A Ruppert’s framework: How do prospective teachers develop analogical reasoning in solving algebraic problems?

It is widely agreed that knowing how prospective teachers develop analogical reasoning in solving problems is important. Some problem solving is domain specific and require particular ways of analogical reasoning skill, therefore this study aims to reveal the development of analogical reasoning and strategies used by prospective teachers. The research design use a qualitative method. As many as 69 mathematics prospective teachers were involved voluntarily to complete algebraic tasks and 12 of them were interviewed to investigate their analogical reasoning and solution strategies. The data analysis used the Ruppert’s framework consisting of four components: structuring, mapping, applying, and verifying. It was found that the first three components were fully performed by the prospective teachers. However, the verifying stage was applied by prospective teachers in different ways. The dominant strategy used was a combined strategy of multiplication and addition. Their strategies varied according to the subjects’ general ability. The more strategies employed in solving problems, the better their analogical reasoning becomes. This implies that instructional designs that will be developed by prospective teachers may vary. Therefore, during their candidature, they should be provided by many solving strategies in problem solving to develop students’ analogical reasoning.