TABLE OF CONTENTS
TITLE PAGE i
APPROVAL PAGE ii
CERTIFICATION iii
DEDICATION iv
ACKNOWLEDGEMENT v
ABSTRACT vi
TABLE OF CONTENTS viii
LIST OF TABLES xi
CHAPTER ONE 1
INTRODUCTION 1
Background of the Study 1
Statement of the Problem 7
Purpose of the study 8
Significance of the study 8
Scope of the study 10
Research Questions 11
Hypotheses 11
CHAPTER TWO 13
LITERATURE REVIEW 13
Review of Empirical studies 13
Conceptual Framework 14
Current Status of Teaching and Learning of Mathematics/Geometry: 14
Concept of Instructional Materials and its Importance 18
Classification of Instructional Materials 21
The Concept and Perspective of Origami 25
Interest and Achievement in Geometry 38
Retention and Achievement in mathematics/Geometry 39
Theoretical Framework 48
Learning theories and the use of Instructional Materials 48
Piaget’s theories of learning: 48
Brunner’s theories of learning 52
Ausubel’s theory of learning……………………………54
Empirical Studies 58
Studies on Achievement in Mathematics 58
Origami Skills and Achievement in Mathematics/Geometry 65
Interest as a Factor in Geometry Achievement 66
Retention as a Factor in Geometry Achievement 69
Gender as a Factor in Students’ Achievement in Geometry 72
Summary of Literature Review 78
CHAPTER THREE 81
RESEARCH METHOD 81
Design of the Study 81
Area of Study 82
Population of the Study 82
Sample and Sampling Technique 82
Instrument for Data Collection 83
Validation of the Instrument 85
Reliability of the Instruments 86
Treatment Procedure 88
Control of Extraneous Variables 89
Method of Data Collection/ Scoring 91
Method of Data Analysis 91
CHAPTER FOUR 93
RESULTS 93
CHAPTER FIVE 105
DISCUSSION OF FINDINGS, CONCLUSION, IMPLICATIONS AND RECOMMENDATION AND SUMMARY 105
Discussion of Findings 105
Conclusion 111
Educational Implications of the Study 112
Limitations of the Study 113
Suggestions for Further Study 114
Summary of the Study 114
REFERENCES 116
APPENDICES 127
LIST OF TABLES
Tables Page
1 Mean Achievement scores and standard Deviation of Experimental and control groups in Pre-test and post-test (GAT)……………….. 93
2 The mean Achievement scores of Gender on experimental groups in PRETEST and POSTTEST (GAT)..…………………………………….94
3 Mean scores and standard Deviation of Experimental and control group in Pre-test and Post-test (GIS)….………………………………………… 95
4 The mean scores of Gender (Sex) on Experimental groups in Pre-test and Post-test (GIS).……………………………………………………………96
5 Mean Retention scores of students in Experimental and control groups of (GRT)……97
6 Mean Retention scores of male and female students in the Experimental group of (GRT)……………………………………………………………………………..….. 98
7 Two-way Analysis of covariance of the control and Experimental group students on geometry Achievement Test Due to Method, Gender and interaction. (For hypotheses 1, 2 and 3)..…………………………….…… 98
8 ANCOVA results of the control and experimental group students on geometry interest scale due to gender; treatment and interaction. (for hypotheses 4, 5 and 6)…….100
9 Analysis of covariance (ANCOVA) of the control and Experimental group
students on geometry Retention Test due to method, gender and Interaction (for
hypotheses 7, 8 and 9).………………………………………………………………102
CHAPTER ONE
INTRODUCTION
Background of the Study
The broad aim of secondary education in Nigeria is to prepare the individual for useful living within the society and for higher education (Federal Ministry of Education 2004).The achievement of this objective requires sound background knowledge of the subject of mathematics, the subject that deals with the relationships among numbers, shapes, and quantities.
Among other physical science subjects, mathematics is the backbone in the National capacity building in science and technology (Ogbonna, 2007). It equips the individual with the capacity to, among others, enumerate, calculate, measure, collate, group, analyze and relate quantities and ideas. In Arts and Humanities, mathematical concepts such as measurement, enlargement, symmetry, sequence, proportion, angle of elevation and depression, provide the baseline for the better understanding of some related universal concepts. It is therefore not a surprise that Mathematics is one of the compulsory core subjects which students must offer and pass at credit level, at the secondary level of education, as a pre-requisite for a useful living within the society and for higher education.
Despite the acknowledged importance of mathematics in national development, and the tremendous efforts being made by educationists and other stakeholders to improve the teaching and learning of the subject in secondary schools in Nigeria, students’ achievement in the subject still remains very low. The statistics released by the National Examination Council (NECO) and West African Examination Council (WAEC) show that less than 40% of candidates who sat for mathematics in the past ten years (2000-2010), obtained a credit pass, at both the Junior- and Senior Secondary levels respectively.
This trend negates the national drive for a sound social and technological development and needs therefore be halted.
The observed low performance of students in Mathematics has been traced to various factors, including weak foundation, especially in geometry, at the formative stage of the students’ education (Kurumeh, 2006), mathematics phobia and lack of interest (Amazigo, 2000), inadequate/ineffective course-delivery strategies adopted by teachers (Ogbonna, 2004; Nzewi, 2000), as well as poor reading/comprehension (poor retention) by students (Agwagah, 1993; Ogbonna, 2007). Many teachers still follow the traditional approach that relies heavily on textbooks, charts and diagrams (Agommuo, 2009). In the words of Nzewi (2000), effective teaching is synonymous with effective learning/high achievement. Mathematics teachers therefore, have the professional responsibility to help, develop and maintain the interest of students in mathematics by exploring and employing modern concepts and instructional materials that will make their course deliveries more meaningful, effective, practical, productive and understandable.
Instructional resources, according to Offorma (1997) and Eya (2004), stimulate learners’ interest and help both the teacher and the learner to overcome physical limitation during presentation of the subject matters. According to Usman and Obidua (2005), the use of appropriate instructional material in the classroom enhances motivation, improves comprehension, encourages effective participation, captures students’ interest and thus enhances learning. Both federal and state governments have since adopted these innovative research findings and recommended the use at primary and secondary school levels, of practical teaching method and instructional material.
One aspect of mathematics that easily lends itself to the utilization of instructional materials is geometry (Akinsola, 2000), the branch of mathematics that deals with shapes and sizes. Just as arithmetic deals with experiences that involve counting, so geometry describes and relates experiences that involve space. Basic geometry allows the determination of properties such as the areas and perimeters of two-dimensional shapes and the surface areas and volumes of three-dimensional shapes. People use formulas derived from geometry in everyday life for tasks such as figuring how much paint they will need to cover the walls of a house or calculating the amount of water a fish tank holds.
The visual nature of geometry makes it more amenable to teaching aids, than the other branches of mathematics. Most of the geometrical figures (square, rectangle, triangle, circles and other polygons) can be reproduced by origami (the art of paper folding) and be brought to the classroom to demonstrate the topic. Most of the shapes can also be commercially produced to ensure availability to large number of students.
Origami (the art of paper folding), is widely used in developed countries to teach children to think logically and to follow directions. According to Wu Joseph (2004), the widespread popularity of modern origami grew mainly out of the efforts of one man, Japanese origami master, Akira Yoshizawa, who in the early 1950s began to publish books illustrating how to fold nontraditional models of his own invention. Akira also developed a set of origami diagram symbols that allow a person who has invented a new figure to show others how to arrive at the same form. Virtually all origami books now use Yoshizawa’s diagram symbols. Exhibitions of Yoshizawa’s work around the world introduced origami to many people and led to the formation of origami associations, including the Origami Center of America (now Origami USA) and the British Origami Society.
There are different types of origami folds. These include:
Basic skills
Simple compound folds
Origami bases
Mid-intermediate skills and
High-intermediate skills
Basic skills for instance, are subdivided into valley fold, mountain fold, pleat fold and blintz fold.
Valley fold: involves folding the origami paper in half to form a “V”.
Mountain fold: is an upside-down valley fold.
Pleat fold: involves several mountain and valley folds back to back and evenly spaced.
Blintz fold: involves folding the corners into the center to create a smaller square.
Origami Bases on the other hand consist of fish base, water bomb base, preliminary fold, bird base and frog base folds etc. When one folds the traditional water bomb base, for instance, then one has created a crease pattern with eight congruent right triangles and every reverse fold (such as the one to create the birds’ neck or tail) creates four more triangles. In fact, any basic fold has an associated geometric pattern. For the purpose of this study, Origami basic skills were employed.
The folding skill is so practical that it creates strong feeling of curiosity in young children. The capacity of the folding skill to arouse curiosity in children makes it a potential useful teaching strategy. This is because interest is a necessary condition for achievement, as students tend to learn more efficiently those things that interest them than those that do not (Agwagah (2008); Ogbonna (2004)).
Another factor of learning is retention, the ability to remember things. Among the attributes of retention that are closely related to success, are the power to recall (i.e., memory) and to recognize (Ogbonna, 2007). Memory is the capacity to retain an impression of the past experiences. Memory, according to Ogbonna (2007), is classified based on duration, nature and retrieval of perceived items. The main stages in information and retrieval of memory from an information processing perspective are:
Encoding (processing and combination to received information).
Storage (creation of a permanent record of encoded information).
Retrieval (calling back the stored information in response to some case for use in process or activity).
From the above discussion, it is obvious that the ability to retrieve an information or learnt item depends so much on what has been retained in the memory. Ausbel (1968) asserted that retention may be difficult if the material presented cannot be related to the existing cognitive structure. Cognitive structure of the individual according to Ausbel is defined as all the information that the individual has about any particular area of experience. Ausbel went further to explain that when students study new materials presented to them, relate the new information to what they know, and organize it into more complete cognitive structure they are engaging in meaningful reception learning that enhances retention. The implication of this is that any instructional material or approach which is effective in making students retain concepts in mathematics, can as well help students perform excellently in mathematics. In view of this, retention is an important variable worth exploring in this study.
Another factor of interest in the current research is gender and its influence on achievement. In the past, there has been a general view that males perform better than females in mathematics. Alio and Harbor Peters (2000) experimented on the Polya’s problem solving techniques and discovered that males have a higher achievement than females in mathematics. Ozofor (1993), however, discovered that male and female students perform equally in mathematics. This view was supported by Ogbonna (2004), who used the Invitation, Exploration/Discovery, Proposing Explanation and Solution, Taking Action (IEPT) constructivist instructional approach to show that there is no significant difference between the achievement of male and female students in mathematics. In a similar study, Adekanye (2008) established that girls perform better than boys in mathematics.
In view of the apparent conflicting results on the influence of gender on students’ achievement in mathematics, coupled with the acclaimed role of mathematics in technological development, there is need to carry out further research to resolve the controversy, by using an instructional strategy that will enhance achievement, foster interest and retention. This can be achieved by the use of appropriate instructional technique that has the capacity to provide equal learning opportunity to both males and females.
Though various strategies have been adopted in the past, for the teaching of geometry, their effectiveness has remained in doubt, as students’ achievement in this aspect of mathematics still remains low. This is why the current research focuses on a new and alternative technique –application of the art of paper-folding (origami), to find out how it can influence students achievement, interest and retention in geometry.
Statement of the Problem
