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
Currently, researchers in my lab are examining how different tasks contexts elicit variability in elementary school children’s thinking about division. Paper forthcoming!