Math proficiency in early elementary school is among the strongest predictors of later academic outcomes, yet many primary students around the world struggle with acquiring foundational numerical skills. While researchers have considered a variety of cognitive and socio-cultural factors that can be recruited to improve math learning, our study drew on the accumulating evidence pointing to the strong links between number and space.

In particular, prior research has shown that numerical magnitude knowledge is represented spatially in the mind. Given the spatial nature of the mental representation of numerical magnitude, it has been argued that the accuracy of this representation can be improved via numerical activities that include spatial cues (e.g., length) conveying magnitude in a concrete and salient way. In turn, improving numerical magnitude knowledge has been theorized to facilitate arithmetic problem solving by constraining the search for plausible answer choices. Based on these theoretical assumptions, the presented study empirically tested the benefits of using spatial information for arithmetic learning. We hypothesized that incorporating spatial cues to numerical magnitude into math instruction would improve arithmetic fluency, such that children would be more likely to retrieve answers closer to the correct response.

Participants (202 first-graders from low-income, racially/ethnically diverse backgrounds) were recruited from eight elementary schools in the US. Children were randomly assigned to arithmetic instruction that either included spatial cues to numerical magnitude or did not (Spatial vs. Non-spatial conditions). Both conditions involved eight 30-minute small-group sessions focused on solving arithmetic problems with totals within 10. The only difference between the conditions was in the type of instructional materials used to model arithmetic operations. In the Spatial condition, children solved problems using materials of varying lengths to represent numbers (i.e., the length of 10 was twice as long as 5). In the Non-spatial condition, children practiced the same problems using equal-sized square tiles to represent numbers (i.e., the size of the 10-tile was the same as the 5-tile). At pre- and posttest, participants completed a timed arithmetic fluency task. Two measures of accuracy were computed: percent of correct responses (out of all items) and the average absolute error (distance between the child’s and the correct response).

Mixed-effects modeling was used to test the differences between conditions, while accounting for the multilevel structure of the data (children clustered within classrooms). The results showed a significant effect of condition: children in the Spatial condition showed greater improvements in arithmetic accuracy: they had a higher percentage of correct responses and, even when their responses were not correct, they were closer to the correct answer (i.e., smaller absolute error). The results clearly demonstrated a causal effect of using spatial representations on children’s arithmetic learning, which has implications for the design of elementary mathematics curriculum.

Keywords: Math development, arithmetic learning, spatial reasoning, intervention study.