Materi : Problem Solving as a Process (steps) part 2
Judul materi : Problem Solving as a Process (steps) part 2
Problem Solving as a Process (steps) part 2
As a process, according to George Polya (1957), problem solving originally has 4 steps. The 1st step is understanding the problem. In this step, students have to carefully read the problem, capable to point out the principal parts of the problem, the unknown, the data, and the condition. George Polya subdivided this step into two stages: 1) getting acquainted and 2) working for better understanding. The 2nd 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 in which 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 is also important for students since by looking back at the completed solution, by reconsidering and reexamining the result and the path that led to it, students could consolidate and develop their ability to solve problems. All these 4 processes 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 and a lecture in University of Georgia, proposes 7-step method to solve math problem. He developed these steps to solve mathematics economy problems since EARAT Manuals deals more with business world. But, these steps also can be applied on any mathematics problems using different strategies. The steps are:
1. ReadThrough the whole problem carefully.
Students need to read the whole problem not partially and try to understand the problem.
2. List the important information that are given in the question.
In order to help them understand the problem, students should make a list of the important information. Listing can be done in many ways such as write it on a paper formally or just underline it. Listing all the important information also help students remembering the problem.
3. Decide what needs to be found.
Students have to be sure and clear about what the question wants them to answer and also what needs to be found first to help them find the solution. This helps students avoiding unnecessary actions and also influences the way they answer the problem or give a conclusion.
4. Decide what method can be used to solve the problem.
Students consider some possible actions or strategies to solve the problem such as drawing a graph, finding a pattern, or making a list and decide the most suitable method.
5. Do the calculations using the steps decided on.
Students solve the problem based on strategies they have decide on the 4thstep.
6. Write your answer
Writing out the answer is not easy. Students have to be aware about what the problem asked and how they state the conclusion.
7. Check to see that your steps and answer seems reasonable and it provides the answer to the problem.
Students check every step they have done. Reexamining the problem and the calculations are very important to anticipate any mistake they made during the process.
In the Polya’s 1st step, students have to read carefully the problem. So, it is obvious that Charles’s first step is belong to polya’s 1st step. In the 2ndCharles step, students need to list every important information given on the problem. This activity similar to what Polya said that students have to be able to point out the principal parts of the problem. Therefore, 2ndCharles step also belongs to Polya’s 1st step.
3rd Charles step encourages students to find out what the question asked and what needs to be found before finding the solution and in the 4th step, students consider and decide the most suitable strategies to solve the problem. All these activities are part of devising plan on Polya 2nd step.
Students do the calculation or the plan in the 5th and write the final answer in the 6thCharles step in which Polya united it in his 3rd step. All the activities are the same with Polya 3rd step. Finally, the 7thstep of Charles is part of Polya’s 4th step where students look back and check every step to fix any mistake they made.
Charles divides the first Polya’s step into two points, read and list, since this 7-step is mostly used to solve mathematics economy problems which have more important information such as figures, charts, or diagrams. Furthermore, he also separate Polya’s 2ndstep into two points, decide what needs to be found and decide what method can be used for the same reason as the 1st. Furthermore, step 6 becomes different points from the 5th step because he argued that many mathematics problems, especially mathematics economy problems, are not easily concluded with simple sentences and many students have difficulties in it.
There is an example included in Charles paper. The problem is:
“An apprentice earns $25.85 per hour and $36.35 for overtime. If he works 40 hours at the regular rate and then works 8 hours of overtime in one week, how much does he make in total?”
How to solve it:
Step 1: Read the problem carefully
An apprentice earns $25.85 per hour and $36.35 for overtime. If he works 40 hours at the regular rate and then works 8 hours of overtime in one week, how much does he make in total?
Step 2: List the important information
An apprentice earns $25.85 per hour and $36.35 for overtime. If he works 40 hours at the regular rate and then works 8 hours of overtime in one week, how much does he make in total?
Step 3: Decide what needs to be found
The words “how does he make…” tell us to figure out what he should be paid.
Step 4: Decide what method can be used
The words “per hour” tell us to multiply and the words “and … in total” tell us to add. Multiply to find the two amounts and then add them to find the total earnings.
Step 5: Do the calculations
$25.85 x 40 = $1034.00
$36.35 x 8 = $290.80
Then add those two numbers
$1034.00
$290.80
$1324.80 in Total
$1324.80 in Total
Step 6: Write your answer
The apprentice makes a total of $1324.80
Step 7: Check to see that your steps and answer seems reasonable.
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.
Charles Craig.2011.Mathematics Skills: Manipulation of Variables.EARAT Manuals.
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