Abstract

Analogical reasoning helps extend mathematical concepts and can be used as a heuristic for solving mathematical problems. In this study, identities of the Horadam sequence were conjectured through conceptual analogy, and the conjectured identities were proved through methodological analogy. In addition, further methods for proving the identities were presented using matrix powers, determinants, and the Cayley–Hamilton theorem. This study is expected to help preservice and inservice teachers experience the process of formulating and justifying mathematical conjectures through analogical reasoning, and to serve as instructional material for providing gifted students with opportunities to gradually expand their mathematical knowledge by using analogical reasoning.