Investigating the effectiveness of schematic representation-based instruction on the ability of solving non-routine problems in mathematics

The aim of the present study is to investigate the effectiveness of schematic representation-based instruction on 6th grade students' ability of solving non-routine problems in mathematics. It is a content analysis and quasi-experimental design research of the pretest-posttest type, follow up by the control group. After studying and educational designing, 40 sixth-grade male students of an elementary school in the academic year of 1396-97 in Yasouj voluntarily participated in the study. They were randomly assigned to experimental and control group and were educated for 12 sessions (one session per week) using representation-based instruction method. Data collection instruments were developed in the content analysis section of the checklist and in the semi-experimental part of the test. Shannon Entropy technique was adopted in order to analyze data in content analysis, and variance analysis test with repeated measures was used for the quasi-experimental part. The results of the content analysis show that the greatest attention for the distribution and the presence of non-routine problems has been directed to hierarchical presentation, part-whole presentation, and network presentation problems, respectively. It was indicated that matrix presentation problems have no place in textbooks. In addition, the results of the variance analysis with repeated measures reveal that there is a significant difference between the averages of all the components of the ablitiy of solving non-routine problems of control group and experimental group (p<0.05). Therefore, it can be concluded that schematic representation instruction increases students' ability of solving non-routine problems in mathematics. Besides, the results indicate that using these methods repeatedly for solving non-routine problems will be consistent over time. The results of the study emphasize the need for special attention to the schematic representations in the sixth grade elementary mathematics textbook, and the necessity of applying these representations in solving non-routine problems by mathematic teachers.