Improving mathematical problem solving: A computerized approach

摘要

Mathematics teachers often experience difficulties in teaching students to become skilled problem solvers. This paper evaluates the effectiveness of two interactive computer programs for high school mathematics problem solving. Both programs present students with problems accompanied by instruction on domain-specific knowledge required in different episodes of problem solving. The first program is based on a direct instructional approach to learning, the second on a constructivist view of learning. The latter approach is expected to be particularly beneficial to weak students.The effectiveness of both computer programs was evaluated by means of an experiment. Four classes worked with the constructivist based computer program, and four worked with the direct instructional program. Five classes that had received traditional mathematics education served as the control group. The computer programs were used in three periods of two consecutive weeks each. The results show that both computer programs improved problem-solving ability more strongly than had traditional mathematics instruction. Contrary to our expectations, both weak and skilled students benefited equally from both computer programs. Specifically, the programs helped the students to improve the quality of their analysis and verification skills during problem solving.