Web page for the Northwestern University Math Problem Solving Group.

There are several approaches for helping students with mathematical problem solving. Some of these approaches target the declarative and procedural knowledge problems, some focus on students' difficulty with conceptual understanding, and others concentrate on improving students' reasoning and critical thinking. These approaches vary depending on the nature and complexity of the problem. For basic problems, some students are taught to search for key words. However, this approach has often been criticized because it does not always prompt the correct mathematical operation and creates a high likelihood of errors. Moreover, it does not require a real understanding of the problem situation and relegates the activity to an imitation of drill-and-practice (Porter, 1989). Another well-researched approach is to teach students with math difficulty cognitive strategies for solving problems. For example, Montague, Applegate, and Marguard (1993) studied the effectiveness of a cognitive strategy instruction. This 7-step strategy ranged from initial steps of learning to read the problem and develop hypotheses to the final steps of checking one's work. This method has proven to be effective in helping students with math difficulty. Similar types of instructional strategies have been applied to technology-based interventions. The majority of these interventions are still in the prototype phase and thus are not yet available commercially.

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Lesh, R. (1981). Applied mathematical problem solving. Education Studies in Mathematics, 12, 235-264.

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The researchers have examined the effectiveness of anchored instruction environments, like the video, on the mathematical problem solving of students with learning difficulties. These environments were found to be more effective than other problem-solving instruction in helping students solve complex, contextualized video problems (Bottge, 1999; Bottge & Hasselbring, 1993; Bottge et al., 2002; Bottge et al., 2004). Students who used the anchored instruction environment also performed significantly better than groups that received other problem-solving instruction on a variety of transfer tasks, including complex text problems (Bottge, 1999; Bottge et al., 2002), contextualized video problems (Bottge & Hasselbring, 1993), and applied construction problems (Bottge et al., 2004). Only one study did not find this type of environment to have a significant effect on transfer for complex text problems (Bottge & Hasselbring, 1993).

Lesh, R. (1981). Applied mathematical problem solving. Education Studies in Mathematics, 12, 235-264.

NU Math Problem Solving Group Web Page

Montague, M., Applegate, B., & Marguard, K. (1993). Cognitive strategy instruction and mathematical problem solving performance of students with learning disabilities.

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