Early fraction concepts often seem at odds with what children already know about whole numbers. There is some evidence that children may think about fractions and problems with fractions as belonging in a different category than whole numbers and whole number problems. However, adults can appreciate the similarities across fraction and whole number arithmetic. In this line of work, I investigate the ways in which students’ arithmetic categories reorganize across development.
Here is a paper examining knowledge organization across development:
Sidney, P.G. & Shirah, J. (2023). Surface-to-structure shift in rational number categories. Cognitive Development, 68(1), 101386. DOI: 10.1016/j.cogdev.2023.101386
We also attempted to look at relationships between whole number and rational number categories by examining people’s attitudes towards math:
Sidney, P.G., Thompson, C.A., Fitzsimmons, C.J. +, & Taber, J.M. (2021). Children’s and adults’ math attitudes are differentiated by number type. Journal of Experimental Education, 89, 1-32. DOI: 10.1080/00220973.2019.1653815
Here are some of the early posters:
Sidney, P.G., & Alibali, M.W. (2015, March). Measuring conceptual change in mathematics: Could learning about fractions provoke changes in arithmetic categories?. Poster presented at the biennial meeting of the Society for Research in Child Development, Philadelphia, PA.