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.
TABLE OF CONTENTS
Title page Pages
Certification ii
Dedication
iii
Acknowledgement iv
Table
of content v
Abstract vi
CHAPTER ONE- INTRODUCTION
1.1 Background
to the study. 1
1.2 Statement of
the problem. 9
1.3 Purpose of
the study. 10
1.4 Research
Questions. 10
1.5 Research
Hypothesis. 10
1.6 The Significance
of the study. 11
1.7 Scope and Limitation
of the study. 11
CHAPTER TWO: A REVIEW OF RELATED
LITERATURE
2.1
Introduction. 14
2.2
Problems
of Teaching Algebra. 15
2.2.1 Professional
Development and Mathematics 15
instruction of
Teachers.
2.2.2 Limited
Pedagogical Knowledge of Teachers. 16
2.2.3
Lack of Realization of the Effects of Students
Algebraic Thinking in effective Teaching. 17
2.2.4
Complexities in Coding Students Responses. 18
2.2.5
Limited content Knowledge base of Teacher. 18
2.2.6
Absence of Teaching Algebra as Modelling Tool. 19
2.3 Problems Students Encounter in Learning
Algebra. 20
2.3.1
Isolation of Mathematical Ideas from Elementary
Algebra.
21
2.3.2 Nature of Learning Environment. 22
2.3.3
Misconception about the Use of
Letters and Symbols. 22
2.3.4
Nature of Algebraic Concepts. 23
2.3.5
Academic Procrastination among Students. 24
2.4 Research Finding on the Solution Strategies
to
the problems of Teaching Algebra . 25
2.4.1
Improved Condition for professional and
Non-professional Mathematics Teacher. 25
2.4.2
Adequate Pedagogical Knowledge of Teachers. 26
2.4.3
Preference to the Effects of Students Algebraic
Thinking to Effective Teaching. 27
2.4.4
Devising projects for Coding Students Response. 28
2.4.5
Adequate Content Knowledge of Teachers. 29
2.4.6
Teaching of Algebra as a Modelling Tool . 30
2.5 Solution to the Problems of Learning
Algebra among Students. 31
2.5.1
Integrating Mathematical Ideas to Elementary
Algebra. 32
2.5.2
Fostering Positive Learning Environment. 32
2.5.3
Positive Concepts about Use of Letter and
Symbol In Algebra. 33
2.5.4
Reducing Abstraction Level in Algebra. 34
2.5.5
Counselling Students with Procrastinating Attitude. 35
2.6 The Dynamics of Problems of Teaching and
learning Algebra in the Secondary
Schools. 36
CHAPTER THREE: DESIGN AND METHODOLOGY
3.1 Introduction. 43
3.2
Research
Design. 44
3.3
Area
of Study. 44
3.4
Population
of the Study. 44
3.5
Sample
and Sampling Technique. 45
3.6
Research
Instruments. 46
3.7
Method
of Data Collection. 47
3.8 Method of Data
Analysis. 47
3.8.1
Scoring Algebra Diagnostic Test. 48
3.8.2
Statistical Treatment of the Data Analysis. 48
CHAPTER FOUR: DATA AND ANALYSIS
4.0 Introduction. 49
4.1 Analysis of the Demographic Information
of the
Respondents (Teachers). 49
4.2 Analysis of the Items in the Teacher’s
Questionnaire .
51
4.5 Representation and analysis of Data
According to
Research Hypothesis and Questions. 62
4.6 Analysis of the Demographic Information
of the Respondents Students. 64
4.9 Representation and Analysis of Data
According
to Research Hypothesis and
Questions. 77
CHAPTER FIVE:
DISCUSSION OF RESULT, IMPLICATION FOR EDUCATION AND RECOMMENDATION
5.1 Discussion
of Results. 80
5.2 Limitations. 82
5.3 Implications
and Recommendation. 83
5.3.1 Science
Teaching and Learning. 83
5.3 2 Education
Policy Makers and Administrators . 86
5.3.3 Parents. 87
5.3.4 Future
Research. 87
5.4 Conclusion. 88
References
Questionnaire
Appendix
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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