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In some ways, math is entirely about solving problems. The earliest uses of math were to solve problems involving counting, measuring, and distributing.
Even the cutting edge math today is evolving through solving problems—some more practical, some more theoretical in nature. The point is that, to succeed in math, students must become comfortable in solving problems.
READ THIS ARTICLE FOR MORE IDEAS AROUND THE SHIFT FROM COMPUTATIONAL MATH TO PROBLEM SOLVING MATH
“A problem-solving curriculum, however, requires a different role from the teacher. Rather than directing a lesson, the teacher needs to provide time for students to grapple with problems, search for strategies and solutions on their own, and learn to evaluate their own results. Although the teacher needs to be very much present, the primary focus in the class needs to be on the students’ thinking processes.”
(Burns, 2000, p. 29)
In this unit, you learned about a classic method that is general enough to solve all kinds of problems—even ones that aren’t necessarily related to math! This generality is the primary strength of Polya’s method. Given any problem,
- you can try to understand it (Step 1),
- make a plan to solve it (Step 2),
- execute the plan (Step 3),
- and then reflect back on how you solved the problem (Step 4).
Figure 1 details the flow of Polya’s problem-solving method.
A common way that Polya’s method is used in math classrooms is through an attack strategy called UPSCheck.
An attack strategy is a general process for working through a math problem, and attack strategies have a strong evidence base for use in math problem solving (Freeman-Green et al., 2015; Krawec et al., 2012).
Figure 2 shows the UPSCheck strategy.
Similar to Figure 1,
Students:
Understand the problem by reading it;
make a Plan for how to solve the problem;
Solve the problem; then go back
Check their work.
Students might find UPSCheck easier to remember than the four steps of Figure 1.
With this four-step attack strategy, students do not receive specific guidance on which strategy to use in Step 2 (Plan) for any given problem. Although the webinar covered several of the most useful strategies, there are countless other strategies. The good news is that you will steadily get more familiar with strategies that you will share with your students as you work more and more at the school setting. In fact, if you regularly practice Step 4 (Check) of Polya’s method by reflecting on how you and your students solve problems, you will develop this skill even more rapidly!
But problem solving is much more than coming up with effective and systematic ways to help students get their math homework done.
- Why educators are so insistent about forcing everyone to take so much math throughout their schooling?
- Why is math a central area that all students—regardless of their field of interest—must pass to graduate high school?
There are several reasons, but one of the main reasons centers on
Problem Solving
Here is a list of some real life problems that we all may face throughout life…
|
Financial crisis |
Health crisis |
Relationship and Romantic concerns |
Workplace dilemmas |
|
Career pressure |
Unfair treatment |
Emotional upheaval |
Confusion and decision making |
|
Friendship problems |
Family life worries |
Dealing with our Past |
Safety and Security concerns |
It makes sense that the education system should somehow prepare us for those problems.
PROBLEM SOLVING SKILLS … can help!!!
Through learning the systematic logic of math, we are more prepared to handle our problems in a rational and successful way. So, as you help students develop their problem-solving skills, keep in mind that you are ultimately helping them succeed in life beyond school!
