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**STUDENTS CHARACTERISTICS AND LEARNING OF MATHEMATIC IN AMONG SECONDARY SCHOOL STUDENTS**

**CHAPTER ONE**

**INTRODUCTION**

**1.1 BACKGROUND OF THE STUDY**

Mathematics is a communication system in science, art and business world. Odogwu, (2008) pointed out that it is used in describing diverse phenomena in both physical and economic situation. It is a science of number and size concerned with logical deduction from general premises of all reasoning, with a wide application in life. The role of mathematics in development of science, technology and even art and humanities is highly indispensable. Its skills, knowledge and correct application help both individuals and nations to solve their everyday problems. In spite of the great emphasis placed on the study of mathematics and the huge investment in it, it can be said without any fear of contradiction that all is not well with its teaching and learning of the subject. Nweke (2015), opined that no teacher in Nigeria concerned with the teaching of mathematics at any stage, from infants upwards and particularly at secondary school level can honestly say to himself that all is well with the teaching of the subject. She further pointed out that the state of mathematics in the country is appalling as the subject is disliked by many students in spite of its utility. There are overwhelming evidences of poor performances of students in mathematics at all levels of our educational system WAEC, 2012; WAEC, 2013). At the secondary school level, both WAEC and NECO chief Examiners have continued lament the poor achievement of students in mathematics. Annual reports of WAEC of 2011, 2012, and 2013 revealed disheartening and alarming poor secondary school student’s achievement in mathematics. Summary of the report shows that only 11.36%, 15.74% and 32.81% of the total enrolment in mathematics for the respective years were able to make up to credit passes in mathematics in the senior school certificate examination. The remaining percentages of 88.64, 84.26 and 67.19 respectively, obtained ordinary passes and failure grades in mathematics in the respective examinations.

The Chief Examiners report further revealed that students were weak in simplification of equations and interpretation of quadratic graphs. This has a direct bearing on the fact that they have poor knowledge of simplifying algebraic expression. According to Emmos (2004), students at JSS level find it difficult to comprehend the concept of inequality. This implies that the students attend SSS level with poor prerequisite knowledge and background of the concept. This, according to Aminu (2007) makes it extremely difficult for the students to cope with further studies of mathematics at higher level. This contributes to the poor achievement of students in Senior School Certificate Examination. There is constantly low enrolment of students in mathematics and mathematics related subject in our higher institutions of learning.

The government admission policy ratio of 60:40 for Science and Art/Humanity subject in our institutions of higher learning is not known to have been met by any institution. A lot of steps have been taken to arrest this ugly situation. Between 1930 and now, the mathematics curriculum has been reviewed many times. The review included effective approaches for teaching and learning. Many approaches have been used in the past for teaching algebra. These approaches include problem solving, discovering, concept development, and advanced organizer. Though each of these methods has been found effective for teaching algebra, none is 100% effective. The results of Abonyi and Umeh (2014) revealed that heuristic problem solving approach has positive effect on student

achievement in Mathematicasic word problems. Research evidence of Igbokwe (2007) revealed that concept development approach is an effective instructional strategy for teaching graph of inequalities.

The work of Chinwoke (2008) revealed that the use of advanced organizer is an effective instructional approach for teaching undefined fraction. Although, these methods or approaches have been found efficacious for teaching matematics, secondary school students’ interest and achievement in Mathematicas are still on the downward side. This tends to suggest that there is a room for further research on how to improve students’ achievement in Mathematicas. This implies that there is that there may be other more effective approach for teaching mathematics at the secondary school level that has not been most appropriately explored. Researchers in mathematics education (Abonyi and Nweke, 2014; Abonyi and Umeh, 2014) recommended that teaching and learning enterprise be structured to accommodate new instructional strategies which will make student good problem solvers.

Problem based learning (PBL) is an instructional strategy for teaching mathematics which has been neglected especially in Nigeria. In problem-based learning, complex problems rooted in real life or world situation are used to motivate students into discovering important concepts, their interconnections and making generalizations (Abonyi 2005). This means that learning begins with a problem presented in the same context, as it would be encountered in real life (Woods, 1985, Abonyi, 2005).

Problem based learning is a cooperative and or active learning approach. Though Problem based learning and other cooperative learning approaches share many features the major difference as pointed out by (White, 1996) is in its component. As he asserts, “an essential component of problem based learning is that content is introduced in the context of complex real-world problems”. When presented with the problem, students begin by organizing their ideas and previous knowledge to define the problem’s broad nature. When they reach the point where certain information is lacking, or where they feel they do not understand the problem any longer, they assign responsibilities to one another to

experiment on the problem or learning issues. In the next class they teach one another the result of their research findings. They summarize their presentations in a way that allows for integration into the problem context.

Where assumptions are made, the student continues to dig progressively deeper into underlying contents and concepts. This therefore means that problem based learning is not a single strategy but rather a collection of strategies, which can be assembled, in different forms. It uses intellectual curiosity as a driving force for students learning.

Since it uses intellectual curiosity as a driving force for learning, a pertinent question that may arise here is whether Problem based learning approach has differential effect on male and female students’ achievement in mathematics. This is due to the facts that some research works show that there are gender inequalities in mathematics achievement and interest in secondary schools. Abonyi and Nweke (2015) establish gender difference in students’ achievement and interest in mathematics. Whether this disparity existing between male and female students’ achievement in mathematics can be adequately addressed by Problem based learning approach is still being speculated and calls for empirical enquiry. Although Problem- based learning approach has been recommended for teaching mathematics and other disciplines based on tremendous successes recorded in its application in the fields of sciences and medicine, its efficiency on students’ achievement in mathematics has not been empirically determined. Empirical assessment of the effects of Problem- based learning approach on interest and achievement of students in mathematics could result in some curious and interesting implications which are worth exploring.

**1.2 STATEMENT OF THE PROBLEM**

** **Mathematics as the bedrock of all scientific and technological advancement is a compulsory subject in secondary education. Mathematics is a human invention, borne out of human mind, resolve to solve human problems. Thus as a creation of mind, it is concerned primarily with ideas, process and reasoning. Of all the factors that affect teaching-learning in the educational system of any society, teaching method seem to constitute the primary issue. Perhaps, the teaching method in use in many schools such as lecture method, demonstration, and laboratory among others seem not to have brought about an effective teaching-learning, and could have resulted in students’ poor achievement in WAEC and NECO examinations. Hence, the need to adopt a better teaching method that would positively influence candidates’ achievement especially in Mathematics. Therefore, the problem to be investigated in this study posed as questions are: Would students improve upon their achievement in Mathematics if problem-based learning method is employed in teaching Mathematics? Would any of the sexes benefit more than the other in Mathematics as an aspect of school mathematics due to the use of this teaching method.

**1.3 OBJECTIVE OF THE STUDY**

1. To examine problem-base learning and students performance in mathematics.

2. To evaluate students’ achievement in Mathematicas.

3. To examine the effect of problem-based learning.and students academic performance in mathematics in secondary school

**1.4 RESEARCH QUESTIONS**

1. Does problem-base learning and students performance in mathematics?

2. Can you evaluate students achievement in Mathematicas?

3. What effect does problem-based learning.and students academic performance in mathematics in secondary school?

**1.5 RESEARCH HYPOTHESES**

H0: Problem-base learning does not relate with students performance in mathematics.

H1: Problem-base learning relates with students performance in mathematics.

H0: Does Problem-based learning does not affect students academic performance in mathematics in secondary school.

H1: Does Problem-based learning afffect students academic performance in mathematics in secondary school.

**1.6 SCOPE OF THE STUDY**

This study covers Problem-based learning (PBL) on secondary school students’interest and achievements in Mathematics in as a case study Pankshin local government area, Plateau State.

**1.7 LIMITATION OF THE STUDY**

This study is characterized by financial constraints which posed serious logistic challenges in terms of distributing of questionnaires and deploying interview method ingathering primary data. It was also characterized by inadequate time frame given for the completion of this study. Apart from these challenges, the study was almost marred by the nonchalant attitude of many of the respondents who showed apathy towards the filling of questionnaire. And finally, it was a Herculean task gathering secondary data on some of the issues raised in the study as they were not readily available.

**1.8 DEFINITION OF TERMS**

**Problem-based learning: **Problem-based learning is an instructional method centered on the learner.

**Academic Achievement:** Achievement is defined as a thing done successfully, typically by efforts, courage or skill.

**Interest: **Interest means the state of wanting to know or to learn something, it is

a state of curiosity or concern about something. Interest is a motivating factor in teaching and learning process.

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