Many students have difficulty with fractions and other rational numbers, and for years researchers claimed that understanding fractions was critical for successful performance and learning in algebra. However, no such empirical evidence existed. Drawing on observations from algebra classrooms as well as findings from our early work about the importance of holding an accurate representation of the numerical system for performance and learning in elementary school, we conducted a study that yielded the first evidence of correlation between of students’ ability to estimate the magnitudes of fractions for algebra, controlling for their ability with whole numbers, and their performance on a variety of algebra-related outcome measures. Subsequently, we established that fraction magnitude knowledge was also predictive of students’ learning in algebra. Recent funding from the US Department of Education has allowed us to test for causal evidence linking fraction knowledge and algebra performance and learning.
Key Publications
- Booth, J.L., & Newton, K. J. (2012). Fractions: Could they really be the gatekeeper’s doorman? Contemporary Educational Psychology, 37, 247-253.
- Booth, J.L., Newton, K.J., Twiss-Garrity, L. (2014). The impact of fraction magnitude knowledge on algebra performance and learning. Journal of Experimental Child Psychology, 118, 110-118.
- Barbieri, C., Young, L., Newton, K.J., & Booth, J.L. (2021). Predicting middle school profiles of algebra performance using fraction knowledge. Child Development, 92(5), 1984-2005.
- deVries, K.J., Booth, J.L., Young, L.K., Barbieri, C.A, Garfield, E.M., & Newton, K.J. (2022). Using worked examples as a scalable practice for teaching fraction magnitude and fraction computation. In P. Jenlink (Ed.), Mathematics as the Science of Patterns: Making the Invisible Visible through Teaching (pp. 125-149). Charlotte, NC: Information Age Publishing.