Teaching Based on Multiple Solutions: A Step Toward Enhancing Mathematical Reasoning

The aim of this study is to examine the effectiveness of teaching based on multiple solutions in enhancing the skills of mathematical reasoning in high school students. The research sample includes 47 students in the experimental group and 54 students in the control group, all of whom were second grade students in public secondary schools for girls in Tehran in the academic year of 2015-2016 who study mathematics and science. The instrument of this study is a test based on the Miyazaki (2000) classification of deductive and inductive reasoning. The research methodology is an action-research one that has enjoyed quasi-experimental research design. Data analysis shows that teaching based on multiple solutions can increase the reasoning skill meaningfully in the students of mathematics major but it has no significant effect on students of science. The qualitative analyses reveal the gap between arithmetic and algebraic thinking, weakness in the math discourse and lack of complete knowledge of students about the necessity of proof, standards of having a valid proof, the concept of variable and the language of algebra, to mention a few.