Supporting Mathematical Discussions: the Roles of Comparison and Cognitive Load

Mathematical discussions in which students compare alternative solutions to a problem can be powerful modes for students to engage and refine their misconceptions into conceptual understanding, as well as to develop understanding of the mathematics underlying common algorithms. At the same time, these discussions are challenging to lead effectively, in part because they involve complex cognitive acts of identifying structural relationships within multiple solutions and comparing between these sets of relationships. While many of the considerations in leading such discussions have been described elsewhere, we highlight the cognitive challenges for students and the core role of relational reasoning that underpins student learning from these interactions. We review the literature on children’s development of relational reasoning and learning from comparisons to highlight particular challenges for students. We also review literature that suggests pedagogical practices for maximizing the likelihood that children will notice the intended relationships among solutions while minimizing overload to their cognitive resources. These practices include providing explicit comparison cues and labels, sequencing comparison before explicit instruction, using spatially aligned visual representations, and capitalizing on teacher gestures.