Project Activities
Researchers will complete three training studies to examine the relationship between spatial representations of magnitude and the acquisition of arithmetic strategies.
Structured Abstract
Setting
Researchers will collect data in elementary schools in three racially and ethnically diverse urban districts in Massachusetts. All other research activities will be carried out at Boston College.
Sample
Researchers will recruitapproximately 554 first graders (6 to 7 years) from urban public schools serving low-income students.
Researchers will examine spatial representations of magnitude.
Research design and methods
In Study 1, researchers will manipulate the type of spatial representation used (spatial/discrete, spatial/continuous, or discrete-to-continuous fading) to teach the retrieval strategy for addition problems with sums up to 10 and subtraction problems with minuends up to 10. In Study 2, researchers will use the same manipulation to examine the effects of each type of spatial representation for teaching the decomposition strategy for addition and subtraction problems with sums and minuends over 10. In Study 3, researchers will build on Studies 1 and 2 by comparing the most effective representation identified in these studies to a business-as-usual control and by examining transfer to broader mathematical skills. All three studies will investigate whether the effects of spatial cues on arithmetic strategy learning are mediated by improvement in numerical magnitude knowledge. Studies will use a pretest/posttest experimental design, with students randomly assigned to conditions within each classroom.
Control condition
Studies 1 and 2 will use a non-spatial strategy control condition in which all aspects of training will be equivalent to the experimental conditions except for the presence of spatial cues. This condition will serve to isolate the role of spatial information in arithmetic learning. Study 3 will use a business-as-usual control in which first graders will receive regular arithmetic instruction for an equivalent amount of time as the experimental condition.
Key measures
Researchers will examine three sets of outcomes:
- Arithmetic knowledge: fluency, frequency of using retrieval and decomposition strategies, and arithmetic accuracy measured as both percent of correct responses and absolute error
- Numerical magnitude knowledge: symbolic number comparison and number line estimation
- A standardized measure of mathematic achievement.
Data analytic strategy
Researchers will use hierarchical linear modeling to compare effects across conditions. In addition to pretest scores, all models will include student and classroom level covariates: gender, parental education, and math curriculum.
People and institutions involved
IES program contact(s)
Project contributors
Products and publications
Researchers will produce a theoretical framework that addresses the relationship between spatial information and numerical magnitude and will report findings in conference presentations and peer-reviewed publications.
Publications:
Cho, H. Y., Vasilyeva, M., & Laski, E. V. (2024). Statistical learning and mathematics knowledge: the case of arithmetic principles. Frontiers in Developmental Psychology, 2, 1370028.
Vasilyeva, M., Laski, E. V., Casey, B., Konstantopoulos, S., Lu, L., Ban, J., ... & Wang, M. (2025). Recruiting spatial-numerical representations to increase arithmetic fluency in low-income students. Developmental Psychology.
Vasilyeva, M., Laski, E. V., Casey, B. M., Lu, L., Wang, M., & Cho, H. Y. (2023). Spatial–numerical magnitude estimation mediates early sex differences in the use of advanced arithmetic strategies. Journal of Intelligence, 11(5), 97.
Wang, M., Vasilyeva, M., & Laski, E. V. (2024). Words matter: Effect of manipulating storybook texts on parent and child math talk. Early Childhood Research Quarterly, 69, 65-77.
Questions about this project?
To answer additional questions about this project or provide feedback, please contact the program officer.
