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Teaching Problem Solving in Mathmatics

applyingThe California Mathematics Framework (2000; Source: California Department of Education) explains that, "Problem solving in mathematics is a goal-related activity that involves applying skills, understandings, and experiences to resolve new, challenging, or perplexing mathematical situations" (p. 8). Further, the Framework states that problem solving "is an essential part of mathematics and is subsumed in every strand and in each of the disciplines in grades eight through twelve. Problem solving is not separate from content. Rather, students learn concepts and skills in order to apply them to solve problems in and outside school" (p. 19). The Framework (p. 10) goes on to explain that problem solving generally follows these stages:

  1. Formulation, analysis, and translation;
  2. Integration and representation; and
  3. Solutions and justifications.


In the following clip, Observe Ms. England as she breaks the Framework's "Problem Solving Stages" down into more easily digestible chunks as her students prepare for the "Hikers Beware!" task.

students workLet's look more closely at Ms. England's "Rule of Four?" She requires students to first understand the situation, then represent it with a table, a graph, and an equation (though the order in which the representations are produced is left to the students). In addition, Ms. England states (and restates) that students must "prove to us that your answers are correct."

However, even when we design problems that take into account the needs of our learners, there are times that our students encounter a new problem solving situation and do not know where to begin. Let?s observe what Ms. England does to help her students when they are not sure how to approach a new problem solving situation.

How did she guide her students to get back on track? She utilized strategic questioning to prompt their thinking. Ms. England guides her students to focus their thinking on the relationship between gallons of water and days. She suggests that they organize this information into a chart. She has helped them to develop a strategy (or heuristic) for making sense of the problem.

Classroom Clip Reflection:

  • How does she use the Rule of Four to help students think about different ways to approach a problem? How might this help students solve problems in the future?
  • How did Ms. England help her student move forward when they were stuck? What other strategies might she have modeled or suggested for them?
  • What are the implications for your own work with students?