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
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
TABLE OF CONTENTS
Title page i
Approval page iii
Table of contents vii
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
CHAPTER FIVE: SUMMARY, CONCLUSION AND RECOMMENDATIION
Appendix I: Questionnaire 55
Appendix II: Pre-test Questions 57
Appendix III: Post-test Questions 59
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
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.
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:
- The effect of interactive geometry software (IGS) on the development of Secondary School students’ conceptual understanding of geometry
- The effect of the use of interactive geometry software (IGS )on Secondary School students’ motivation to learn geometry
- Ways in which interactive geometry software IGS provides support for student-centred learning in a geometry class
In pursuance of the purposes stated above, the following research questions were formulated to guide the study:
- To what extent does the use of interactive geometry software (IGS) affect Secondary School students conceptual understanding of geometry?
- How does the use of interactive geometry software (IGS) motivate Secondary School students to learn geometry?
- In what ways do interactive geometry software (IGS) support student-centred learning in a geometry class?
In order to answer the research question 1, the following null and alternative hypotheses were formulated.
HO: There is no difference in the understanding of geometry between the Control and Experimental groups.
H1: There is significant difference in the understanding of geometry between the Control and Experimental groups.
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.
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.
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
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