ABSTRACT

This study was designed to explore the effects of Origami instructional approach on JS I students’ achievement, interest and retention in geometry. Six research questions and nine hypotheses were formulated to guide the study. The study adopted a quasi-experimental non-equivalent control group design and was restricted to Nsukka local Government Area of Enugu State. Two Co-educational Secondary Schools were drawn for the study using random sampling technique. Out of the two selected schools one was randomly assigned to Origami Group (OG) while the other one to the Control Group (CG). A sample of 101 JS one students was involved (65 female and 36 male students). The instruments for data collection were geometry achievement test GAT) and geometry interest scale (GIS). Data collected were analyzed using mean, standard deviation and analysis of covariance (ANCOVA). The result of the study revealed that use of Origami in teaching geometry to junior secondary school students enhanced their achievement, interest and retention in geometry. The study also revealed that the use of Origami had no statistically differential effect on male and female students’ achievement, interest and retention. Furthermore, there was no significant interaction between gender and instructional approach on students’ achievement and interest. On the other hand, the study revealed that, there was a significant interaction effect between gender and instructional material on retention of the concepts taught during the study. Based on the findings, the researcher recommended that use of Origami should be adopted in the teaching of geometry (mathematics) in primary, secondary, and tertiary levels of education system. It was also recommended that seminars, workshops and conferences should be mounted by professional bodies, federal and state ministries of education on the use of Origami for mathematics teachers, students and others. This will enable the mathematics educators, serving teachers, students and all to benefit from such an approach.

CHAPTER ONE

INTRODUCTION

Background of the Study

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.

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

It is a well-known fact that the subject of mathematics affects all aspects of human life and that the social, economic, scientific and technological aspects of man are centered on numbers. Being the basic skill that underlies all scientific and technological skills, mathematics is generally seen as the language of most branches of science and technology. It is closely related to other school subjects that deal with numeration, variation, graphs, fractions, logarithms and indices, algebraic processes, solution of equation, as well as areas and volume computations. Expectedly, a sound background in basic mathematical principles has become a pre-condition for progression to tertiary education and thus one of the key requirements for a gainful professional employment. Among the other branches of mathematics, mensuration, which comprises geometrical and trigonometrical concepts of the JSS Mathematics Curriculum, represents the most difficult area (Kurumeh, 2006; Chief examiner’s report, 2006). Even though various instructional techniques have been adopted by teachers to improve students’ achievement in mathematics, very few of these appear to have focused on the teaching of geometry. Traditional teaching aids for mathematics include chalk boards, coins, and legos, while visual aids and drawing of pictures have been used in teaching of geometry. Helpful as these measures may be, they have not proved to be effective for the improvement of students’ performance in mathematics. There is therefore need to explore the effectiveness of other alternative teaching strategies, such as origami, in the improvement of students achievement, interest and retention in geometry. Therefore the problem of the study put in question form is “Would the use of origami as instructional approach/materials enhance students’ achievement, interest and retention in geometry?”

Purpose of the study

The purpose of this study is to determine the effect of origami on students’ achievement, interest and retention in geometry.

Specifically, this study sought to determine:

1. Effect of origami on students’ achievement in geometry.
2. Effect of origami on the interest of students in geometry
3. Effect of origami on students’ retention in geometry.
4. Influence of gender on students’ achievement when exposed to origami.
5. Influence of gender on student interest when exposed to origami.
6. Influence of gender on students’ retention when exposed to origami.

Significance of the study

Research results abound on the teaching of mathematics most of which are based on pedagogical theories applicable to the teaching and learning of mathematics. This implies that, the search for any new and relevant methods of teaching mathematics is expected to be based on a particular pedagogical theory. Consequently, this study uses Piagetian constructivist theory of learning which emphasizes the teachers’ ability to present instruction in such a way that students are actively involved. Piaget also emphasizes on the use of actual objects to teach young children up to the age of twelve or thirteen, for without it, the subject will become very abstract. The study also took into consideration blooms taxonomy of education in sequencing instruction. This was to ensure that the students’ interest is made proficient in the three domains of cognitive, affective and psychomotor. The implication of this is that if this instructional material is found appropriate, both the teacher, students, curriculum planners, textbook authors, the government and the society at large will benefit.

The outcome of this study will help teachers to present geometry in JS1 in such a way and manner that the student will understand it, appreciate it and participate in solving such problems as properties of plane shapes, angles and triangles, bisecting of lines without much difficulty. More so, it will enable the teachers to discard the use of the conventional instructional approach which do not help to reduce abstraction. In other words, the result of the present study will help mathematics teachers to adjust their teaching strategies.

It is hoped that the finding of this study will enable students’ show much interest in the study of geometry, thereby increasing overall achievement in mathematics. This study can be seen as a concrete step towards the attainment of the global goal of mathematics for all. The use of origami has the potentials of creating uniform conditions for both boys and girls in the learning of geometry. In this way, students irrespective of their sex can have unimpeded access and participation in geometry and mathematics at large.

The outcome of this present study could also lead to the attainment of cognitive skills which can be applied to other areas. As a result, more students may be going for mathematics courses which will lead to scientific and technological advancement of the country.

The result of this study is expected to motivate the curriculum planners and government to

1. incorporate origami into the pre-service training of mathematics teachers,
2. sponsor further researches on the effects of origami in other aspects of science and technology;

The outcome of this study when made available to ministries of education can generate interest and need for workshops on how to use this aspect of mathematics.

The findings of the study would provide authors of secondary school text books with information on the efficacy of origami. This will reduce abstraction in their presentation of geometry topics in their textbooks. More so, the findings may also reveal the activity-oriented nature of origami and thus provide additional useful mathematical instructional strategy/material for the teaching and learning of geometry.

The findings of this study would also help the society in the sense that, more students would be achieving higher in mathematics. This in turn will reduce the rate of failure in mathematics at both internal and external examinations, thus, making the parents happy.

Scope of the study

This study focuses on geometry, the aspect of mathematics where Junior Secondary School students have been shown to record the lowest achievement (Kajuru, 2006). The study is conducted using JSS-1 students in the Nsukka Local Government Area of Enugu State. In terms of content coverage, the topics selected include:

1. Plain shapes and their properties
2. Angles between lines and sum of angle on a straight line
3. Sum of angles in a triangle
4. Construction of triangle, and
5. Construction of parallel and perpendicular line

These topics are as provided in Junior Secondary-one Mathematics curriculum (FME, 2007)

Research Questions

The following research questions guide the study:

• What is the mean achievement score of students taught geometry, using origami and those taught using the conventional approach?
• What is the effect of gender on the mean achievement scores of students taught with origami in the geometry achievement test?
• What is the mean interest scores of students taught with origami and those of the control group?
• What is the effect of gender on the mean interest scores of students taught with origami?
• What is the mean retention scores of students taught geometry using origami
• What are the mean retention scores of male and female students taught geometry using origami?

Hypotheses

The following null hypotheses (HOs) were formed to guide the study and were tested at 0.05 level of significance.

HO₁: There is no significant difference in the mean achievement scores of students taught geometry using origami and those taught using conventional approach.

HO₂: There is no significant difference in the mean interest scores of students taught geometry using origami and those taught using conventional approach.

HO₃: There is no significant interaction effect of origami and gender as measured by the geometry achievement test.

HO₄: – There is no significant difference in the mean achievement scores of male and female students taught geometry using origami.

HO₅:  There is no significant difference in the mean interest scores of male and female students taught geometry using origami.

HO₆:  There is no significant interaction effect of origami and gender as measured by the geometry interest inventory or scale.

HO₇: There is no significant difference in the mean retention scores of students taught geometry using origami and those taught using the conventional approach.

HO₈: There is no significant difference in the mean retention scores of male and female students taught geometry using origami.

HO₉: There is no significant interaction effect of origami and gender as measured by the geometry retention test.

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