Children and adults show variability at a number of different levels: across time, across contexts, and even across simultaneous behaviors. Dr. Martha Alibali and I have explored the role of this variability in development more broadly, and in fraction understanding specifically:
Alibali, M. W., & Sidney, P. G. (2015). The role of intraindividual variability in learning in childhood and adolescence. In M. Diehl, K. Hooker, & M. Sliwinski (Eds.) Handbook of intraindividual variability across the lifespan (pp. 84-102). New York, NY: Taylor and Francis.
Alibali, M.W., & Sidney, P.G. (2015). Variability in the natural number bias: Who, when how, and why?. Learning and Instruction, 37, 56-61. DOI: 10.1016/j.learninstruc.2015.01.003
My colleagues, Dr. Clarissa Thompson, Rajaa Thalluri, and Morgan Buerke, and I have demonstrated that using a variety of strategies is advantageous when reasoning about how big fractions are, especially for adults with more limited working memory and math experience. Also, people who were more anxious about math were worse at reasoning about fractions, but not necessarily because they used fewer strategies to solve problems. Here’s the full paper:
Sidney, P. G., Thalluri, R., Buerke, M., & Thompson, C. A. (2018). Who uses more strategies? Linking mathematics anxiety to adults’ strategy variability and performance on fraction magnitude tasks. Thinking and Reasoning. DOI: 10.1080/13546783.2018.1475303
We have also found that different sorts of tasks reveal different relationships between math performance and math anxiety:
Mielicki, M.K., Wilkey, E.D., Scheibe, D.A. +, Fitzsimmons, C.J. +, Sidney, P.G., Bellon, E., Ribner, A. D., Soltanlou, M., Starling-Alves, I., Coolen, I., Ansari, D., & Thompson, C. A. (2023). Task features change the relation between math anxiety and number line estimation performance with rational numbers: Two large-scale online studies. Journal of Experimental Psychology: General. DOI: 10.1037/xge0001382
Most recently, my lab is examining how different sorts of tasks, with different contexts (e.g., physical objects, stories, diagrams) elicit variability in elementary school children’s and adults’ thinking about division.
Here is our papers about children:
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
Sidney, P.G., Shirah, J. +, Blake, J.*, & Kruczkowski, A.* (2023). Adaptive variability in children’s conceptual models of division. Journal of Experimental Child Psychology, 236(1), 105743. DOI: 10.1016/j.jecp.2023.105743
And adults:
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
Sidney, P.G., Shirah, J. +, Zahrn, L.*, & Thompson, C.A. (2022). Diagrams support spontaneous transfer across whole number and fraction concepts. Contemporary Educational Psychology, 69, 102066. DOI: 10.1016/j.cedpsych.2022.102066. IF: 6.92