Problem Solving Methods

Problem Solving Methods

Mathematics is an essential discipline because of its practical role to the individual and society. Through a problem-solving approach, this aspect of mathematics can be developed. Presenting a problem and developing the skills needed to solve that problem is more motivational than teaching the skills without a context. The problem methods  aims  at presenting the knowledge to be learnt in the form of a problem.

 The child is curious by nature. He wants to find out solutions of many problems, which sometimes are puzzling even to the adults. The problem solving method is one, which involves the use of the process of problem solving or reflective thinking or reasoning. Problem solving method, as the name indicated, begins with the statement of a problem that challenges the students to find a solution.

Procedure for Problem solving:

1. Identifying and defining the problem:

The student should be able to identify and clearly define the problem. The problem that has been identified should be interesting challenging and motivating for the students to participate in exploring.

2. Analysing the problem:

          The problem should be carefully analysed as to what is given and what is to be find out. Given facts must be identified and expressed, if necessary in symbolic form.

3. Formulating tentative hypothesis

Formulating of hypothesis means preparation of a list of possible reasons of the occurrence of the problem. Formulating of hypothesis develops thinking and reasoning powers of the child. The focus at this stage is on hypothesizing – searching for the tentative solution to the problem.

4. Testing the hypothesis:

Appropriate methods should be selected to test the validity of the tentative hypothesis as a solution to the problem. If it is not proved to be the solution, the students are asked to formulate alternate hypothesis and proceed.

5. Verifying of the result :

No conclusion should be accepted without being properly verified. At this step the students are asked to determine their results and substantiate the expected solution. The students should be able to make generalisations  and apply it to their daily life.

Example :

Define union of three  sets. If A={2,3,5}. B={3,5,6} And C={4,6,8,9}.

Prove that A È (B È C) = (A È B)  È C

Solution :

Step 1: Identifying and Defining the Problem

After selecting and understanding the problem the child will be able to define the problem in his own words that

(i)           The union of two sets A and B is the set, which contains all the members of a set A and all the members of a set B.

(ii)          The union of two set A and B is express as ‘A È B’ and symbolically represented as A È B = {x ; x Î A or x Î B}

(iii)         The common elements are taken only once in the union of two sets

Step 2: Analysing the Problem

          After defining the problem in his own words, the child will analyse the given problem that how the problem can be solved?

Step 3 : Formulating Tentative Hypothesis

After analysing the various aspects of the problem he will be able to make hypothesis that first of all he should calculate the union of sets B and C i.e. (B È C). Then the union of set A and B È C. thus he can get the value of

A È (B È C). Similarly he can solve (A È B)  È C

Step 4: Testing Hypothesis

Thus on the basis of given data, the child will be able to solve the problem in the following manner

In the example it is given that

B È C                   =       {3,5,6} È {4,6,8,9}

                                      =                   {3,4,5,6,8,9}

A È (B È C)        =       {2,3,5} È {3,4,5,6,8,9}

                                =              {2,3,4,5,6,8,9}

Similarly,

A È  B        =       {2,3,5,6}

(A È B)  È C       =       {2,3,4,5,6,8,9}

After solving the problem the child will analyse the result on the basis of given data and verify his hypothesis whether A È (B È C) is equals to

 (A È B)  È C or  not.

Step 5 : Verifying of the result

After testing and verifying his hypothesis the child will be able to conclude that A È (B È C) = (A È B)  È C

Thus the child generalises the results and apply his knowledge in new situations.

Merits

1.       This method is psychological and scientific in nature

2.     It helps in developing good study habits and reasoning powers.

3.       It helps to improve and apply knowledge and experience.

4.     This method stimulates thinking of the child

5.      It helps to develop the power of expression of the child.

6.     The child learns how to act in new situation.

7.     It develops group feeling while working together.

8.      Teachers become familiar with his pupils.

9.      It develops analytical, critical and generalization abilities of the child.

10.                         This method helps in maintaining discipline in the class.

Demerits

1.      This is not suitable for lower classes

2.      There is lack of suitable books and references for children.

3.     It takes  more time and energy.

4.     Teachers find it difficult to cover the prescribed syllabus.

5.     To follow this method talented teacher are required.