Abstract
The purpose of this paper is to practically examine the effectiveness of the method of teaching and learning of mathematics with inductive and analogical reasoning through the lessons dealing with the division of decimal fractions. This method is constructed of the teaching and learning process and its means in each phase. This process is as follow: Phase 1. Cognition/Understanding of new mathematical knowledge utilizing inductive or analogical reasoning; Phase 2. Solving the problems similar to problems used in the Phase 1 utilizing analogical reasoning; Phase 3. Constructing a schema through the problems in the Phase 1 and 2 are made an object and schema induction is utilized; Phase 4. If analogical reasoning was utilized in the Phase 1, comparing the bases in the Phase 1 with the schema in the Phase 3. As a result, the following points are showed: (1) It is possible to enhance children's understanding of contents with the method; (2) It is possible to enhance children's ability of reasoning, especially of analogical reasoning with the method; (3) In both inductive and analogical reasoning, it is a important role to recognize not only the similarities but also the differences, especially recognize the relations of alignable differences.
