TEACHING OF MATHEMATICS

Though Mathematics being so important subject and occupying a central position since the Ancient period still it has not been the interest of many students. The gaps are found between aspiration and achievement. Mathematics is highly abstract. It is concerned with ideas rather than objects; with the manipulation of symbols rather than the manipulation of object. It is a closely-knit structure in which ideas are interrelated. Mathematical concepts are hierarchical and interconnected, much like a house of cards. Unless lower-level concepts are mastered, higher-level concepts cannot be understood. Students who discover some of the structures of mathematics, are often impressed by its beauty. They note the lack of contradiction, and they see how a new technique can be derived from one that has already been learned.

Teaching of mathematics is not only concerned with the computational know how of the subject but is also concerned with the selection of the mathematical content and communication leading to its understanding and

application. So while teaching mathematics one should use the teaching methods, strategies and pedagogic resources that are much more fruitful in gaining adequate responses from the students then we have ever had in the past.  The teaching and learning of mathematics is a complex activity and many factors determine the success of this activity. The nature and quality of instructional material, the presentation of content, the pedagogic skills of the teacher, the learning environment, the motivation of the students are all important and must be kept in view in any effort to ensure quality in teaching-learning of mathematics.

In this blog an effort to discuss teaching mathematics, under teaching methods, strategies and pedagogic resources. The process of innovation is generally described as consisting of three essential steps, starting with the conception of an idea, which is then proposed and is finally adopted. Though many ideas have been conceived to bring about change in the teaching of mathematics, it is yet to be proposed and adopted. So, the innovations discussed may not be new in terms of the idea but is new in terms of practice.

Education is imparted for achieving certain ends and goals. Various subjects of the school curriculum are different means to achieve these goals. So with each subject some goals are attached which are to be achieved through teaching of that subject. According to Sidhu (1995) the goals of teaching mathematics are as below:

1. To develop the mathematical skills like speed, accuracy, neatness, brevity, estimation, etc.

2. To develop logical thinking, reasoning power, analytical thinking, critical-thinking.

3. To develop power of decision-making.

4. To develop the technique of problem solving.

5. To recognize the adequacy or inadequacy of given data in relation to any problem.

6. To develop scientific attitude i.e. to estimate, find and verify results.

7. To develop ability to analyze, to draw inferences and to generalize from the collected data and evidences.

8. To develop heuristic attitude and to discover solutions and proofs with the own independent efforts.

9. To develop mathematical perspective and outlook for observing the realm of nature and society.

Looking to the aims of teaching mathematics it can be seen that more focus is laid to the higher level of objectives underlying the mathematics subject, like critical thinking, analytical thinking, logical reasoning, decision-making, problem-solving. Such objectives are difficult to be achieved only through verbal and mechanical methods that are usually used in the class of mathematics. The verbal methods of instruction give all importance to speech and texts, to the book and to the teacher. From an historical point of view this method was majorly used until the end of the nineteenth century. In one of these verbal methods teachers are simply satisfied with giving the mathematical rules to pupils and having them memorize it. They justify this method by saying pupils would not understand explanations. Their task is to transmit to their pupils the knowledge which has accumulated over the centuries, to stuff their memory while asking them to work exercises, e.g. The rule of signs and formulas in algebra, students memorize this and remember it! Another verbal method involves explanation. Teachers who use this method assume that the mental structure of the child is same as the adult’s. But a developmental stage according to Piaget is a period of years or months during which certain developments take place. Teachers think teaching must imply logic, and logic being linked to language, or at least to verbal thought, verbal teaching is supposed to be sufficient to constitute this

logic. This method leads to series of explanations and students at the initial steps of logical explanations trying to understand and grasp but slowly the gap is created between the explanations transmitted by teacher and received by students which lead to the poor understanding on part of students and they develop a fear of the subject: Mathsphobia. The Education Commission (1964-66) points out that “In the teaching of Mathematics

emphasis should be more on the understanding of basic principles than on the mechanical teaching of mathematical computations”. Commenting on the prevailing situation in schools, it is observed that in the average school today instruction still confirms to a mechanical routine, continues to be dominated by the old besetting evil of verbalism and therefore remains dull and uninspiring.