*Problem-solving is a process—an ongoing activity in which we take what we know to discover what we don't know.*

Problem-solving involves three basic functions: Problem-solving is, and should be, a very real part of the curriculum.

It presupposes that students can take on some of the responsibility for their own learning and can take personal action to solve problems, resolve conflicts, discuss alternatives, and focus on thinking as a vital element of the curriculum.

It provides students with opportunities to use their newly acquired knowledge in meaningful, real-life activities and assists them in working at higher levels of thinking (see Levels of Questions).

Here is a five-stage model that most students can easily memorize and put into action and which has direct applications to many areas of the curriculum as well as everyday life: For younger students, illustrations are helpful in organizing data, manipulating information, and outlining the limits of a problem and its possible solution(s).

The goal is to expose students to multiple problem-solving strategies and to build deep and flexible mathematical knowledge.“In math class, you should have opportunities to talk about different approaches, and comparison helps us to think not only about what works in mathematics, but also about how and why things work,” says Star.

“Our materials are designed to be used by algebra teachers to supplement their regular curriculum, to provide a stronger focus on the learning of multiple strategies.“ The curriculum materials were developed with middle and high schoolers in mind, but there are some applications for elementary schoolers as well.

The idea is that you use your first incorrect guess to make an improved next guess. In relatively straightforward problems like that, it is often fairly easy to see how to improve the last guess. Children themselves take the role of things in the problem.

In some problems though, where there are more variables, it may not be clear at first which way to change the guessing.2 Act It Out We put two strategies together here because they are closely related. In the Farmyard problem, the children might take the role of the animals though it is unlikely that you would have 87 children in your class!

We now look at each of the following strategies and discuss them in some depth. If they can also check that the guess fits the conditions of the problem, then they have mastered guess and check.

You will see that each strategy we have in our list is really only a summary of two or more others.1 Guess This stands for two strategies, guess and check and guess and improve. This is a strategy that would certainly work on the Farmyard problem but it could take a lot of time and a lot of computation.

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