and unique forms
of ‘quizzes’. In Ghana, teachers tend to use traditional methods of assessment
(test, class exercise and home work) rather than alternative assessments (oral
presentation, observation and project work) (Nabie, Akayuure and Sofo, 2013)
and mainly asked facts-eliciting questions that demanded students to make
simple logical mathematical deductions from procedures and not that which
challenged them to investigate (Hattori and Saba, 2008).
It must be noted that the assessment procedures practiced by
teachers in the classroom is informed by several factors. One of such factors
is the how the teacher perceives assessment (Brown, 2004). Chester and Quilter
(1998) believed that studying teachers’ perceptions of assessment is important
in the sense that it provides an indication of how different forms of
assessment are being used or misused and what could be done to improve the
situation.
From the above, it can be elicited that, teachers’ assessment
practices represents what teachers do in the classroom as far as assessment is
concerned whereas the perception of teachers indicates what teachers think
assessment is all about. The question then is whether teachers really put into
action what they think should be done in assessment to ensure improved teaching
and learning especially in the Ghanaian context. The answer to this question
needs further research.
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