teaching and learning mathematics 1

7/27/2019 Teaching and Learning Mathematics 1

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ISSUES IN LEARNING AND TEACHING: MATHEMATICS

Prof. ANANT VYAWAHARE, M. MOHOTA SCIENCE COLLEGE,NAGPUR INDIA, [email protected]

1. Mathematics is a subject to be prepared mentally and manually both.It needs to practice this subject than to read only as a fiction forentertainment. Hence skill and intelligence to understand the subjectare needed .Not only this, memory is equally an important factor .Tounderstand the subject, three factors are responsible: pedagogy,

Androgogy and Mathetics.

(i) The subject communication does not exist in absence of properpedagogy, the science of learning. This requires not only skill butalso inborn genius quality to become a successful teacher.Expertise in pedagogy is based on the knowledge of the subject..For this, teacher should be a lifelong learner; he should update hisknowledge of subject. New researches in mathematics are pouredin the treasure of mathematics. Knowledge, not information, is abasic requirement of a teacher. Pedagogy is an outcome of thesefactors. A creative teacher aims at the subject and the studentsboth. If his fundamental concepts are clear, he can deliver thegoods more effectively.

(ii) Androgogy deals with the problems of teachings and learning inreference to mass education and adults. This has an implication tolifelong learning again. Burners cognitive theory and Rogersempathy models are useful to deal with Androgogy. A standardformat cannot be derived to deal with this factor of education.Each case may have a different solution. A teacher inmathematics should have an instant and knowledge-basedanswer to overcome the situation.

(i) Mathetics is a science of individual learning. Mathetics has its ownimportance in this subject for the reason that unless the insight ofthe subject is not achieved, mere understanding and practice isnot enough. Mathematics cannot be learnt en mass; an individuallearning is necessary in order to fulfill the needs of every pupil.Collective learning may not be so effective for good outcome .Itmay be useful for general mathematics, but to acquirespecialization, personalized system of instructions should be usedto make the learning subject-specific.
mailto:[email protected]:[email protected]


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2 Retention and transfer of knowledge are the basic aims of teachingand learning mathematics. Psychomathematics, dealing with behavioralscience towards mathematics learning, shows that in addition toconcentration and hard work, insight of the subject is necessary. Learnershould be able to think of the situation and be able to read between thelines, To every statement in mathematics, he should ask himself thequestion` Why` which may increase his grasp of the subject.Counterthinking also helps in retention of subject.

3. Mathematics teaching is a creative art and learning is science.Imagination in teaching and giving instructions is a model the teacher hasto know. Teacher has to develop interest about the subject among thelearners. This model will depend upon the requirements of learner. Thatis his primary goal. Mathematics includes classification of facts,recognition and reorganization of the sequences and relative significance.Objectivity, precession both in thought and practice are necessary for the

achievement of these skills of teaching and learning. It is imperative thatthe teaching of mathematics reflect objectivity, precession and challengeof verification in thought and action.

4. It is falsely presumed that a popular teacher in mathematics is one whodoes maximum frontal teaching and solves maximum problems. But thisconcept is misleading. A good teacher inspires and encourages studentsto work him or herself. He has to create the importance of learning thesubject using his skills. He should be student friendly in the sense that heshould not be merely a tutor or a counselor but makes the students to`do Mathematics.

5 One cannot learn mathematics without solving the problems andpracticing the proofs of the theorems. The best way to understand amathematical theory is to find a prototypal concrete example of theoryand study it. Without solving problems not much can be done in thesubject. It is because of this realization that abstractionism inmathematics is decaying. There are two ways of mathematicalpresentation. One is induction in which the theory is explained byexamples first and then the proofs follow. It is explained as going forparticular to general, simple to complex, local to global. Appliedmathematics is a branch to be dot in this way. The other type is

deduction in which the rules are mentioned and then the examples aregiven in the support of the theory. It is of the form: global perspective tolocal occurrence. The more general the presentation is the more useful itis for the learners. So there is a tie between the two concepts ofinductivism and deductivism. But both are equally relevant. The axiomaticapproach to mathematics is dealt by the deductive method.


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6 There are sum small units of learning which are to be thought undercognitive approach. Behaviorism is an inductive approach whereascognitivism in mathematics education is deductive.

7 There are four levels of learning:(i). Learning for knowledge of the subject: This gives a broad-basedconcept of mathematics. Every topic cannot be discussed in details butthey are necessary a vital in applications. A student of mathematicsshould have the knowledge of all branches but he can be an expert inone or two heads.

(ii). Learning for doing mathematics: This is required to attain the skill ofthe subject inspiration for higher development and attainment ofcompetency in the subject. It will also lead to the stability andperformance.

(iii). Learning to live together: For collective responsibility, mutualunderstanding and sense of development of coexistence. This concept isglobal and is community based.

(iv). Learning to `be for lifelong learning. This encourages self-development, personality and introspection. This leads to development ofan individual in reference to community living.

8 For learning mathematics all the arguments mentioned above aredirectly or otherwise useful. Specially learning mathematics is learning to`do mathematics. The mathematical education aims at to make it

communication effective both in theory and practice formal and non-formal systems, global and local also.

9 Good teaching is subtle and intuitive. Mathematics contents both finiteand infinite. Hence inductivism and deductivism are equally relevant.Mathetics as mentioned above depends upon learners behavior andneeds priority attentions for the uplift of the subject. Cognitive learningis useful for long term retention. Learning is achieved by practice only.The more he reads the more will be followed by the student. Matheticsis a non-ending process. Whatever a student sees, hears experienceshis learning begins. Hence lifelong Mathetics is to be achieve by a

student and his teacher.

10 Evaluation of what is taught and learnt needs to be discussed in thelight of efforts for the popularization of mathematics. It is theresponsibility of the teachers to make the subject popular, broad based


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and application friendly. Considering the exception of low levelstudents, the evaluation of students performance depends upon a goodteacher only. Hence mathematics teacher has to lecture the subjectalong with self-evaluation. Teaching is not lecturing only; lecturing is tobe supplemented by evaluation. Similarly, regular assignments willexplain the depth of knowledge of a student. Hence, Mathetics includesevaluation along with learning.

Number of words: 1217

Reference:

1. B.P.Parashar, Teaching and learning Mathematics University News,

AIU, New Delhi, India

teaching and learning mathematics 1

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