The effect of year-long instruction in mathematical problem solving on middle-school students' attitudes, beliefs, and abilities

Abstract Three classes of middle-school students who received 1 year of problem-solving instruction were compared with 3 classes of students who were taught mathematics in a more traditional manner. At the end of the school year, all the students completed a questionnaire that explored their mathematical beliefs. In addition, 3 students of varying ability levels per class were interviewed and asked to solve 4 nonroutine problems. Compared with the students who had received traditional mathematics instruction, the students who had received problem-solving instruction displayed greater perseverance in solving problems, more positive attitudes about the usefulness of mathematics, and more sophisticated definitions of mathematical understanding. A limitation of the problem-solving instruction is that the students tended to equate problem solving with the problem-solving skills they had learned, seeing them as “rules” to solve all problems. The implications of these findings for the reform of mathematics instr...