Mathematics Instruction

This article is part of an ongoing dialogue on mathematics instruction and is part of a shift in the literature from a behaviorist learning theory of mathematics to a constructivist or cognitive theory. This article offers a context for understanding and using cognitive strategy instruction to improve students' performance in mathematics. The author reviews the theoretical and research base for strategy instruction and discusses the characteristics of students who have difficulties in mathematics from a developmental perspective. She then offers a practical illustration of cognitive strategy instruction used to assess and teach mathematical problem solving to middle school students with learning disabilities.

Montague notes that mathematics learning has recently been reconceptualized as a constructivist process through which children construct mathematical knowledge by linking new learning to previously acquired concepts, and this approach assumes that individuals set goals leading to the construction of new knowledge. This new knowledge then leads to new goals and new knowledge. Cognitive learning theory postulates a spiral effect in learning, and in this view, a number of social and learning interactions are influential in mathematical learning, including cognitive development, social interactions, affec

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eluschen, Borkowski, & Hale 1990). Efficacy training promotes selfregulation by teaching students how to evaluate the effectiveness of strategies and revise and change strategies based on their efficacy. Attributional training focuses on the role of effort inperformance and on using successoriented dialogues and dialogues aimed at coping with failure; such dialogues link attributions to behavior (Reid & Borkowski, 1987). Researchers have stressed the importance of expanding strategy instruction "to include executive processes that direct strategy use as well as attributional processes that energize strategic routines" (Groteluschen et al., 1990, p. 81). COGNITIVE STRATEGY INSTRUCTION RESEARCH Cognitive strategy instruction, which directly addresses students' comprehension and problemsolving deficiencies, has improved the academic performance, strategic knowledge, and affective responses of students with learning disabilities across academic and socialemotional domains (Englert, 1993; Graham & Harris, 1994; Montague, Marquard, & LeBlanc, 1993; Scruggs & Mastropieri, 1993; Scruggs & Wong, 1990; Vauras, Lehtinen, Olkinuora, & Salonen, 1993; Wong, 1992, 1993). Wong (1993) cited the following three reasons for why cognitive
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Approximate Word count = 8817
Approximate Pages = 35 (250 words per page)

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