PROBLEM SOLVING

Minu Michael

Mathematics

M.G.U.C.T.E Nedumkandam

Abstract Problem solving consists of using generic or ad hoc methods, in an orderly manner, for finding solutions to problems. Some of the problem-solving techniques developed and used in artifical intelligence, computer science,engineering, mathematics, or medicine are related to mental problem-solving techniques studied in psychology.The study was conducted in G.V.H.S.S Nedumkandam. The 22 students of 8 C were selected as the subjects for the study.

    

1. INTRODUCTION

                                                          Problems are a central part of  human life. Everybody in this world, from birth onwards faced with some problems. Any single work of in the life situation is in a sense of problem, simple or complex requiring solution. One of the objective of the modern education is to develop problem solving skills.

       Problem solving ability is sometimes reffered to as reasoning.One should be trained to reason in a systematic and orderly manner to find solutions to problems. Solutions to problems are drawn out of experiences.

  The problem solving behavior involves convergent and divergent thinking. The former involves generalization and the latter discrimination or differenciation. The problem solving behavior results from the leaving of new and more complex higher order rules. The present experiment minimizes the verbal component of thinking, while one arrives at a solution for the problem.

            After identifying the existence of a problem,we must define it’s scope and goals. Problem solving does not usually begin with a clear statement of the problem;rather most problems must be identified in the environment ;then they must be defined and represented mentally.

                Psychologists have described the problem solving process in terms of a cycle. The cycle constitute following stages in which the problem solver must:

1)   Identify the problem.

2)   Define and represent the problem mentally.

3)   Deveop solution strategy.

4)   Organise his/her knowledge about the problem.

5)   Allocate mental and physical resources for solving the problem.

6)   Monitor his/her progress towards the goal.

7)   Evaluate the solution for accuracy.

 

Problem :-

                   To study the process of reasoning through analysis of the subject behavior while solving similar problems of increasing difficulty.

2. METHOD

a)  Subjects:

                                 There are 22 children of the class 8 C in G.H.S.S Nedumkandam is selected as subject s for the problem solving.

b)  Apparatus:

                           Five wooden blocks varying in size with a stand having 3 poles and stop clock.

c)  Procedure:

                          Three positions below labeled A,B,C were used. The poles of  wooden blocks arranged in the order from the largest at the bottom and the smallest was placed at the top. Then the subject was seated comfortably. The following instructions were given.

                     “You are to move this wooden blocks placed in the pole A to either pole B or C ,moving only one block at a time, and never placing a large block upon a smaller one. Use all the three positions in making the moves. Try to think ahead of each time and formulate mentally a plan of actions before you start to moving the blocks. If it seems impossible to form a plan you may start with trial and error and formulate a plan as you work alone. Ready go.”

A.       B.      C.

The experiment was started with the simplest problem of  2 blocks, the number of moves for each problem was restricted. The highest level of the problem was with the 5 blocks. For each child the time taken  was note down using stop clock. When the subject succeed in two consecutive trials in a particular problem , she was asked to go to the next higher problems. When the subject failed to solve the problem in two consecutive trials, the experiment was stoped. Soon after the experiment, introspective report was collected and was recorded in after in the table.

3. RESULTS

The table shows the group data in the problem solving experiment.

4. DISCUSSION

The present experiment has been conducted to study the process of reasoning through analysis of the subject’s behavior while solving similar problems of increasing difficulty. Problem solving reffers to an individual’s ability to find out the solutions  to the problem or finding out all the possible alternatives for the same problem. Since we are living in a competitive world, one of the important aim of education is to develop a problem solving ability in an individual and hence it is imparitive to analyse the problem solving ability of an individual.

                         On analysis of the group data, it is found that all the 22 subjects in the group have taken the minimum of the 2 trials for the two block problem. The subject JPP has taken the highest time of  23 seconds and the subject NS has taken the lowest time of 6 seconds. The subject AB has taken the highest time of 25 seconds, and the subject SS has taken the lowest time of 15 seconds for three block problem.

                                                                     The subject SB has taken the highest time of  38 seconds and the subject AV has taken lowest time of  33 seconds for four block problem. Except AV and SB all others failed to complete the four block problem.

5. CONCLUSION

        i.            The majority of the subjects in the group able to solve the the problem with 3 blocks.

     ii.            Individual differ in the problem solving ability.

6. REFERENCE

I.       Davis, G.A. Psychology of problem solving, Newyork: Basic Books.1973.

II.    Newell, A and Simon, HA. Human Problem Solving, Engle Wood Cliff, Newjercy : Prentice Hall, 1972.

Reflective Journal:

  It’s very interesting to do the problem solving experiment among the students. They are very interested to the experiment. Some of the students succeed in 4 block probem. But none of them succeed in 5 block problem.  All of them have a competition mentality towards the problem.

Appendix

Sl.No	Initial	2 Blocks			3 Blocks			4 Blocks			5 Blocks
		No.of trials	Time(sec)	Success/ failure	No.of trials	Time(sec)	Success/ failure	No.of trials	Time(sec)	Success/ failure	No.of trials	Time(sec)	Success/ failure
1	AJ	2	15	S	5	20	F	-	-	-	-	-	-
2	AMK	2	12	S	5	19	F	-	-	-	-	-	-
3	AR	2	11	S	5	22	F	-	-	-	-	-	-
4	AV	2	11	S	3	20	S	3	33	S	5	49	F
5	AN	2	10	S	5	18	F	-	-	-	-	-	-
6	AS	2	9	S	5	14	F	-	-	-	-	-	-
7	BPM	2	8	S	5	19	F	-	-	-	-	-	-
8	JPP	5	23	F	-	-	-	-	-	-	-	-	-
9	NS	2	6	S	5	21	F	-	-	-	-	-	-
10	PR	2	14	S	5	17	F	-	-	-	-	-	-
11	SB	2	12	S	3	15	S	4	38	S	5	40	F
12	SS	2	10	S	5	18	F	-	-	-	-	-	-
13	STS	2	10	S	5	23	F	-	-	-	-	-	-
14	AKS	2	9	S	5	22	F	-	-	-	-	-	-
15	AM	2	8	S	5	20	F	-	-	-	-	-	-
16	AR	2	9	S	5	21	F	-	-	-	-	-	-
17	AH	2	7	S	5	21	F	-	-	-	-	-	-
18	AA	2	10	S	5	19	F	-	-	-	-	-	-
19	AB	2	20	S	5	25	F	-	-	-	-	-	-
20	ACA	2	20	S	5	24	S	5	30	F	-	-	-
21	AJ	2	16	S	5	23	F	-	-	-	-	-	-
22	NV	2	13	S	5	23	F	-	-	-	-	-	-