Design and evaluation of practice-oriented materials fostering students’ development of problem-solving competence
The case of working backward strategy
Keywords:design research, mathematics education, problem solving, working backward strategy, reversibility, reversing tasks, explicit heuristic training
In a design-research project on problem-solving, theory-based and practice-oriented materials were developed with the goal of fostering systematical development of students’ problem-solving competence in a targeted manner by learning heuristics. Special attention was given to working backward strategy, which has been shown difficult for students to learn and use. In the study, 14 Grade 5 students participated in explicit heuristic training. The results show that even though the students intuitively reversed their thought processes before the explicit training, they experienced difficulties when solving complex reversing tasks, which improved considerably after explicit heuristic training. Thus, the study results showed that the developed materials using design-based research-approach promoted the development of students’ flexibility of thought when problem-solving by working backward. At the end of the paper, the results are discussed with regard to their theoretical and practical implications.