PROBLEMS ASSOCIATED WITH TEACHING AND LEARNING OF GEOMETRY IN SECONDARY SCHOOL USING EXPERIMENTAL SOLVING APPROACH

**CHAPTER TWO**

Mathematics, students usually performed poorly which does not attribute to the fact that, it is a very difficult subject to learn or question are always above the students level of understanding through the question may be very simple but students require the basic understanding, if the principle which always conspicuously is lacking in lacking in the answering of some student.

Educators and researchers have probe into the causes of poor performance of secondary school student. In concept in Geometry with emphasis placed on the qualities of teacher, poor background which can also be as a result of poor method of teaching employed by most of the teachers in schools.

Problem with the status of geometry in mathematics curriculum have been apparent for years. Since Royalment Conference (1989) and Dieudonne. Ultimate to the effect that “EUCLID MUST GO” the geometry curriculum has been in disarray because of this disarray, teachers decided that their valuable and limited class time should be better spent working on other areas of mathematics curriculum other than geometry.

Geometry can become boring and you will dislike the subject but when it is done in practical way with many exercises by the pupils, it is extremely interesting. From the above point, it shows that any strategy adopted in the teaching of mathematics develop the child either positive or negative attitude toward the students.

This study therefore is to consider the approaches to teaching and learning concept in geometry with focus on experimental approach and its effectiveness in teaching and learning of geometry.

2.1 OBJECTIVES OF J.S.S. MATHEMATICS CURRICULUM

The Junior Secondary School (J.S.S.) period consist of the first three years of the six years in secondary school system in Nigeria.

It was founded to provide general education for those moving into various trades and to lay a solid foundation in Education for those moving into the Senior Secondary School.

The mathematics at Junior Secondary School level is designed to attain the following objectives.

- To enable the students, to have a further and better primary school mathematics
- To arouse students competence in manipulating letters in algebraic work.

- To familiarize students with the properties of geometrical objective and their measurements.

- To arouse student still in calculating accurately and in making reasonable estimation.
- To give a solid foundation for this study of mathematics at the Senior Secondary School.

- ORIGIN OF GEOMETRY

The beginning of the subject was older than the art of writing. According to Herodotus and Aristotle, they placed the origin to the EGYPTIAN CIVILIZATION. Herodotus had the belief that geometry had originated in Egypt that had promoted the pursuit of geometry.

Egyptians geometers sometimes were referred to as rope stretchers. This they used in laying out temples and in realizing the obliterated boundaries.

Nodithic peoples designs and suggest a concern for special relationships that paved the way for geometry, pottery, weaving and basketry show instances of congruencies and symmetry which are in essence parts of elementary geometry. Simple sequences in design such as in the figure below suggest a sort of applied group theory as well as propositions in geometry and arithmetic. The design makes it immediately obvious that the area of triangle are to each other as on a side or through counting, that the sum of consecutive odd numbers, beginning from unity are perfect squared for the prestoric period. There are no documents, hence, it is impossible to trace the evolution of mathematics from a specific design to a familiar theorem.

Egyptian discover mathematical ideas very informally through the art of measurement which they practiced over centuries of years in their bid to portion out precisely their parcel of land for purpose of agriculture. Through the use of what the called “ROPE STRETCHING”, they evolved a very skillful method of portioning out pieces of land in most imperceptible manner. They discovered empirically what later become known as geometry which means earth measurements. All their discoveries in geometry were practical. They did not formulate rules of theorems all they know was that their method of practical geometry worked.

They were so skillful in doing it, that it led to the art of structural building like pyramids sphinx, the art developed into architecture and geometrical drawing such as we know today.

Thales the milestus nicknamed as the “father of deductive reasoning” Thales who had contact with Egyptian through MERCENTILE ACTIVITIES, studied the Egyptian art of earth measurement and started to look triangler, rectangles and other parallelograms worked out the way they did. He discovered many logical reasons why most geometrical fact as we know them today are true he renamed the Egyptian EARTH MEASUREMENT AS GEOMETRY.

2.3 NATURE OF GEOMETRY

Geometry originated from the ancient Egypt. It was formed from two Greek word, Geo and Metry. Geo means Earth while Metry means measurement.

Therefore, Geometry literally means earth to deductive science in which logical connection are established between the available facts.

Geometry is a branch in mathematics that deal with the properties of space and objects in space. It was late that, it realize that geometry ned not be limited to the study of flat surface (plane geometry) and rigid three dimensional objects (solid geometry) but that even the most abstract image must be refreshed and developed in geometric terms.

2.4 WHY TEACHING GEOMETRY

Many mathematicians and mathematic educators have attempted to define major objective of geometry teaching.

The objective is as follows:

- It help in acquisition of information about geometric figures in the plane and space.
- It help in the development of an understanding of the deductive method as a way of thinking and a reasonable skill in applying this method to mathematics situation
- It help to provide opportunities for original and accurate thinking with the main objective, it allow the student to perform some functions.

- FUNCTION OF GEOMETRY

- To systematize the information and extend it to some of the broader and more general aspect of the everyday life.
- To aid the student in becoming familiarize with the basic geometrical concepts and understanding the fundamental technique such as the use of the straight edge protractor, compass and the technique of measurement and construction.

- To acquaint the students with the characteristics of good geometrical rotation.

- To bridge the gap from the largely manipulation types of geometrics experiences to the more formal logical processes of demonstrative geometry.

- METHODS OF TEACHING GEOMETRY

There are different approaches to teaching geometry in mathematics.

Before a teacher can teach any aspect of mathematics, he ahs to know the content of the topic, the content will dictate the approach to be used.

In real sense, a teacher who is choosing any approach in teaching geometry has to be very sound in knowledge of the nature of geometry.

The nature of geometry according to Odili (1986) was as follows:

- It is abstract in nature
- It must be applicable to nature
- It helps to visualize object
- It is problem solving in nature
- It makes use of symbols and signs
- It is coherent, logical and sequential
- It encourages inductive and deductive reasoning.

The approach used in this research is experimental approach which relies on the educational thoughts of Rousseau, Froebel, John Dewey and Montessori which place the child at the centre of learning.

Experimental approach implies that activity and direct involvement of student in teaching and learning situation with direct exposure and interacting with correct objects or instructional materials, where the teacher encourages students to perform experiment and discover new facts. The experiment could be within the laboratory or outside the laboratory. The students are expected to discover relationship between the objects, ideas and events. The teacher does not give knowledge to students, but expect them to discover knowledge. It will be meaningful, be in his memory for a long time and he will be able to transfer such knowledge to another person.

Experimental approach as a general overall procedure said approach has many merits. It secures thinking on the part of the students, it makes the students to depend on themselves rather than their teachers because the students are responsible for what they learnt. It also helps in realizing the basic objectives of science teaching that is, to develop manipulative skill and discovering of facts through careful observation. It is flexible and learners can actively participate in the learning process and it’s evaluation through active participation in the lesson. Students gain knowledge on his own, this develops his mind for solving problems in future.

- LABORATORY AND INSTRUCTIONAL MATERIALS IN TEACHING

Since experimental approach is a practical oriental approach to teaching, it therefore requires the need for a place where proper investigation can be carried out through experimentation.

For effective use of experimental approach therefore, there must be a place called LABORATORY (Mathematics Laboratory) where students can learn mathematical theorem, concepts and principles with direct interaction with learning materials or concrete objects.

Mathematical laboratory should consist of charts of solid, of different shapes, globe (for longitude and latitude), mathematical instruments, cardboards, wire materials and host of others. These materials could be the sophisticated ones or impoverished ones but must be relevant in teaching and learning process.

When teaching a particular concept, the learners will therefore be allowed to interact with the materials built on improvised themselves where the need be, so they can discover some hidden facts.

Topics like bearing direction, mensuration, construction, longitude and latitude, elevation and depression, geometry, statistics and probability to mention a few which appear to be too abstract and difficult for the students understanding of concept in Geometry and make learning to be permanent.

- PRACTICAL APPROACH TO TEACHING AND QUALITIES OF TEACHERS

Practical approach to teaching is synonymous to experimental approach to teaching in the sense that the experimental approach “is a practical oriented approach which makes room for the students to interact with teaching materials and carried out investigation”.

It is now pertinent to look at how mathematical concepts, theorems and principles can be taught with the use of practical approach which enhances experiment. As earlier said, there is always the need for mathematic laboratory with instructional materials before any concepts can be fully practicalised. All branches concepts and principles in mathematics can be taught using practical approach so as to make mathematics a reality and not abstract.

It is observed that many secondary school students have problems in geometry because most teachers themselves do not understand the concept.

These categories of teachers did not teach the students mathematics rather they copy textbooks for the students. Supporting this facts, Adewumi (1982) says most of this type of teachers lack initiative in teaching the subject and thereby tends to follow the textbooks religiously without adequate explanation to the students.

Such teachers cannot motivate the students. Consequently, many students who are interested in mathematics are not geared toward knowing it thereby reducing the number of interested students.

Kalejaiye (1977) emphasized on the problem of quality of mathematics teachers and its effects on students attitude towards the subject saying that “whatever effect is put into providing suitable syllabus and teaching material for schools little result will be achieved without qualified teachers to make effective use of them”.

Kalejaiye still on the importance of method of teaching mathematics says “Teachers should employ modern teaching techniques based on recent experiments and finding of psychologists and educators. The teacher should move away from the chalk and talk long explanation”. This implied that crude method should not be used in the teaching of this subject but recent method should be used and more explanation should be made instead of just writing on the chalkboard.

If the concept is taught using practical approach, it becomes more understandable and permanent in the memory of the learners. In essence, laboratory is useful than mere teaching scientific concepts and also give students a perspective on the native of scientific inquiry.

Literature review has shown that the type of teaching methods adopted in classroom can determine the type of attitude to be developed by students. Most researchers are of the opinion that the methods of instruction that involve practice restricted to transmitting information involve telling, reading and memorizing. In other words, any method when essential experiments are made available for students to interact with, could be effective in promoting thought and changing attitude.

Bloom (1971) was of the opinion that many inter-personal problems may come up when the experimental approach is used. The experimental approach was criticized on the ground that students may become frustrated, if the teacher refused to tell what he obviously know, more especially one day when discussion has been unproductive.

Moreso, it is likely that some students will want to monopolize the discoveries or findings in as much the whole class will rarely experience in sight at the same moment. It is therefore observed that this situation will create jealously, feeling of inferiority in students who could not come up with their own findings.

Despite the problems connected with the experimental approach, Bigge (1971) had adequate evidence to back up his support for the approach. He made it clear that in teaching with experimental approach students scored higher, highly motivated, gain critical insight and are more likely to participate in out of class study.

Gagne (1975) made a more clearer and explicit analysis when he said that experiment appears to be a very fundamental principle of good instruction.

From the review of literature, most researchers seem to agree that learning is more effective with the use of experimental approach due to its effect in the mastery learning materials, the transfer of learning and in the acquisition of problem solving skills. It should be noted that teachers have traditionally emphasized the product of mathematics and often failed to give the students an understanding of means of solving objectives for mathematics instruction.

**CHAPTER THREE**

- RESEARCH, DESIGN AND METHODOLOGY

This chapter entails the methodology, research design, population of the study, Area of the study, Research Instrument, Construction and validation of research instrument and data analysis to be used in the research work. For purpose of this study on experimental control design will be used to investigate the effectiveness of experimental approach to teaching and learning of concept in geometry.

Pre-test will be administered to the selected student used in the three selected schools to determine the entry behaviour of the students in concept of geometry in mathematics after which post-test will be conducted to the student having exposed them to a learning task using experimental approach for the control group. The post-test is used to determine the cognitive achievement and performance of the groups in concept of geometry.

3.1 AREA OF THE STUDY

This research work is to be carried out in Ojo Local Educational district of Lagos State using three secondary schools which are randomly selected from the area (Ojo L.G.)

The schools are:

- Lagos State Model College, Agric.
- Ajangbadi High School, Afromedia.

- Awori College, Ojo.

3.2 POPULATION OF THE STUDY

The target population of students to be used for the study is one hundred and twenty (120) students drawn from J.S.S. II and J.S.S. III of the selected schools.

3.3 SAMPLE AND SAMPLING PROCEDURE

Three secondary schools were randomly selected from Ojo Local Government Area in Lagos State are used for the study. In each school, 20 JSS II and 20 FSS III students were used. These students (120) were grouped into experimental group and control group each of which consist of 40 students. These students will be exposed to pre-test and post-test to test their entry behaviour in concept of geometry in mathematics and the cognitive achievement in concept of geometry in mathematics respectively. The pre-test was administered before exposing them to learning task.

All the returned tests will be further subjected to scrutiny to eliminate inaccurate and incomplete findings so that, the ones properly filled will be used for the study.

3.4 RESEARCH INSTRUMENT

In testing the research hypothesis, two sets of tests namely:

- Pre-test to determine the learners’ general knowledge in concept of geometry;
- Post-test

will be used.

While the pre-test is to measure the previous knowledge of the students, the post-test will determine the ability of the students to retain what they have learnt.

The test will consist of Part A and part B. part A will be used to collect information on the subject demographic characteristics like name, school, age, class, sex and so on. Part B will consist of twenty items objective questions, which the subject will be exposed to. The items will cover the topics taught in the class based on geometry.

These tests are to evaluate the performance of the subject (student) and how much they gain using experimental and convention approaches. This will help to determine how effective experimental approach is.

3.5 CONTRUCTION AND VAIDATION OF RESEARCH INSTRUMENT

Two tests were conducted, the test were different only because data are different answers. This types of tests are constructed by the researcher, that is, pre-test and post-test.

The test was given to two experts in mathematics for necessary correction. It was confirmed adequately by two mathematics educator and my supervisor before been administered.

Researcher employed the help of the mathematics teachers in the particular Junior Secondary School, class teachers of the selected schools in supervising the students to make sure that they follow the instruction given.

The pre-test was administered to make sure that the schools selected were in the same level of understanding in the concept of geometry. This schools were divided into two groups A and B. Group A were taught with experimental approach while group B were taught with conventional approach. After two weeks, the post-test was administered. The performance of the two groups were compared with the help of grading.

- METHOD OF DATA ANALYSIS

The purpose of the study is to conduct investigation into the effect of experimental approach to teaching and learning of concept in geometry in mathematics at Junior Secondary Schools in Nigeria using Ojo Local Educational district of Lagos State as a case study. To achieve this, data collected will be analysed statistically using mean (x), standard deviation (SD), percentage (%) and t-test. In the course of this analysis, the research question and hypothesis in chapter one will be answered. In addition to the above methods, Pearson Product Moment Correlation analysis was also used to determine the reliability of the instrument.