Measuring Fences and Sharing Pizzas: Current Advances in Nonsymbolic Fraction Interventions

Abstract

By the end of elementary school, students should be able to solve fraction arithmetic and comparison problems. However, less than 30 % of students in the United States have accomplished these educational milestones by the eighth grade. Not only is fraction knowledge as vital to learn more complex math, like algebra, it also has major implications on individuals' health and employment outcomes. Thus, it has become crucial to develop educational methods to enhance students' fraction understanding. In contrast to these struggles with symbolic fractions, young children can work surprisingly well with nonsymbolic representations of proportions, and nonsymbolic ratio processing skills are also positively related to fraction ability in older children and adults. These findings have led to educational interventions which leveraged nonsymbolic skills, primarily via numberlines, to enhance symbolic fraction understanding. This paper aims to offer a systematic review of these emerging intervention and training studies. We identified 19 papers, representing 22 studies, which we grouped in three categories: classroom-based interventions, multiple-session trainings, and single-session training studies. These studies provide an optimistic picture of the malleability of students' fractions skills: Across categories, placing nonsymbolic and symbolic representations of fractions on numberlines successfully enhanced fraction skills of low and typically achieving students, resulting in small-to-large effect sizes. These results suggest that fostering nonsymbolic skills may be important in addressing the persistent bottleneck that fractions pose in mathematical knowledge.

Middle-schoolers' misconceptions in discretized nonsymbolic proportional reasoning explain fraction biases better than their continuous reasoning: Evidence from correlation and cluster analyses

“…For instance, before formal instruction, children can compare and match objects based on their proportional magnitudes (Boyer et al, 2008;Hurst & Cordes, 2018;Jeong et al, 2007). Combined with correlational evidence for the positive relationship between nonsymbolic and symbolic proportional reasoning (Begolli et al, 2020;Matthews et al, 2016;Möhring et al, 2016), these findings have led researchers to develop fraction instructions that scaffold on nonsymbolic representations (Abreu-Mendoza et al, 2021;Braithwaite & Siegler, 2021;Gouet et al, 2020;Hamdan & Gunderson, 2017); for a review, see Abreu-Mendoza and Rosenberg-Lee, (2022). However, the mechanisms underlying the relationship between nonsymbolic and symbolic proportional reasoning remain unknown.…”