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THE PROBLEMS
OF TEACHING AND LEARNING ALGEBRA AT THE SENIOR SECONDARY SCHOOLS
ABSTRACT
This
research was designed to identify the problems teachers and students
encountered when teaching and learning algebra at the secondary school level.
A total of
seventeen (17) mathematics teachers and one hundred (100) students randomly
selected served as the subjects of this study.
The
instrument used for this research were Algebra Diagnostic Test (ADT) for
students and Questionnaire for teachers and students. The data collected were
analyzed using the statistical package for social sciences (SPSS) which include
simple percentages, the mean, standard deviation and analysis of variance
(ANOVA).
The research
questions were investigated and two null hypothesis were tested. The findings
revealed that;.
i. There are significant problems
encountered by teachers while teaching algebraic concepts that adversely affect
students’ appreciation and achievement in algebra classes.
ii. There are significant problems
encountered by students when learning algebraic concepts that lead to poor
performance in mathematics and application to other subjects.
Based on
these findings, appropriate recommendations were made and it was concluded that
problems of teaching and learning algebraic concepts affect students
achievement and performance in algebra test and mathematics in general.
CHAPTER ONE
INTRODUCTION
1.1
Background to the Study
The place of
mathematics in any enterprise is all encompassing and divergent in thought processes and
logical reasoning. (Oshin, 1995). It’s usefulness and applications to other
subject disciplines in the education system is undeniably feasible; as most of the
algorithms, systematization, organization, interpretation and analysis in
presentation of facts, points, generalizations and argument has helped to order the sequence of
synthesized knowledge to producing comprehensive volumes of materials to be
taught and learnt in these disciplines; some of which are sciences, commerce,
economics, medicine, maritime, defence and vocations. (Olayinka & Omoegun
2006;Butter& Wren 1951 cited in Udeinya & Okobiah, 1991 and Sule, n.d).
Olayinka
& Omoegun (2006) and Usman & Umeano (2006), submitted that mathematics
is an indispensable tool for national development it helps to build the
computational, manipulative, deductive and inductive thinking as well as
problem solving skills of prospective individuals to function effectively
within his ever dynamic world, through self discovery, development, worth and
actualization. Mathematics is unique in diversities. It is resourceful in
scientific industrial, technological social and vocational progress of any
society. (Asikhia, 2010).
The teaching
and learning of mathematics concepts has been ranked as one of the most
important activities in the education system. It’s distinctive nature as
enunciated by Piaget (1972) and Piaget &Garcia (1998) cited in Cooley,
Martin, Vidakovic &Loch (2007) and Mashooque (2010) attest to the crucial
placement of concepts learning and appreciation as well as utilization of
mathematics ideas to solve problems and analyze concepts in other school
subjects. They highlighted visualization, abstractness, hierarchy of concepts,
problem solving and discovery nature of mathematics as the tremendous
implication to the teaching and learning processes. In view of these,
stakeholders (teachers, parents, educational planners and government) in
educational planning and implementation have helped to structure the
mathematics curriculum into concept sequence to be taught and learnt at all
levels of Nigerian education system. (primary secondary and tertiary).
At the
secondary schools, topics that make up the branches of mathematics, such as
measuration, geometry, inequalities, statistics, functions, algebra among
others have been structurally arranged and discussed in sequence, content,
teaching activities and aids with respect to sub concepts, concept hierarchy,
simplicity, difficult, technicality and applications (Macre, Kalejaiye, Chima,
Garba, Ademosu, chairman, Smith and Head, 2001) so that mathematics idea would
be taught in such a way that repetition for re-inforcement, understanding and
appreciation of topics are made at each level but with elements of advancements
in technicality and structure at higher classes in the secondary schools.
Algebra, as
a branch of mathematics has been reckoned
with as an important concept in mathematics. It is a generalized
arithmetic which require the use of known and unknown quantities. (Osta and
Laban, 2007). They further define algebra as that branch of mathematics in
which situation of life are represented with a first degree equations where the
unknown appear in both sides of the equal sign. In the same vein, Mashooque,
(2010) disclosed that algebra uses symbols, letters and signs for generalizing
arithmetic which have different meanings and interpretations in different
situations. It’s usage and applications to effective acquisition of knowledge,
skills and understanding the titbits of other
concepts in mathematics (measuration, geometry, inequalities, indices,
statistics etc) sciences, social sciences, maritime, medicine, defence and
vocations among others: (Mashooque , 2010), attest to the crucial ordinal
placement of this multidimensioned branch of mathematics in solving problems.
Diophantus
and Al-Khawarzmi Mohammed Ibn Musa; founder and consolidator of algebra cited
in Oshin, (1995) revealed that algebra is one of the earliest mathematics
inventions that transited from arithmetic’s and got separated from it when
equations and methods for reducing them were introduced. They proffered algebra
as the science of transposition and cancellation. It is the branch of
mathematics that involves the solution of equation by such device as transposition and
cancellation. In the same vein, Oshin (1995) revealed that as time passes,
Al-Khawarizmi name was distorted into “algorism” meaning “ the art of
calculating” now referred to as Arithmetic, which has helped in the revolutionized
mathematical manipulation, thereby making long division rather simple for
children and served as a model for later writings in their applications of arithmetic and algebra to the distribution of
inheritance and astronomical inventions.
Deductively,
algebra is wide in concept, forms, structure and applications, since it is
studied virtually at all levels of education. (NCTM, 1989 cited in Cooley,
Martins, Vidakovic and Loch 2007). It is popularly known as Arithmetic in the
primary schools, where pupils are taught the titbits and rudiments of counting,
simple equations on sum, difference, product, divisions and word problems.
Algebra with it’s subdivisions retain it’s name at the secondary and tertiary
schools with dissimilarities in concept sequence, classifications, technicality
and application. For instance, at the senior secondary schools, algebra was
divided into equations (simple simultaneous and quadratic), set theory,
inequality and variation with distinctive techniques for solving their problems
(Macrae, Kalejaiye, Chima, Garba, Ademosu, Channon 2001). All these concepts
are taught and learnt at the senior secondary schools to facilitating
proficiency of students in applying the techniques therein to solve problems in
other subjects.
Inspite the
utilitarianism of algebra to the material world in developing skills in
computation, manipulation, balancing and analyzing equations, logical
reasoning, deductive thinking and problem solving in individual to adapting and
functioning effectively in the technologically dynamic world, students in the
secondary schools; especially those in the senior secondary Two (ss2) have not
explored the resourcefulness of algebraic concepts, evident in their poor
performance in not only algebraic sections of mathematics examination but also
in mathematics in entirety and subjects like physics, chemistry, Economics etc.
(Kucheman, 1981 cited in Mashooque, 2010). This development is traceably linked
to the problems associated with teaching and learning algebraic concepts at the
senior secondary schools.
Teaching and
learning are tools for implementing educational policies and programmes. They
constitute the basis for drawing out and developing the innate potentials of an
individual to aiding usefulness to oneself and the society. Teaching; a process
of making someone attend, observe, reason and think. (Akande, 2004) and
learning; a relative permanent change in behaviour due to experience
(Nwadinigwe, 2001) are two sides of a coin; as one complements the other in
terms of effectiveness. The teaching
and learning of mathematics concepts with algebra inclusive is beset with many
problems; most of which have adversely affected the performance of students in
mathematics examinations despite several viable efforts put in by stakeholders
to ameliorate the appreciation achievement and utilization of mathematics
concepts. (Okereke, 2005). Chimere, (2007) submitted that this ;pose grave
danger to national development.
Teaching
algebraic concepts has become evolving, multidimensional and divergent
(Catherine, 2005). With the adventures in technological discoveries and
mathematical inventions in algebraic simplification, expression, manipulation
and problem solving, concepts in this encompassing branch of mathematics absorb
complexities in forms, structures and algorithms that directly affect
proficiency farewell of students in mathematics as whole and other subjects, many of which have
advance the course of effective teaching. To this end, Catherine (2005)
observed that these complexities have implications on the content and
pedagogical knowledge of teachers in effectively communicating algebraic ideas
to the understanding and appreciation of the students, and submitted that the
adequacy or otherwise of content and pedagogical knowledge of teachers affect
the achievement level of students in algebra classes.
But in most
teaching and leaning encounters, it is revealed that teachers do the greater
works by exposing titbits, algorithms
and structures of algebra to students. Thereby, leaving him or her to
nothing for self discovery, attitudes of appreciation, which invariably
discourage curiosity for further learning. This affects the true essence of
self development (Catherine and Vistro, 2005). Moreso, Udeinya & Okobiah
(1991) highlighted poor methods of teaching, unqualified mathematics teachers,
poor condition of service for teachers and apathy towards mathematics by the
general public as some of the threat hampering mathematics growth and
development. They and Okereke, (2005) opined that it is a common knowledge that
many mathematics teachers, mathematicians and the general public are distressed
about the state of general mathematics
instruction in the country, inspite the pivotal role mathematics play as a key
subject in the school curriculum.
On the part
of students, Michele and Assude in their project work opined that algebra is a
crucial domain as regard the relationship students develop with mathematics.
This shows that algebra is fundamental to students competence in mathematics
ideas, structures and problems solving. Thus, it is an important concept that
serves as a tool for analyzing other concepts in mathematics Algebra also play
a crucial role in facilitating students proficiencies in other subjects like
physics, chemistry, economics etc because calculations, use of equation and
expressions that are algebraic in nature are absorbed by authors of the
subjects to expound, analyse and solve concepts in these subjects. (Sule, n.d).
But, the
state of affairs in the performance scale of student in mathematics and other
subjects like physics, chemistry, economics etc is at a low ebb. Mashooque
(2010) identified poor understanding of algebra fundamental of students in the
use of symbols, letter and signs, misconceptions in algebraic processes and
poor attitude towards problems solving as some of the factors inhibiting
students appreciation and proficiencies in algebraic processes. Asikhia (2010)
submitted that these anomalies emanated from the learning difficulties and
challenges students encounter in the teaching and learning process, which have
implication to students functionality and adaptation in other subject as well
as their future career.
In Sule,
(n.d) project work on the relationship between attitude and problem solving in
mathematics of secondary students in Kogi state stated that algebra concepts can
be used to solve a multitude of problems
arising form diverse academic field, such as physics, chemistry, Economics,
Sociology, Astronomy and statistics. By implication, poor academic performance
in these field could be linked to deficiency of students in interpreting,
analyzing, balancing and solving algebraic expressions arising from numerous
problems they encountered in learning algebra concepts.
1.2
Statement of the Problem
Inspite the
utilitarian nature of algebra in facilitating potency in students to understand
and apply basic concepts like equations, inequalities, set theories, variation,
problem solving techniques to interpret, analyse and solve problems in other
branch of mathematics as well as other school subjects like physics, chemistry,
economics etc for better functionality and adaptation of their rudiments and
structural patterns for improved
performance, students have not been able to explore the usefulness of
algebra to better their proficiency in these subjects due to the difficulties
encountered by teachers and students in the teaching and learning of algebra
concepts. The students incessant poor performance in examination is posing
threat to their educational and teacher’s professional growth and development.
1.3 Purpose
of the Study
The main
purpose of this study is to identify the problems of teaching and learning
algebraic concepts at the senior secondary school Two (SS 2) by undertaking a
diagnostic test analysis of selected mathematics teachers and students in Apapa Local Government
Area of Lagos State Secondary Schools.
1.4 Research
Question
In this
study, the following research questions were raised:
i. What are the problems teachers encountered
while teaching algebraic concepts, that adversely affect students’ appreciation
and achievements in algebra classes?
ii. What are the problems students encountered
while learning algebraic concepts that lead to poor performance in mathematics
and application to other subjects.
1.5 Research
Hypothesis
The
following hypothesis stated below would be tested in this study.
HoI: There
are no significant problems encountered by teachers while teaching algebraic
concepts that adversely affects student’s appreciation and achievement in
algebra classes.
HoII: There
are no significant problems encountered by student’s while learning algebraic
concepts that lead to poor performance in mathematics and applications to other
subjects.
1.6 The Significant of the Study
This study
is significant because it would help to provide valuable information to
acquaint.
i. Teachers on problems of teaching algebra
at the senior secondary schools and model for improved instruction.
ii. Students on problem of learning algebraic
expressions and model for improved appreciation and performance in mathematics
as well as application to other subjects.
1.7 Scope
and Limitation of the Study
Considering
the broad nature of algebraic concepts
taught and learnt at different levels of education with their antecedent
problems, massiveness in the number of mathematics teachers and students at these
schools, limited time frame, space and resources, this research study intend to
focus on studying the problems of teaching and learning algebraic concepts
among selected mathematics teachers and SSS2 students in Apapa Local Government
Area of Lagos State Secondary Schools.
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