Comparing representations and reasoning in children and adolescents with two-year college students

Problem solving and justification of a diversified group of two-year college students was compared with approaches of younger elementary and secondary school students working on the same tasks. The students in this study were engaged in thoughtful mathematics. Both groups found patterns, justified that their patterns were reasonable and, utilized similar strategies for their solutions and methods of justification. They were also able to make connections and build isomorphisms among the various problems.