George Polya - Hungarian born mathematician
interested in problem solving
The 4-step model goes like this:
Step 1 - Understand - what I know
Step 2 - Devise a plan
Step 3 - Solve the problem by carrying out the plan
Step 4 - Check to see if you have in fact solved the problem
Solving a Problem
So, here's the story. Carol and Dina start with the same amount but at the shops Carol goes crazy and splurges to the tune of $345. Dina, a veritable model of restraint, only spends $80.
Our student uses the 4-step model beautifully.
Step 1 - here's what I know, the facts from the story
Step 2 - really interesting that our student decides to use a "before and after" representation. This is a nice way to represent the story given that it is told in a "before and after" style. Nice strategy.
Step 3 - is the calculations in the "Model" column but also represented in the diagram in Step 2
Step 4 - yep - student has checked by substituting back into the story. By working backwards they end up with the starting amount - all good!!
Same story, new student.
Note that this student goes straight for the jugular. Not needing to show the starting point, this student focuses right on the question of how much cash is left?
In fact, they didn't really need to know how much Dina and Carol started with. The calculation in Step 3 got them there:
$53 x 6 = $318
But some very nice application of the 4-step model.
I am getting the feeling that having a system for solving problems is a useful tool.
Polya's 4-step idea is not that dissimilar from the 9 steps I saw in the school in Japan.
The beauty of both models is that they are general enough to provide a framework that is useful in a variety of contexts but not so general as to lack practical application.
Stay tuned - I feel a "Ferrington" model can't be far away....