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# Problem-Solving Strategies: Algorithms and Heuristics (page 2)

By — Pearson Allyn Bacon Prentice Hall
Updated on Jul 20, 2010

#### Teaching Problem-Solving Strategies

Occasionally students develop problem-solving strategies on their own. For instance, many children invent simple addition and subtraction strategies long before they encounter arithmetic at school (Carpenter & Moser, 1984). But without some formal instruction in effective strategies, even the most inventive of students may occasionally resort to unproductive trial and error to solve problems.

To be truly effective problem solvers, students must have a solid grounding in—that is, a conceptual understanding of—the subject matter in question (more about this point shortly). But they also benefit from explicit instruction in the use of both algorithms and heuristics. The following are some strategies we might use:

For teaching algorithms:

• Describe and demonstrate specific procedures and the situations in which each can be used.
• Provide worked-out examples of algorithms being applied, and ask students to explain what is happening in each step.
• Help students understand why particular algorithms are relevant and effective in certain situations.
• When a student’s application of an algorithm yields an incorrect answer, look closely at what the student has done, and locate the trouble spot

For teaching heuristics:

• Give students practice in making ill-defined problems more specific and well defined.
• Teach heuristics that students can use in situations where no specific algorithms apply; for example, encourage rounding, identifying subgoals, and drawinganalogies.

For teaching both algorithms and heuristics:

• Teach problem-solving strategies within the context of specific subject areas (not as a topic separate from academic content) and, ideally, within the context of authentic activities.
• Engage in joint problem-solving activities with students, modeling effective strategies and guiding students’ initial efforts.
• Provide scaffolding for difficult problems (e.g., break them into smaller and simpler problems, give hints about possible strategies, or provide partial solutions).
• Ask students to explain what they are doing as they work through a problem.
• Have students solve problems in small groups, sharing ideas about problem-solving strategies, modeling various approaches for one another, and discussing the merits of each approach. (R. K. Atkinson, Derry, Renkl, & Wortham, 2000; Barron, 2000; Chinn, 2006; Crowley & Siegler, 1999; Gauvain, 2001; Kirschner et al., 2006; Mayer, 1985; Reimann & Schult, 1996; Renkl & Atkinson, 2003; Rogoff, 2003)

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