Diagrams can support students’ understanding of difficult concepts by making explicit the relationships between various aspects of that concept. For example, in trying to understand what it means to divide by a fraction, it may be helpful to visualize the role of the divisor (the fraction) in relation to the role of the dividend (the first number). We used diagrams in many of my other studies, and I am interested in the ways in which these diagrams may be supporting learning.
In a new project with Drs. Clarissa Thompson and Ferdinand Rivera, we are examining children’s conceptual understanding of fraction operations (division and multiplication, specifically) when asked to learn or problem solve with various types of visual models. In a paper that is currently under review, we report differences in children’s fraction division reasoning when provided with number lines, circles, rectangles, or no diagram at all. Preliminary findings were presented at the annual meeting of PME-NA:
Sidney, P. G., Thompson, C. A., & Rivera, F. D. (2018). Using visual models in fraction division: Number lines support children’s accuracy and conceptual understanding. Proceedings of the 40th annual meeting North American Chapter of the International Group for the Psychology of Mathematics Education.
In another project with Dr. Jenny Cooper, we have examined undergraduate’s trigonometry reasoning in the context of diagrams and illustrations. While diagrams are really useful, students who like and value math benefited from using visuals more than students who did not like and value math.
Cooper, J. L., Sidney, P. G., & Alibali, M. W. (2018). Who benefits from diagrams and illustrations in math problems? Ability and attitudes matter. Applied Cognitive Psychology.