TABLE
OF CONTENTS
CHAPTER
ONE
1.1 INTRODUCTION
1.2 STATEMENT OF THE PROBLEM
1.3 PURPOSE OF THE STUDY
1.4 SIGNIFICANCE OF THE STUDY
1.5 SCOPE AND LIMITATIONS OF THE STUDY
1.6 RESEARCH QUESTIONS
1.7 INSTRUMENTS USED FOR THE RESEARCH
CHAPTER
TWO
2.0
LITERATURE REVIEW
2.1 HISTORY AND IMPORTANCE OF MATHEMATICS
2.2 HISTORY OF GEOMETRY
2.3 RATIONALE
FOR THE INCLUSION OF SOLID GEOMETRY IN THE SCHOOL MATHEMATICS CURRICULUM
2.4 DIFFICULTIES IN SOLVING PROBLEMS ON SOLID
GEOMETRY.
CHAPTER
THREE
METHODOLOGY
3.1 INTRODUCTION
3.2
POPULATION AND SAMPLE
3.3 RESEARCH
INSTRUNENTATION
CHAPTER
FOUR
PRESENTATION,
ANALYSIS AND INTERPRETATION OF DATA
4.1 INTRODUCTION
4.2
PRESENTATION OF STUDENTS PERFORMANCE IN THE OBJECTIVE TEST
4.3
PRESENTATION OF STUDENTS’ PERFORMANCE IN THE DIAGNOSTIC TEST
4.4 ANALYSIS
OF THE STUDENTS’ PERFORMANCE AND STATEMENT OF DIFFICULTIES ENCOUNTERED BY
STUDENTS.
4.4.1 DIFFICULTIES ENCOUNTERED BY STUDENTS IN THE
OBJECTIVE TEST
4.4.2 DIFFICUTIES ENCOUNTERED BY STUDENTS IN THE
DIAGNOSTIC TEST
4.5
ANALYSIS OF TEACHERS
QUESTIONNAIRE RESPONSES
4.6 SUMMARY OF FINDINGS
CHAPTER FIVE
5.1 CONCLUSION
AND RECOMMENDATION
5.2 CONCLUSION
5.2 RECOMMENDATIONS
APPENDIX A: STUDENTS QUESTIONAIRE
APPENDIX B: TEACHERS
QUESTIONAIRE
CHAPTER
ONE
1.1 INTRODUCTION
Every
aspect of human life requires mathematics. We use mathematics at home, on the
job, in the market, on the bus and in our communities. Besides these,
mathematics is the driving force behind the scientific and technological
revolutions mankind has witnessed. It is also on record that virtually every
discipline derives its credibility and reliability from mathematics.
Having
given the enormous importance of mathematics, it is expected that every
community and society should devise strategies of promoting mathematical
literacy. It is also necessary that every student is given an opportunity to
acquire the concepts, principles and skills of mathematics.
Unfortunately,
the teaching and learning of mathematics has been fraught with challenges which
prevent many students from performing well in both internal and external
examinations. The examinations are based on the components of mathematics which
are:
1. Number
and numeration
2. Algebra
3. Geometry
and mensuration and
4. Statistics
Geometry is a branch of mathematics that
deals with the study of figures in space of a given number of dimensions of a
given type.
Erric (1999) defines geometry as an
intuitive feel for shape and space. He further said that geometry involves the
ability to recognize, visualize, represent and transform geometrical shapes. It
also involves less formal activities of two and three dimensional shapes such
as paper folding, transformations, tessellation and projection.
Geometric figures and relationships have
played an important role in society’s sense of what is aesthetically pleasing.
From the Greek discovery and architectural use of the golden ratio to some of
the world’s most recognizable works of art, geometry and the visual arts have
had strong connections. (Erric 1999)
Well constructed diagrams allow us to
apply knowledge of geometry, geometric reasoning and intuition to arithmetic
and algebra problems. Other mathematical
concepts which run very deeply through modern mathematics and technology
such as symmetry are most easily introduced in geometric context. Whether one
is designing a building, an electronic circuit board, a dress, a bookshelf, an
airport or a newspaper page, an understanding of geometry is required.
Geometry is all around us in art, nature
and the things we make. This topic is of importance to students in that it will
help them apply their spatial sense (ability to think about space) and
knowledge of the properties of shapes and space to the real world around them.
SOLID
GEOMETRY
The
geometry that is commonly studied thus far has been largely plane geometry that
is geometry of figures each of which lies entirely in one place. It is known
that plane figures have no dimension or 2 dimensions. For example, a point has
no dimension, a line has one-dimension – length and a rectangle has
2-dimensions – length and width.
But, we live in a 3-dimensional world
and it is only natural that we should extend our study of geometry to include
figures having 3-dimensions that is having thickness as well as length and
width.
The points and lines of a 3-dimensional
figure do not necessarily lie in the same plane. In the 3-dimensional figure
below, the points A B C and D lie in one plane, the points D C F and G lie in a
third plane. How many planes make up the surface of the figure shown below?
We
sometimes call the geometry of 3-dimensional figure 3 dimensional geometry or
space geometry. Since many 3-dimensional figures are said to be geometric
solids, we usually call 3-dimensional geometry, solid geometry. A geometric
solid is a surface completely enclosing a portion of space. (Obodo, 1991)
The
cuboid, cone, cylinder and sphere are familiar examples of geometric solids.
The
study of solid geometry will help us discover and organize evaluable
information about the dimensional space information that will be helpful to
those who have interest in engineering, architecture, engineers, architect,
draftsmen, tool designers, machines and so on as well as those who merely wish
to be able to read with understanding and to converse intelligently about the
world’s great engineering and scientific feats.
In
early elementary school, a rich and qualitative study of geometric objectives
helps young children develop spatial sense (knowledge of space) and a strong
intuitive grasp of geometric properties and relationships. Eventually, they
develop a comfortable vocabulary of appropriate geometric terms. Thus the need
and relevance of geometry in the education of the child is not
bargainable. Studies have revealed that
students consider geometry as a difficult topic in mathematics as a result of
what goes on in the classroom.
Learning
is an interwoven concept that cannot be independently talked about without
mentioning teaching. In fact, learning is a result of teaching either by an
instructor or through experience. (Nwadinigwe. 2000).
Also
Lawler, (1998) maintained that students are task or problem centered in their
orientation to learning. Students want to see how what they are learning apply
to their life unlike the study of geometrical proofs that are abstract in
nature. Therefore, technology based instruction is more effective as it uses
real life examples or situations this students may encounter at home or in
other places.
However,
teaching and learning solid geometry at senior secondary is not an easy task.
Due to its nature, it is becoming increasingly difficult for mathematics
teachers to teach this concept (geometry) and for students to learn it
successfully (Sanni, 1999). He further mentioned that representation of
3-dimensional objects, teaching basic rules and axioms in geometry,
unavailability of practical instructional materials and the use of
inappropriate instructional techniques are part of the problems plaguing the
study of geometry in senior secondary schools in Nigeria.
1.2
STATEMENT OF THE PROBLEM
The way mathematics instructions are
delivered in schools has continued to be a cause for concern. Students
achievement in mathematics has continued to decline.
The examiner’s report of WAEC has consistently
shown that students dread some important aspects of mathematics. These aspects
are mostly related to solid geometry. (Oyedeji, 1987, Fagbola, 1984)
Possible causes of this behavior include:
1. The
way mathematics instructions are delivered.
2. Lack
of teaching aids in solid geometry
3. Teachers
not being able to teach the topic due to lack of lack of deep knowledge in the
subject area.
4. Lack
of interest by students.
1.3
PURPOSE OF THE STUDY
This study intends to find out major
causes, problems and issues involved in ineffective teaching and learning of
solid geometry and how best to tackle this problem.
It has the following objectives:
1. Find
out difficulties faced in learning solid geometry in some selected senior
secondary schools.
2. Identify
factors responsible for these difficulties faced by teachers in teaching.
3. Factors
responsible for these difficulties faced by students in solving problems of
solid geometry.
4. Identify
solutions to problems discussed during the course.
5. Recommend
solutions to difficulties encountered in solving problems in solid geometry.
1.4
SIGNIFICANCE OF THE STUDY
The identification of the difficulties
confronting students in learning sets and the solutions that are suggested in
this study will be of tremendous benefits to the following groups of people
1. Students
2. Teachers
3. School
administrators
4. Future
researchers.
5. The
Nation.
1. Students
This
sudy will help students in developing conceptual and procedural strategies in
overcoming the challenges or difficulties in learning solid geometry. This will
translate into a better understanding of the subject and also impact positively
on their future performances in both local and international examinations.
2. Teachers
This study will help teachers appreciate
students thinking and problem solving strategies in order to design effective
teaching strategies that would facilitate maximum learning of solid geometry. It
will also guide them to be flexible in their teaching to accommodate the
diverse needs of the learners.
3. School Administrators
It will help school administrators when
initiating curriculum reforms that would be suitable for the needs of students
in Senior Secondary School.
4. Future researchers
The results of this study will provide
insights for conducting similar researches in similar or related components of
mathematics.
5. The Nation
The findings of this study will help the
nation in promoting mathematical literacy in general and solid geometry in
particular.
1.5
SCOPE AND LIMITATIONS OF THE STUDY
This study will identify the
difficulties that students encounter when solving solid geometry in the Senior Secondary School one (SSS I)
mathematics curriculum. It will also suggest solutions in surmounting those
difficulties. Due to financial constraints the study will be limited to
selected schools in Ojodu and Shomolu local governments of Lagos state.
Another limitation of the study is that
the students used in this study were not randomly selected.
1.6
RESEARCH QUESTIONS
This study intends to provide answers to
the following questions:
1. What
is the level of performance of students in S.S.S 1 and 2 in solid geometry?
2. What
are the challenges faced in the solving of problems in solid geometry in senior
secondary schools?
3. What
factors inhibits the effective learning of solid geometry at S.S.S 1 and 2?
4. In
what ways can the difficulties or problems in learning solid geometry be
addressed?
1.7
INSTRUMENTS USED FOR THE RESEARCH
1. Questionnaires
2. Written
and objective tests
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