Teaching of mathematics

After attending mathematics workshop at Dungurpur, in which Umar ji and Dharmendra ji took the sessions. Idea stroked on mind write something on mathematics.  I jot down the some points how should be mathematics teaching?

Start with my favorite line-

v  “Every student can learn mathematics and every student should learn mathematics.”

v  Manipulative skills in mathematics cannot be obtained by doing a large number of drill-sums. These cannot be obtained only by understanding the structures of the systems under consideration. Drill very often impedes the learning process since it makes learning monotonous and it makes the subject look trivial. Thus the intellectual content of school arithmetic is very little and rebellion of the children against arithmetic, which is very often ascribed to the difficulty of the subject, is really against the triviality of the subject.

v  The best way to teach mathematics is to let the students recreate mathematics for themselves. Mathematics is learnt b doing it rather than by listening passively to it. Students should be helped to discover as much of mathematics as possible themselves. The teachers’ role is to help the students in discovering mathematics.  Mathematics should be taught not as a finished product but as an evolving discipline.

v  The philosophy and nature of mathematical thinking should influence and be influenced by thinking around us.  In mathematics we have to consider all possibilities, in life also neglect of any possibility leads to errors. Mathematics teaching should aim at producing citizens who are rather precise in language, who are strong in their logical reasoning, who are not passive learners, who can detect fallacious reasoning, who can argue in depth, who have an appreciation for intellectual aesthetics and who have the willingness and ability to climb intellectual mountains.

v  The unity of mathematics should be emphasized throughout. Every opportunity should be taken to point out how different mathematical concepts illuminate one another and how these relationships give great power to mathematics.

v  Discussion of unsolved problems will show mathematics as open-ended discipline.

v  Teaching of mathematics should be integrated with the other subjects, as far as possible, especially in schools.

v  The teacher should encourage questions both inside and outside the class rooms and he should not appear annoyed even if the questions are not relevant.

v  The teacher should not be over anxious to help a student who is struggling with a problem. The student may have to muddle around on a problem before it becomes clear to him. The muddling process is the core of creative thinking. The teacher may give hints but should not deny the students the chance to think.

v  Creativity is the heart and soul of mathematics. Curiosity and creativity are key-stones in mathematics.