**
**

**THE EFFECT OF INTERACTIVE GEOMETRY SOFTWARE ON SENIOR SECONDARY SCHOOL STUDENTS UNDERSTANDING OF, AND MOTIVATION TO LEARNING GEOMETRY.**

**A CASE STUDY OF IKERE LOCAL GOVERNMENT**

**BY**

**EMINGHOTEI BUNA TINATEI**

**A RESEARCH PROJECT SUBMITTED TO THE DEPARTMENT OF MATHEMATICS EDUCATION, FACULTY OF EDUCATION, UNIVERSITY OF NIGERIA, NSUKKA**

**IN PARTIAL FULFILMENT OF THE REQUIREMENT FOR THE AWARD OF THE DEGREE OF BACHELOR OF SCIENCE IN MATHEMATICS EDUCATION**

**MAY, 2016**

**TABLE OF CONTENTS**

Title page i

Certification ii

Approval page iii

Dedication iv

Acknowledgements v

Table of contents vii

Abstract xi

**CHAPTER ONE**:

**INTRODUCTION**

Background to the Study 1

Statement of the Problem 8

Objectives of the Study 9

Research Questions 9

Research Hypotheses 10

Significances of the study 10

Delimitation of the Study 11

Organization of the Study 11

Definition of Terms 11

**CHAPTER TWO:**LITRATURE REVIEW

Conceptual Framework 13

Concept of Geometry 14

Effects of ICT on the Teaching and Learning of Plane
Geometry 17

Causes of Learning Difficulty in School Geometry 18

Concepts of Mathematics 20

Effects of IGS on Students Conceptual Understanding
Mathematics 21

The Use of Technology in the Teaching of Geometry 22

Theoretical Framework 27

**CHAPTER THREE: METHODOLOGY**

Research Design 29

Population of the Study 30

Sample and Sampling Techniques 30

Instrument for Data Collection 30

Validity of Instruments 31

Reliability of the Instrument 31

Administration of the Instrument 32

Method of Data Analysis 32

**CHAPTER FOUR: RESULT AND DISCUSSION**

Data Analysis 33

Hypotheses Testing 35

Discussion 38

**CHAPTER FIVE: SUMMARY, CONCLUSION AND RECOMMENDATIION**

Introduction 40

Summary 40

Conclusion 41

Recommendations 43

References 44

Appendix I:
Questionnaire 55

Appendix II:
Pre-test Questions 57

Appendix III: Post-test Questions 59

**ABSTRACT**

The
study sought to find out the effect of the use of interactive geometry software
(IGS) on Secondary school students’ conceptual understanding of, and their
motivation to learn, plane geometry. It investigated ways in which IGS provides
support for student-centred learning in a geometry class. The study was carried
out in 3 secondary schools, 90 students in total, 30 students from each school.
Purposive sampling was used to sample the school, while simple random sampling
was used to select students to respond to the interview guide.The participants
wrote pre-test after which IGS was used to teach the Experimental group to
improve students’ conceptual understanding. The participants then wrote post-test
as well as answered questionnaires to ascertain their experiences about the
effect of IGS on their motivation and understanding. In the pre-test, the
findings indicated that the Experimental group had a mean score of 20.11, while
the Control got 18.07.However there is no significant difference between the
post-test score of students exposed to IGS and those taught using textbook. The
t-test results revealed that t-calculated (0.826) was less than the t-test
critical t-value (1.987) at p<0.05. The findings indicated no significant
difference between the post-test score of students exposed to IGS and those
taught using textbook. The findings also
showed that students were highly motivated to learn geometry, because they
enjoyed the IGS lessons. It further revealed that the use of IGS supported
student-centred learning in a number of ways; the lessons were activity based,
very interactive in nature, students worked in groups and learn collaboratively
through discussions.

This chapter provides an introduction to
the research study. The introduction includes the background of the study,
statement of the problem, the purpose of the study and research questions which
guided the study. It further highlights the significance, the delimitations and
organization of the study.

## 1.1 Background to the Study

Development in science, technology and mathematics is
increasingly gaining recognition as one of the most reliable indicators for
determining the socio-economic and technological development among nations
(Atebe, 2008; Anne and Obinna,2010 and UNESCO, 2012). For example, Wasagu
(2005) reported that, the impact of Science, Technology and Mathematics
Education (STME) on the economy of Japan today has made it not only the second
largest economy but a threat to even the world‟s strongest economy, the United
States of America (USA) which has remained the most successful in harnessing
scientific and technological development for the attainment of its national
objectives. In modern societies world over, including Nigeria, there is strong
emphasis on the need for the provision of good qualitative Science, Technology
and Mathematics Education. It is in this regard that, Nigerian government in
its National Policy on Education (FRN, 2004) made Mathematics a compulsory
(core) subject of study at both primary and secondary school levels. Indeed,
for a candidate to gain admission into science and science- related courses in
tertiary institutions, he/she must have credit pass in Mathematics. This is
because Mathematics plays a pivotal role in science and technology advancement.
Musa (2010) buttressed this in his study that, Mathematics provides the laws,
formula and the theories that empower the scientific and technological
developments. Therefore, the study of Mathematics by individual is essential
because it provides avenue for thinking, developing scientific structure,
drawing conclusions as well as solving life problems. Thus, it has useful links
to many other fields of human endeavor.

However, as useful as this
subject is, there is ample evidence of continued low performance of students in
both the standardized and teacher made examinations, (Benjamin and Agwagah,
2006). For example, both national and international evaluation shows that, on
completion of basic education, many pupil‟s mathematics knowledge and
competences fall short of the expected level. More over, the disparities
observed between and within the countries give course for concern (UNESCO,
2012).Also in a related report a comparative study of Mathematics and Science
performance of students around the world showed that United States students‟
mathematical achievement lagged behind those of several other countries.
Specifically in geometry content area, United States students achievement was
bottom third of all countries tested. 38 countries outperformed the US in
geometry with Japan at the top with a score of 575 and international average of
473 in geometry, (Unal, 2013). Also in Nigeria, results from examination bodies
like West African Examination Council (WAEC) and National Examinations Council
(NECO) reports indicate students‟ low performance in Mathematics as contained
in the chief examiner‟s report, (2000, 2002 and 2005). Going by the above
reports, Pussey (2003) and Atebe, (2008) opined that, performance in
Mathematics is a good indicator of performance in geometry specifically. Many
reasons have been advanced for this poor state of students‟ performance in
Mathematics in general and geometry in particular. Some researchers viewed
teachers‟ subject matter incompetence as a contributing factor, (Benjamin and
Agwagah 2006; Unal, 2005). Others like Ishaku (2003); Tahir (2006) attributed
this consistent poor performance in Mathematics by the students to Mathematics
teachers‟ lack of necessary skill and competence in both the content and
delivery.

Development in almost all areas of life
is based on effective knowledge of Science and Mathematics. There cannot be any
meaningful development in any area of life without knowledge of Science and
Mathematics. It is for this reason that the education systems of countries that
are concerned about their development put great deal of emphasis on the study
of mathematics. It is therefore not surprising that the government of Nigeria
made mathematics a core subject at both the Basic and Secondary levels of Education
in Nigeria. The Senior secondary School syllabus in Nigeria is based on the
notion that an appropriate mathematics curriculum results from a series of
critical decisions about three inseparably linked components: Content, Instruction
and Assessment (Olayemi, 2010). Plane geometry is one of the major content
domains the mathematics curriculum covered to promote the acquisition of
mathematical knowledge and skills for life. Plane geometry in the Senior
Secondary School mathematics curriculum covered angles of a polygon,
Pythagoras’ and circle theorems including tangents (Olayemi, 2010).

Geometry is the study of shapes and
space. Ibu, J.E, Ngban, A.N & Maliki,
A.E. (2011) defined geometry as a branch of
mathematics that provides a rich source of visualization for understanding,
algebraic, arithmetic and statistical concepts. Geometry appears naturally in
the structure of the solar system, in geological formation of some rocks and
crystals, in plants and flowers, and even in animals. It is also a major part of
our synthetic world such as art, architecture, cars, machines, and virtually
everything humans create. The knowledge of geometry is so important that its
utility is needed by everyone. Fortunately geometry is well represented in the
Nigerian mathematics curriculum at all levels of education.

The applications of geometry are diverse
and universal in all aspects of life. In the school, studying geometry provides
many foundational skills and helps to build logical thinking skills, analytical
reasoning and problem solving among others. Geometry has an applicable link to
many other topics in mathematics, specifically Measurement. Consequently, a
very good grip of the knowledge of geometry prepares students to adequately
respond to the challenges of further mathematics in life. In the place of work,
geometry is used by architects, engineers, physicists, pilots, captains of
ships and land surveyors. More importantly, a teacher without a good knowledge
of geometry cannot adequately convey the concepts and the beauty that comes
along side its teaching to students.

In order to draw the full benefits of
geometry in the mathematics curriculum, classroom instructions should aim at
enhancing students’ geometric thinking. Improving students’ geometric thinking
levels is one of the major aims of mathematics education. This is because
geometrical thinking is an important tool in many scientific, technical and
occupational areas. One of the best descriptions of students’ geometric
thinking level on two-dimensional shapes is the Van Hiele theory of Geometric
Thinking (Batista, 2007). Teaching geometry at the Senior High level should be
done in ways that promotes geometric thinking.

However, Mehdiyev (2009) stated that in
Azerbaijan the teaching and learning of geometry tend to focus on having
students learn a list of definitions and the properties of shapes. According to
Mehdiyev, textbooks for use at the Senior High Schools provided only pencil and
paper illustrations that are not comprehensive, because, they lack the visual description
of a complete interactive process needed for the construction of geometrical
concepts. These illustrations, often lead to memorization and does not target
development of conceptual understanding. This situation is not different from
what is happening in Nigerian schools. Fredua-Kwarteng and Ahia (2005) observed
that the teaching and learning culture of mathematics in Nigeria schools have the following characteristics:
Students learn mathematics by listening to their teachers and copying from the
chalkboard rather than asking questions for clarifications and justification.
Furthermore, students learn mathematics by regurgitating facts, theorems or
formulas instead of probing for meaning and understanding of mathematical
concepts. Students in the learning process hardly ask the logic or philosophy
underlying those mathematical principles, facts, or formulas. Consequently,
students learn mathematics as a body of objective facts rather than a product
of human invention.

Instead of memorising properties and
definitions, Battista (2007) suggested that students should be made to
personally develop meaningful geometric concepts and ways of reasoning that
enable them to carefully analyze spatial problems and situations. This calls
for an alternative teaching approach where Information and Communication
Technology (ICT) can be used to enhance students’ thinking and problem-solving
skills.

One change that has irresistibly
affected education institutional delivery globally has been the introduction of
technology into society which results in the explosion of computers into
schools. Technology in schools, particularly the computer with its
communicative abilities, has become the focus and substance of strategic
planning in shaping national economies. Governments of both developed and
developing nations have recognized, as a matter of urgency, the role of
computer technology in redefining their economic activities (World Bank, 1998).
This then calls for the integration of ICT into the teaching and learning situation
in the world over. The integration of ICT into education is recognized as:
providing opportunities for developing skills that has the potential to
transform pedagogical practices, and for reforming curricula (Roschelle, Pea,
Hoadley, Gordin, & Means, 2000). Recent advancement in communication
technology has contributed immensely to minimize the effect of distance in
education. Roblyers (2006) aptly describes the situation as the “death of
distance”. She writes that the death of distance has given new life to
education.

From the discussions above, the
researcher observed that ICT is a powerful tool that can accelerate the
attainment of educational goals. According to Butzin (2001), the focus of ICT
in education should be on integrating technology into teaching and learning and
must not be predicated on learning. This entails the application of ICT tools
to facilitate the teaching and learning situation in the school. The use of ICT
as suggested by Reynolds, should supplement classroom activity by accessing
existing information and knowledge, rather than as an integral part of
pedagogical practice Ibu, J.E, Ngban, A.N & Maliki, A.E. (2009)..

In Nigeria, the goal of ICT is to enable
every Nigeria to be able to use ICT tools and resources confidently and creatively
to develop the skills and knowledge needed to achieve personal goals and be
full participants in the global economy by 2015 (MOE, 2006). The ICT for
accelerated development policy document outlined some guiding principles
towards the integration of ICT into classroom practice. The policy stipulated
that a curriculum reform is necessary for effective integration and utilization
of ICT in the classroom. It encouraged teachers to explore and use ICT tools in
teaching to improve students’ learning in order to develop skills necessary for
the competition in the knowledge `economy and information society. Exploration
of ICT is crucial to provide best experiences for educators to incorporate this
new technology into teaching (Ibu, J.E, Ngban, A.N & Maliki, A.E. (2009), as
the positive impact of ICT depends on how teachers use ICT in their teaching
and learning activities (Galbraith, 2006). Consequently, efforts are being made
to integrate ICT into the Ghanaian mathematics curriculum and researchers are
calling for the adoption of strategies that will make ICT integral to teaching
and learning processes (Assuah, 2010; Yidana & Amppiah, 2003; Dontwi,
2001). Achieving this requires extensive research that will identify strategies
applicable in the Ghanaian classroom.

Mehdiyev (2009) stated in his study on
students’ learning experiences using dynamic geometry software that, the
teaching and learning of geometry in Dynamic Geometry Environment (DGE)
established positive effects on students’ conceptualisation of Mathematics
concepts. The DGE encouraged students to discuss, interact with each other and
explore the content collaboratively. The students are not coerced to accept the
geometrical content with absolute certainty. Rather, students are motivated to
learn in a student-centred dynamic environment. Mehdiyev later in his research
described the traditional teaching and learning of geometry at secondary
schools as “teacher-centred”, which is at variance with learning geometry in a
DGS environment. Personal experience and empirical research (Mereku, 2010)
indicated that teaching in the Ghanaian classroom is teacher-centred. Thus the
student is made a passive listener in the learning process, which makes the
student deficient in mathematical analysis and logical reasoning. Therefore,
Mathematics achievement in Kanton Senior High School is poor. It appears that
something is wrong with the way mathematics is learnt and assessed in Ghana.
The Trends in International Mathematics and Science Study (Asabre-Ameyaw &
Mereku, 2009; Anamuah-Mensah, Mereku & Ghartey-Ampiah, 2008;
Anamuah-Mensah, & Mereku, 2005), report that Ghana remained second from the
bottom in 2003, 2007, out of the number of countries that participated in the
examination. The reports stated that students’ performance in geometry was the
lowest in the five domains the test covered. Also National Educational
Assessment (NEA), which is an indicator of the overall national status of
Mathematical achievement in the primary school system in Ghana. The NEA
reported that mean scores percent of primary 3 and primary 6 pupils in
mathematics respectively of 41.8% and 39.6% was far below the average of 50%
(CRDD, 2009). In Addition, the West African Examination Council Chief
Examiner’s annual reports for the SSSCE & WASSCE from 2003 to 2006 observed
that candidates were weak in Geometry of circles and 3-dimensional problems.
The reports repeatedly indicated that most candidates avoided questions on
3-dimensional problems. Where they attempted geometry questions, only few of the
candidates showed a clear geometrical understanding of the problem in their
working process.

Even though there are some research
works on the integration of ICT into the teaching and learning of Mathematics
in Ghana (Assuah, 2010; Yidana & Amppiah, 2003; Dontwi, 2001), little is
known about the use of interactive geometry software in the teaching and
learning process in the Ghanaian classroom. This study is therefore developed
to explore the teaching and learning of geometry in an Interactive Geometry Environment
(IGE) in Ghanaian classroom using Geogebra.

## 1.2 Statement of the Problem

In recent
times, the teaching and learning of Mathematics in secondary schools in Nigeria
has witnessed a great setback with students, irrespective of sex, performing poorly
and showing lack of interest. This is evident in the performance of the
students in Basic Education Certificate and Senior Secondary Certificate
Examinations. Mathematics is a very important subject, yet it is a subject that
many students fear, fail and possibly dislike. The problems have been
attributed partly to lack of instructional materials

especially the
modern educational facilities like Information and Communication Technology
(ICT). Other problems include little or no motivation for teachers and
students, and overcrowded classes. The aforementioned could be adversely
affecting the teaching and learning of Mathematics in Nigerian secondary
schools. GeoGebra, an ICT Mathematics software package for teaching Geometry,
Algebra and Calculus has been developed by Markus Hohenwarter in response to
this lack, but its effect on students’ learning outcomes such as performance
and attitude to Mathematics has not been established in Nigeria; hence this
study

## 1.3 Objective of the Study

The
major objective of this study is to investigate the effect of interactive
geometry software on secondary school students.

The
specific objective is to find out:

1.
The effect of
interactive geometry software (IGS) on
the development of Secondary School students’ conceptual understanding of geometry

2.
The effect of the use
of interactive geometry software (IGS )on Secondary School students’ motivation to learn geometry

3.
Ways in which interactive
geometry software IGS provides support for student-centred learning in a
geometry class

## 1.4 Research Questions

In pursuance of the purposes stated
above, the following research questions were formulated to guide the study:

1.
To what extent does the
use of interactive geometry software (IGS) affect Secondary School students conceptual understanding of
geometry?

2.
How does the use of interactive
geometry software (IGS) motivate Secondary School students to learn geometry?

3.
In what ways do
interactive geometry software (IGS) support student-centred learning in a
geometry class?

**Research Hypothesis**

In
order to answer the research question 1, the following null and alternative
hypotheses were formulated.

*H*: There is no difference in the understanding of geometry between the Control and Experimental groups.

_{O}*H*

_{1}_{:}There is significant difference in the understanding of geometry between the Control and Experimental groups.

## Significance of the Study

The study explores the effect of interactive
geometry software (GeoGebra) on students learning experiences in an interactive
geometry environment. The findings of this study will be a resource for policy
makers, teachers and other stakeholders to help improve students’ geometric
reasoning in Nigeria, through the use GeoGebra. It will generate information
that could inform policy makers on ways of implementing the national policy on
the integration of ICT into the teaching and learning of mathematics.

Again, the findings of the study will
serve as a resource for curriculum developers and teachers to improve students’
learning outcomes in schools especially in Ikere local government in Ekiti
state and the nation at large. The study will also serve as a baseline document
for other researchers investigating into the effects of IGS on motivation and
student-centred learning. It will further make a significant contribution to
existing literature.

## Delimitation of the Study

The
study covered three randomly selected secondary schools in Ikere Ekiti. The area was chosen because of its familiarity
to the researcher. The choice was made with the belief that population for the
study would be easily accessible to the researcher. The study explored students learning
experiences when using interactive geometry software.

## Organization of the Study

The
study is organized into five chapters. Chapter one covers the introduction,
background to the study, statement of the problem, research questions, purpose
of the study, significance of the study, organization of the study and
delimitation. The second chapter reviews related literature and discusses the
theoretical framework. Chapter three deals with the research methodology; this
includes the research design, population and sampling, instrumentation,
procedures for gathering data and how the data were analyzed. The presentation
of the results and the discussion of the findings are described in chapter
four. The final chapter which is chapter five looks at the summary,
conclusions, recommendations and areas for further research.

**Definition of Terms**

**Attitude**: This is the disposition that a student has about Mathematics before and after the introduction of GeoGebra software to the class. It indicates the students’ disposition or feeling towards Mathematics.

**Performance**: These are the scores derived from Student Achievement Test in Mathematics.

**Learning Outcomes**: These are determined by the students’ performance and attitude towards Mathematics.

**Technology**: This is the application of scientific knowledge to provide solutions to human problems. In most cases it is referred to as Information and Communication Technology (ICT).

**GeoGebra**: GeoGebra is an interactive dynamic Mathematics software on geometry, algebra, statistics and calculus application, designed for teaching and learning of Mathematics from primary school to university level.

**Geometry:**is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space