Math Teaching

Introduction 

                Mathematics is a creation of human mind, concerned chiefly with ideas, processes and reasoning. It is much more than arithmetic, algebra, geometry, trigonometry and statistics.

Methods of Teaching Mathematics 

                  Methods are the ways to understand and practice teaching. Methods deal with the "how" of mathematics. " How to impart it's knowledge?  How to enable the child to learn it. "

                    It is final step of execution of what we plan to teach in mathematics. 

1. Lecture Method 

                     Teacher prepares his talk at home and pours it out in class.  Students sit silently, listen attentively and try to catch the point. Lecture is an informational method while goes against independent and original thinking of learner. 

                        Very few topics lend themselves to effective treatment by this method. However, it is conceded that,  on lectures by experts from outside may be arranged and would be found successful on topics like income tax and insurance.

2. Dogmatic Method 

                         Rules and formulae are given to class. Teacher tells pupils what to do, What to observe, how to attempt and how to conclude. He works out the model, sums on blackboard and pupils have to follow the patterns. 

3. Inductive and Deductive method 

      Inductive Method :  It leads from concrete to abstract, particular to general and from example to formula. It is the method of constructing a formula with help of sufficient number of concrete examples. It is based on induction which means proving Universal truth by showing that if it is true for a particular case and is further true for reasonably adequate number of cases, it is true for all such cases. 

                        A formula or generalisation is thus arrived at through a convincing process of reasoning and solving of problems. After a number of concrete cases, successfully attempts generalisation. 

Example : Give students cases a+b, x+y, l+m,p+q and ask them to find squares in each case, by multiplication and then they can generalise that (a+b)2 = a2+b2+2ab

Deductive Method :  It is opposite of inductive method.  Learner proceeds from general to particular, abstract to concrete and formula to example.  A preconstructed formula is told and asked to solve relevant problems. 

Example : S. I = P*T*R/100

By explaining application of this formula,  teacher will be problems. 

4. Heuristic Method 

             " Heuristic " is a Greek word,  which means " I find". Here,  child is put in place of a discoverer. It involves finding out by students, instead of merely telling by teacher. It aims at removing short comings of lecture method. It demands complete self-activity of learner. 

5. Analytic and Synthetic method 

Analytic method 

           It proceeds from unknown to known.  Analysis means " Breaking up" of problem in hand so that it ultimately gets connected with something obvious. 

                   Starts with what is to be found out.  Then think of further steps and find desired result. 

Example : Teacher has given 3 pens to Vinay, 6 to vikram. Vikram gave all his pens to Vinay. How many pens Vinay has? 

What we want to know ----> No.  of pens Vinay has. 

Vinay has taken 3 pens from teacher 

                                            +

Vinay has 6 pens from Vikram 

 Total number of pens = 3+6=9

Synthetic Method 

                    It is opposite of analytic method. One proceeds from Known to unknown. Synthesis is complement of analysis. 

                     If a/b =c/d, prove that 

ac-2b2/b = c2-2bd/d

Synthetic Proof :

               a/b=c/d

a/b-2b/c =c/d-2b/c       

ac-2b2/bc= c2d-2bd/dc

ac-2b2/b = bd2-c2/d        {Cancel 1/c on both sides }

Hence proved. 

6. Laboratory Method

          Maths has to be learnt by doing rather than by reading. Doing of maths, gives to need of suitable method and suitable place.  Laboratory method is the answer to it. It is based on principle of "learning by doing ".

7. Project Method 

           Based on John Dewey's philosophy of pragmatism, Dr.  Kilpartrick, defines it as, " A project is a unit of whole hearted purposeful activity, carried on preferably, in it's natural setting. "

8.  Topical method 

              Breaking up of a topic into suitable portions is concentric method, whereas topical method aims at keeping it intact. Topic is taken as a whole unit. Any topic when begun shouldn't be left half done. 

9. Concentric method 

                 It is widening of knowledge just as concentric circles go on widening. It is a system of arrangement of sub - matter. Study of topics spread over a number of years. 

10. Problem Method 

                   Teaching of maths demands solving of inmmerable problems. Efficiency and ability is a guarantee for success in learning this subject.