Analogical Reasoning Profiles of Prospective Elementary Teachers in Triangle and Quadrilateral Problems

Analogical reasoning allows prospective primary school teachers to connect familiar mathematical ideas with unfamiliar problems, yet recognising a resemblance does not always lead to a sound solution. This study explores how prospective primary school teachers establish and use mathematical relationships when solving an analogy task involving triangles and quadrilaterals. Using an exploratory qualitative design, the study examined written responses from 41 participants and conducted in-depth interviews with five selected participants, one from each response profile. The analysis considered four interrelated processes: encoding, inferring, mapping, and applying. Written responses were classified as advanced (2), explicit (12), implicit (7), incomplete (8), and non-analogy (12). The interview cases revealed distinct difficulties in identifying a relevant relationship, transferring it from the source to the target, and completing the calculation. Notably, one participant explored two different relationships, while another identified a plausible relationship but made an arithmetic error. These findings show that successful analogical reasoning involves more than obtaining the correct answer. Preparing future primary school teachers to explain, compare, and verify mathematical relationships may strengthen their understanding of geometry and their capacity to support children's mathematical thinking.