PROBLEM SOLVING METHOD

Maths is a subject of problem. Its teaching learning process demands solving of innumerable problems.A problem is a sort of obstruction or difficulty which has to be overcome to reach the goal.

Problem solving is a set of events in which human beings was rules to achieve some goals – Gagne

Problem solving involves concept formation and discovery learning –Ausube

 

Steps in Problem Solving / 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 or checking 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 two sets. If A={2,3,5}. B={3,5,6} And C={4,6,8,9}.

Prove that:  AU(BUC)=(AUB)UC

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

1. 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.
2. The union of two set A and B is express as ‘AUB ’

• 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. ‘BUC’ Then the union of set A and’BUC ’. Thus he can get the value of AU(BUC) . Similarly he can solve (AUB)UC

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

After solving the problem the child will analyse the result on the basis of given data and verify his hypothesis whether A U (B U C) is equals to  (A U B)  U C or not.

 

Step 5 : Verifying of the result

After testing and verifying his hypothesis the child will be able to conclude that

A U (B U C) = (A U B)  U C

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

 

Merits

• This method is psychological and scientific in nature
• It helps in developing good study habits and reasoning powers.
• It helps to improve and apply knowledge and experience.
• This method stimulates thinking of the child
• It helps to develop the power of expression of the child.
• The child learns how to act in new situation.
• It develops group feeling while working together.
• Teachers become familiar with his pupils.
• It develops analytical, critical and generalization abilities of the child.
• This method helps in maintaining discipline in the class.

 

Demerits

• This is not suitable for lower classes
• There is lack of suitable books and references for children.
• It is not economical. It is wastage of time and energy.
• Teachers find it difficult to cover the prescribed syllabus.
• To follow this method talented teacher are required.
• There is always doubt of drawing wrong conclusions.
• Mental activities are more emphasized as compared to physical activities.

 

Conclusion

Problem solving is a suitable approach in teaching of mathematics. It develops in the learners the ability to recognize analysis, solve and reflect upon the problematic difficulties.

you can used all the methods discuss in my blogs as per the requirements. The twin combination of inductive deductive method and analytic synthetic methods are recommended as your day to day class. The inductive deductive method will be more suitable for arithmetic and algebra whereas analytic synthetic method will find greater application in plane geometry, trigonometry and solid geometry.

In some of the topics, it will be quite interesting to use project method or laboratory method. To budget the timing it will be good to use dogmatic method of teaching and for introducing new topic  and reviewing topic lecture method with example  can be more effective. At the end I can say that everyone have their own way of teaching and you can make your teaching more interesting by using combination of  your own method and the method discuss in my blog.

 

Source: The Teaching of mathematics by KULBIR SINGH SIDHU (Sterling Publisher Pvt Ltd)