ABSTRACT

The ultimate goal of mathematics instruction is for students to use mathematical concepts and procedures to solve real problems. Mathematicians define problem solving as “engaging in a task for which the solution method is not known in advance” (NCTM, 2000, p. 52) or “finding a way out of a difficulty, a way around an obstacle, attaining an aim which is not immediately attainable” (Polya, 1965). Both the NCTM’s Principles and Standards for Mathematics (2000) and the Common Core Standards emphasize problem solving at every grade level. However, international assessments show that American students struggle when asked to solve problems, and the task is especially difficult for students who have the greatest difficulty with mathematics (Geary, 2003; Hanich et al., 2001). The metacognitive competencies required for problem solving are precisely those skills that students with mathematical disabilities find difficult: (1) processing the language of the problem and understanding what is being asked, (2) identifying and organizing relevant information, (3) selecting a problem-solving strategy, (4) remembering and executing the strategy steps in the proper sequence, (5) performing necessary computations and accurately recording solutions, and finally (6) checking to make sure the computation was executed successfully and that the answer makes sense. For students who have difficulty with executive functioning, this is a daunting task.