**CHAPTER ONE**

**INTRODUCTION**

Teaching is a complex system which affects what will happen in classes through the interactions among the factors of teachers, students, curriculum, local setting and others (Stigler and Hilbert, 1998). Rubenstein (2004) supported teaching as a complex endeavor. The knowledge base behind mathematics teaching includes the knowledge of mathematics of connections among mathematical ideas, of student’s learning and school culture. The process of teaching involves creating a learning community, challenging students to make sense of mathematical ideas and supporting students’ developing understanding. Rubenstein (2004) stated that teachers are considered as one of the most important factors playing on role in students’ achievement and teaching process.

Effective mathematics learning is one in which students and teachers interact in ways that allows students to have an opportunity to maximize how much they learn. These are variety of ways in which students and teachers interact in a learning environment. Some interactions result in student learning classroom discussion, teachers and students initiated questions. Cooperative group work, peer tutoring and a host of other feedback system such as assignments, examinations and electronic responses system such as the personal responses system (PRS) and the personal data assistant (PDA) are instructional strategies that provide a measure of two-ways communication in which information about what is taught and what is learned is exchange between two people on the other hand, there are instructional strategies in which students sit passively in classrooms where there is one-way communication from teachers to students. On many colleges and university campuses. For example, the professor operates as the proverbial “Sage on the stage” and the didactic lecture is the model way of teaching. And although the lecture is an efficient method for transmitting information from a teacher to a large group of students, telling information to some one does one does not mean that learning take place in order to determine whether is occurring-infant to ensure that learning is taking place, there must be teacher-student assessment interactions along with the instructional interactions.

Assessment interactions between students and teachers occurs when teachers gather information about students learning and use that information help students better understand concepts and principles and apply knowledge, not just learn factor. This type of assessment interaction referred to as formative assessment is defined as follows: Formative assessment is a process used by teachers and students during instruction that provides feedback to adjust on going teachers and learning to improve students’ achievement of intended instructional outcomes (council of chief school states officers, 2008). It is clear from this definition that formative assessment is a process that may employ tests or various other types of assessments, but it may also employ interactive instructional strategies such as classroom discussion, assignment, homework, quizzes, project, investigations electronics response system or oral question to guide and improve students learning (Angelo and Cross 1993, Fennell, 2006) creating an interactive learning environment inside the mathematics classroom in which students are engaged in mathematic learning can be challenging.

Student may experience discomfort about their own level of mathematics content knowledge and may shy away from participating openly in class discussion or responding to teachers’ oral question. Further, this complex negotiation of teachers talk, students talk and classroom dynamic while remaining on task require certain skills and know how. In some models of “best practices” in mathematics teaching and learning these classroom dynamic are viewed as a social Endeavour (Cobb and Bauersfield, 1995) in which the classroom function as a learning community where thinking, critiquing disagreeing and agreeing are encourage. When this dynamic work well, the result can be the creation of a learning environment in which critical thinking and quantitative reasoning develop, students learning thrives, and students take increasing responsibility for their own learning.

According to Motani and Garg (2002), a successful learning environment is one in which students and teachers interact easily, continuously and without any inhibition. In this type of learning environment, students learning is not left to chances, rather, teachers knows whether their student understand intended concept. The key to this success is the implementation and use of an instantaneous feedback system. Instantaneous feedback enables teachers to intervene immediately when students misunderstand a concept or principle which is important in meeting the learning objectives. A teacher may have to adjust a teaching strategy, provide different example or often alternatives explanations. In making these adjustments, teachers’ shows that they recognize and appreciate that previous attempt at teaching the concept or principle were not effective.

Guskey (2003) stated that making adjustments in teaching instantaneously with the aim of reaching all students, and especially less successful students, leads to improved learning for all students. Mathematics teachers can use several strategies to get and give feedback about how well students are learning materials that is being taught.

Motanic and Garg (2002) observe that there are electronics and non-electronic mechanism for getting feedback. Non electronic mechanism may include class discussions, cooperative group work, board-work, seatwork or answering questions that are posed orally. While these interactive strategies are effectives, a major short coming is that at any particular time, only a subset of the students in the class are actively providing information to the teachers about their learning and receiving feedback from the teachers. In order to engage more student in the interactive activities. Even when teachers employs interactive assessment strategies such as assignment or examinations to determine what and how much students have learned, care must be taken so that these strategies are effective in improving students learning. One reason that care must be taken is because the feedback to students does not occur during the instruction. When students respond to question on an assignments or examination, they may have moved on to “learning” new content. If understanding the old content and if there were misunderstanding of the old content that were not addressed immediately when it was presented, then the cumulative effect of understanding couples with no correlative feedback could put students at risk of under performance or even failure. A second reason is that students generally focus on doing what is necessary to get the highest grade possible on assessment strategies used by students in this content may result in very little learning.

In addition to this, the writers will agree with the view of Tyler (2000) which noted that learning of mathematic should take place through the active behaviour of the students and impressive teaching of the teacher.

Finally, according to Tyler (2000) said it is not what the teacher does, but through what the students does that learning takes place.

**1.1 BACKGROUND OF THE STUDY**

In general, mathematics has been playing important role in the development of the society both locally and internationally. But this study will lay an emphasis on the perception of teachers in teaching mathematics in schools with 50%-100% students as mathematics learners with their perception in learning mathematics. One could observe that out of thousands of students passing out from the secondary school every year, very few of them (about 0.52%) choose mathematics as a discipline. Even those that choose the subject as a career does so when there is no other alternative. There is shortage of qualified mathematics teachers in some schools, somebody that read Economics, Geography, Biology, and P.H.E etc. are assigned to teach the subject mathematics. This type of arrangement has an advert effect on the performance of students in mathematics and allied subject such as the science and the applied science which are of great importance to the nation, socially, economically and technologically.

More so, the study will encourage the mathematics teachers to keep up with the reform and the development in the educational literature to be skillful enough for realization their role. If this is realized by the teachers, students learning level will be realized. In conclusion, the study will help to improve and overcome some of the problems the secondary schools teaching encountered when teaching mathematics which is likely to improve students’ performance in mathematics.

**1.2 STATEMENT OF THE PROBLEM**

This study was aimed at examining different facts within the teaching and learning of mathematics in Nigeria secondary schools. This is an area that has been researched however there are certain as facts that research have not attended yet. Overview of many aspects of attitudes towards mathematics including a review of instructional is still unclear how the school environment affects the development of studies attitudes towards mathematics.

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