Problem Solving as A Process (steps)

Problem Solving as a Process 
 As a process, according to George Polya (1957), problem solving originally has 4 steps. The first step is understanding the problem. In this step, students have to carefully read the problem, decide what they are going to do, and indentify the important data.  The second step is devising a plan where students consider some possible actions or strategies such as drawing a graph, finding a pattern, or making a list. Furthermore, the next step is carrying out the plan. Students implement a particular plan to solve the problem, if necessary, create a new plan. Finally, students reflect and look back at what they have done, what worked, and what didn't. This process should be seen as a dynamic, non-linear and flexible approach. By using these steps, students will deal more effectively and successfully with most types of mathematical problems.

Some experts modified Polya’s steps into five steps or more. Charles Craig (2007), a member of EARAT Manuals, proposes 7-step method to solve math problem. The steps are:

1.      Read Through the whole problem carefully.

2.      List the facts and figures that are given in the question.

3.      Decide what needs to be found or calculated, rereading the question if necessary.

4.      Decide what method can be used to find the answer.

5.      Do the calculations using the steps decided on.

6.      Write your answer including any units

7.      Check to see that your answer seems reasonable and it provides the answer to the problem.

Charles divides the first Polya’s step into two points, read and list since this 7-step is mostly used to solve economic mathematics which has more figures, charts, or diagrams. Furthermore, Polya’s second step is also separated into two points, decide what needs to be found and decide what method can be used. Step 5 and 6 are originally part of the Polya’s third step while step 7 belongs to the Polya’s fourth step.

Burris Pearson (2010) suggests a five-step mathematics problem solving process. The steps are:

1.      Understand the problem

2.      Devise a plan

3.      Carry out the plan

4.      Look back

5.      Extend the problem

Burris’s modification does change significantly since the process generally is the same with polya’s steps. The difference is that he adds 1 more step after ‘look back’, which is named ‘extended problem’. It seems that he miss understand that problem solving as a process and problem solving as an approach because he stated ‘it is important for teacher to extend the problems’ in his fifth step.

Many experts developed Polya’s step into 8-step, 9-step, or 12-step, mostly, in order to adjust the steps for more specific use only. For instance, Charles Craig make his 7-step to solve economic math, Woei Hung (2008) invented his 9-step for instructional designers and educators, and Phil Wankat (2011) sets up a 12-step problem solving process for introductory thermodynamics.

References

George Polya.1957.How to Solve It, A New Aspect of Mathematical Method.USA.

Charles Craig.2007.Basic Steps in Problem Solving.EARAT Manuals.

Burris Pearson.2010.Excerpt from Understanding the Math You Teach Content and Methods for Prekindergarten Through Grade 4.http://www.education.com/reference/article/five-step-problem-solving-process/ diakses tanggal 20^th September 2013.

Woei Hung.2008.The 9-step Problem Solving For Problem Based Learning: Aplication of The 3C3R Model.Elsevier Ltd.

Phil Wankat.2011.Problem Solving in 12 Steps For Introductory Thermodynamics.ChE Division.