Abstract

This exploratory research study characterizes the reasoning of first-year engineering students when they determine that a system of linear equations (SLE) has an infinite solution. Students solve learning tasks that are part of a hypothetical learning trajectory (HLT) on solving SLE. The HLT is designed in terms of the mechanism of reflection on activity-effect relationships and on the design heuristic of the emergent models. The results show that solving a SEL with infinite solutions is not easy to represent for students since the solution is not immediate nor intuitive. This is unlike a SEL that has a unique or empty solution. It is concluded that characterizing student reasoning when determining that a SEL has infinite solutions is a useful tool to be considered for planning math content.