**EFFECT OF GUIDED DISCOVERY METHOD ON MATHEMATICS PERFORMANCE OF LOW AND HIGH AVERTED SECONDARY SCHOOL STUDENTS IN FCT ABUJA, NIGERIA**

**ABSTRACT**

This study find out the effect of guided discovery method in teaching students with low or high mathematics aversion. The study examined the academic performance of high and low averted students in mathematics and the relationship between guided discovery and expository. Chapter one focuses on the background of the study, it also examine the research problem, research objective, research hypotheses, the significant of the study and the scope/delimitation of the study. Chapter two dealt with the review of related literature by renowned scholars on problems militating against the effective teaching of mathematics and how to tackle such problems like aversion to achieve more functional teaching and learning of mathematics, which was reviewed under the following headings: Theoretical Framework,Conceptual Framework, Concept of Aversion in Mathematics Teaching, Sources of Mathematics Aversion in Secondary Schools, Effects of Aversion on Learning Mathematics in Secondary School, Methods of Teaching Mathematics in Senior Secondary Schools, Mathematics Aversion, Instructional Methods, Achievement and Implication of Literature Reviewed for the Study. Chapter three described and discussed the research design, population, sample and sampling techniques, instrumentation, data collection, data analysis and also the pilot study. Chapter four focused on the result and analysis of data collected for the study. It also gives general description of the data, hypothesis-by-hypothesis testing, analysis and interpretation of findings. Statistical techniques, such as the means score, standard deviations and the t-test were used. All hypotheses were tested at 0.05 level of significance. Chapter five reviewed the summary of the procedure and findings of the study. Recommendations are made on how to carry out further studies on the effect of guided discovery methods on mathematics achievement of low and high averted students in senior secondary schools. The data for the study was collected by administering two forms of test (MAT & MARS) to 207 students selected from Government senior secondary school kwali, Government senior secondary school Yangoji, Government Girls Senior Secondary school Dutse Sagwari and Government Day Senior Secondary School Bwari all from Bwari and Kwali area councils respectively in Federal Capital Territory. First, a modified fennana-sherma mathematics aversion rating scale was used to identify students with high and low mathematics aversion levels. Then students within each level of mathematics aversion were randomly assigned to treatments of guided discovery and expository methods. Four groups, with each group forming a cell. The students were taught for eight (8) weeks at the end of it, mathematics achievement test (MAT) was administered. The results of the tests form the main data for the study. The statistics mean, standard deviation and t-test were used in analyzing the data and testing of the hypotheses. The findings shows that:-Students with low mathematics aversion performed better when taught by the guided discovery method, while Expository method has upper hand under high mathematics version. In order to make the students perform at their best, mathematics teachers.

**CHAPTER ONE**

**THE PROBLEM**

**1.1** **Background to the Study**

In this era of technological quest and high attainment in modernization, no nation can afford to allow her teaming population to shy away from mathematically related sciences, Obiefuna (2005). This is because technological development is hinged on strong mathematics foundation. It is therefore no longer conventional fact that mathematics and mathematical sciences are indispensable. The issue at hand is which method can change the attitude of the learners and attract their interest towards mathematics and mathematical sciences.

Mathematical sciences in this context are those school subjects like Mathematics, Chemistry and Physics. At the tertiary institutions of learning, all science courses that usually involve mathematical calculations are included under the topic mathematical sciences. According to Okunade (2000) one may ask the question why mathematics should be taught in schools. Mathematics as a discipline has many advantages for human beings some of which are:-

- Utilitarian: – In almost all human activities, both in academic pursuits or professional training and practice, mathematics is an effective tool for realizing results. Onogu (2002), said it is engineering language through which insights are presented to analyze and synthesize engineering problems. This made the subject to be taught from lowest to the highest levels of knowledge that the child‟s ability can allow.
- Social activities: – Mathematics is used in the area of social activities like birth/ death control, census, marketing, and a host of others.
- Cultural activities: – Human beings right from inception express their cultural heritage by means of figures and signs using mathematics. It could be said that its study originated from cultural activities, like Egyptian‟s irrigation plots, pyramids and a host of others.
- Aesthetic: – Ogbodu (2004), Observed that, Men derive pleasure and joy in beautiful mathematical designs found in their domain, the beautification also takes its origin from mathematics that are used in art, architecture and textiles.

As a result of its uses,Fatius (2000), said that, the world is becoming more mathematical,while Makarfi (2001), commented that the role mathematics played in social, economic, technological and industrial development of any nation cannot be over emphasized. In line with this, Olumase (2004), stressed on the need for strong mathematical foundation among the youth. Mathematics as explained by Audu (2005), is the queen of all sciences, because it is the tool for all disciplines since no scientific advancement (practical applications and approach) could be achieved without it. Kajuru (2005), emphasize on the impacts mathematics make on all aspects oflife. The usefulness is therefore extended to the field of physical sciences, technology, social and business sciences. Besides these numerous advantages, Nigerian Students seem to approach the subject with coldness and no sense of zeal Njku (2004).

Every nation has set goals for the education of her citizens. The national policy on education spells out government‟s ways of attaining those goals through education. One of the goals set for secondary education in Nigeria after leaving the school is to contribute to national development through technological manpower training. In demonstrating the resolve of government towards the provision of qualitative education at secondary schools level, the national policy of education stressed on the need for all teachers in secondary schools to undergo training in the methods and techniques deof teaching. According to Bello (2001) with the advancement in the socio-economic and technological field, life of the individual is becoming more and more complex with a lot of problems, which the individuals and society have to face in the near future. Therefore, the role of the school becomes increasingly important in developing scientific attitudes in students so that they will be able to solve their problems independently and adjust well in the future complex society. The students need mathematics to develop the scientific thinking and aptitude, which is synonymous to mathematical thinking. Odeyemi (2005) asserts that, if thinking is a way of improving understanding and extending control over the environment, mathematical thinking uses particular means to do this. Therefore, the need to have good methods of teaching the operations processes and dynamics of mathematics cannot be over emphasized.

According to Ojoloye (2005) students are ill equipped from secondary schools to handle mathematics problems, because there are poorly taught. Ahmed (2002), said, therefore, it is important that mathematics educators should work closely with the secondary school teachers in finding better alternative methods of instruction and discuss what should be included in the mathematics programmes. Hence thepurpose of this study was to find out instructional method, which will suit students, especially those having mathematics aversion. He further stated that due to poor teaching methods and lack of qualified mathematics teachers and public prejudices against mathematics, students view mathematics with apprehension. Therefore the search for a better instructional method that should reduce such apprehension and aversion in students cannot be over emphasized. According to Agosto (2000), the learning difficulties among students which one observes as a teacher of mathematics raises many other questions that one might seek an answer from theories and methods of teaching. For example, although reflection on our own experience should suggest to us that learning cannot be achieved in a hurry, Elaime, & Johnson, (2002), havethis to say, that some students appear to learn slowly, some make very rapid progress and few even make outstanding progress given the opportunity to learn at their rate rather than the class rate. Therefore, it is only possible to accelerate the learning of mathematics for the majority of students when one uses the appropriate instructional method for each type of students.Individual differences are very significant in many spheres of human activity. Some of us are barred from particular subject because of physical characteristics, like being too small, too heavy or having poor sight. Bolaji (1995), in discussing mathematicians drew attention to great differences in the kind of mathematical aptitude, which individuals have displayed. He further explained that, in the classroom, it might be that different learning environment and different styles are needed for different students. Therefore any acceptable theory or method, which enables us to understand individual differences among our students, would be very valuable.

As has been suggested by Agosto (2000), the learning environment might be an important factor in promoting and understanding mathematics. It might therefore be seen that the richer (encourage) the environment, the more efficient the learning. Hence, what constitutes a rich environment is a subject which is basically a creation of a human mind and in which the aim is to enable abstract arguments to take place through manipulation of symbols, appropriate learning techniques, learning materials and most of all understanding the needs of students within the rich environment. The theory of meaningful learning proposed by Ausubel (1980) was a general theory and was not specific to mathematics alone. He states that meaningful learning is a process through which new knowledge is absorbed by connecting it to some existing relevant aspect of the individual‟s knowledge structure. Achuonye & Ajoku (2003), viewed it that if there are no relevant concepts already within the mind to which knowledge could be linked, the new knowledge would have to be learnt by rote and stored in an arbitrary and disconnected manner. Offoma (2003), said, if a new knowledge was assimilated within the existing knowledge structure as a related unit, and appropriate modification of prior knowledge took place, the result is meaningful learning. It is therefore not necessary for all, or perhaps even much knowledge to be acquired by process of discovery method. According to Akudolu (2002), Good expository knowledge teaching could ensure that new knowledge should be relevant to existing ideas, and this might not only be more economical (in terms of time) than discovery, it might be more effective in terms of length and breath of teaching. Therefore if one could really ascertain what the students already knew, who they were (with or without aversion), one would then know how and what to teach them. Apart from the introduction of new contents and the proposal for better organization of mathematics curricula, the dominant themes of revisionists is emphasizing on understanding, students‟ involvement and discovery learning. McCain (2000). Inview this, Onukaogu (20002), said, since mathematics aversion has been found to be related to mathematics achievement, and also discovery approach is an important method for improving students‟ performance, then finding out the relationship between mathematics aversion and this method and how it affects mathematics achievement becomes very important to kill down the assumption student may have toward mathematics.

**1.2** **Statement of the Problem**

It is the researcher‟s observation and experience over the past 20 years of teaching that students seem to assume that mathematics has no relevance in day to day‟S living. For this purpose those doing well in it at lower level of education, suddenly decline on getting to higher level of studies. A teacher came in contact with 11 year old girl while teaching in a secondary school. The girl asked him, what he intended to further his education with? And the teacher replied “mathematics”. On hearing this, she shouted “mathematics!” The acclamation did not just come to her, but resulted from the aversion she has for mathematics. It is possible that this aversion was created in her by the parents, peer groups, or poor handling of the subject by her teacher. That might have given her the impression that mathematics is not a subject to further with. The aversion affected the girl‟s performance from her usual 2^{nd} or 3^{rd} position in mathematics class, but found her-self in position 15^{th} and above. The researcher believed that, “Many students fail mathematics not because they cannot make it, but because of aversion”. While this is hampering the success of the students, it will be very unfortunate for potential mathematicians to refuse practicing mathematics.

Odeymi (2005) said that many students failed mathematics examination as a result of negative attitude towards mathematics, the results obtained in mathematics by students in both schools and public examinations as pointed out by Emah (2005), is so alarming. Obanya (2002), said that the attitudes exhibited by many people especially students and adults in the society towards mathematics need special attention for the young developing nation desirous to practicing scientific technology and industrial developments.

Studies have showed that high achievement in mathematics is related to low mathematics aversion level and low achievement in mathematics is related to high mathematics aversion level for secondary school student as observed byBello (2001). However, the researcher observed that both students with high and low aversion level are taught by the same methods of teaching. This therefore, led the researcher to feel that there is need to find out an instructional method suitable to students with mathematics aversion, which can assist them in overcoming such aversion in mathematics and to come out with the suitable method this study attempted to find out: This study investigate into the effect of guided discovery method on mathematics achievement of high and low averted secondary school students, thus, the study out to identifIied the method that would best achieve the aim of mathematical science teaching, improve performance, retention ability and also enhancing positive attitude towards mathematics at secondary schools level, irrespective of the age level of students.

**1.3** **Objectives of the Study**

The objectives of this study were to:

examine the mean performances of secondary school students taught with guided discovery methods and those taught with expository. compare the academic performance of secondary school students with low mathematics aversion taught with guided discovery method and those taught with expository method. examine the academic performance of the secondary school students with high mathematical aversion taught with guided discovery method and those taught with expository method.

**1.4** **Research Questions**

The study attempted the following research questions.

What is the difference between the mean performance of secondary school students taught with guided discovery methods and those taught with expository method?

What is the difference between the academic performances of secondary school students with low mathematical aversion taught with guided discovery method and those taught with expository method?

What is the difference between the academic performance of secondary school students with high mathematical Aversion taught with guided discovery method and those taught with expository method?

**1.5** **Research Hypotheses**

**I**n order to achieve the objectives of this study the following hypotheses were formulated and tested:-

H_{01:} There is no significant difference between the mean score of secondary school students taught with Guided discovery method and those taught expository method.

H_{02:} There is no significant difference between the mean score of secondary school students with low mathematics aversion taught with Guided discovery and those taught with expository method.

H_{03:} There is no significant difference between the mean score of secondary school students with high mathematics aversion taught with guided discovery method and those taught with expository method.

1.6 **Significance of the Study**

Although the new national policy on education in Nigeria has greatly laid emphasis on mathematics education and other science subjects, as suggested by FRN (1981), found in Uwah, (2005).Aversion on mathematics education at secondary school level is yet to receive special attention, Mbakwem (2005). In line with this,the study provide mathematics educators and curriculum planners with the instructional method that will aid them in planning the mathematics programme in future, which will go along way in reducing aversion of mathematics. This study was significant, since the result of the study furnished mathematics educator and curriculum planers with information that will help them plan and predict the outcome of their curriculum when implementing. In view of the above, therefore, the study provided solution(s) to the problem(s) of understanding mathematics face by students haven high and low mathematics aversion. The study provides mathematics teacher and educators with insight into the proper understanding of their students and the type of instructional methods to use in order to obtain optimum performance in mathematics. Such a study was also significant since it enabled teachers to create a suitable and conducive atmosphere in the class for effective teaching and learning. The study is beneficial to mathematics teachers in secondary schools in developing an improved plan for averting the aversion among students in their various secondary schools, therefore it is significant. This study is also significant, since it serve as a useful guide to guidance counselors and parents, in helping the students to avert the aversion in the field of mathematics. However, the results of this study throw more light on the existing aversion problems in mathematics. It is also believed that the result of the findings will make a modest contribution to the learning of mathematics in our secondary schools.

Essien (2004), said, Aversion level is a factor that can be consider while predicting mathematics achievement. Hence this study is significant since it aimed at finding instructional methods that are relevant to the aversion level of students, which can also help mathematics educators to predict the mathematics achievement of students. Abiola (2007), said that, all is not well with the teaching of mathematics in secondary schools as a result Akubue (2003), pointed out that many students today are bewildered by mathematics. Makarfi (2001), ascertainthat Great aversion has also been expressed by government, parent, employers and teachers about the fact that large numbers of students, after secondary school course are unable to perform simple mathematics operation needed in their every day live. Therefore, if a way (method) can be found to make mathematics more interesting and easy for student to understand, it will reduce the aversion level in the subject thus helping the students perform better in this era of technological development. Hence this study is significant. The continuity of knowledge acquired to be significance to the students after leaving school. So, this study is significant, since it produce a blue print of instructional method, which is to be used by teacher to provide the continue significance mathematics needs. Finally, it is hoped that the study will prove a good basis for further research.

1.7 **Scope/delimitation of the Study**

The scope of this study was delimited to Kwali and Bwari Area Council of Federal Capital Territory Abuja; the investigation was conducted on SSII mathematics students, from some selected government senior secondary schools. GSS Kwali, GDSS Yangoji, GGSS Dutse-Sangwari and GDSS Bwari were used as representative examples.

The finding obtained was generalized to cover schools not selected. The researcher limited his investigation to two out of six Area Councils of Federal Capital Territory Abuja since the state operates a common admission policy and make use of the same curriculum for the schools. Due to time frame, the researcher limited his finding to the use of two out of many instruments which are mathematics achievement test and mathematics aversion rating scale. Due to financial constrain the researcher limited his finding to Discovery method.