Resumen

Researchers have found that students as young as elementary school can engage in mathematical reasoning. Specifically, particular tasks tend to encourage this reasoning. This paper provides insight into some general characteristics of tasks that may lead to arguments that represent varied forms of reasoning. In this paper we report on arguments built by diverse student groups, of different ages, that were used to justify their solutions to problems from the fraction and counting strands of longitudinal and cross-sectional studies. We compare the characteristics of the two tasks and suggest how the implementation of tasks such as these can help elicit varied student reasoning.