External representations, like 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.

We have found that number lines uniquely support children’s reasoning about fraction division:

**Sidney, P. G., **Thompson, C. A., & Rivera, F. D. (2019). Number lines, but not area models, support children’s accuracy and conceptual models of fraction division. *Contemporary Educational Psychology*, *58*, 288-298. DOI: 10.1016/j.cedpsych.2019.03.011

And that diagrams, in general, support analogies between whole number and fraction division:

**Sidney, P.G.**, Shirah, J.^{ +}, Zahrn, L.*, & Thompson, C.A. (2022). Diagrams support spontaneous transfer across whole number and fraction concepts. *Contemporary Educational Psychology*, Advanced online publication: 102066.

Number lines also uniquely support reasoning about health-related ratios:

Mielicki, M.K., Fitzsimmons, C.J.^{ +}, Schiller, L., Scheibe, D.^{ +}, Taber, J.M., **Sidney, P.G.,** Matthews, P.G., Waters, E.A., Coifman, K., & Thompson, C.A. (2022). Number lines can be more effective at facilitating adults’ performance on health-related ratio problems than risk ladders and icon arrays. *Journal of Experimental Psychology-Applied*. DOI: 10.1037/xap0000456 IF: 2.81

Fitzsimmons, C.F., **Sidney, P.G.,** Mielicki, M. , Schiller, L.K., Scheibe, D.^{ +}, Taber, J.M., Matthews, P.G., Waters, E.A., Coifman, K.G., & Thompson, C.A. (2023). Worked examples and number lines improve adults’ understanding of health risks as ratios. *Journal of Applied Research in Memory and Cognition.* DOI: 10.1037/mac0000120.

Fitzsimmons, C.F., Woodbury, L. *, Taber, J.T., Mielicki, M., **Sidney, P.G.**, Coifman, K.G., & Thompson, C.A. (2023). How do visual displays impact health-risk estimates? It depends on display size, shape, and prior knowledge. *Journal of Behavioral Decision Making*, *36*(5), e234. DOI: 10.1002/bdm.2341

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*.