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 the above studies, and I am interested in the ways in which these diagrams may be supporting learning.
In one 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. (accepted). Who benefits from diagrams and illustrations in math problems? Ability and attitudes matter. Applied Cognitive Psychology.
Look for future work in this line on children’s reasoning about fraction division with diagrams with different features!