PUBLICATIONS

Study results and related publications will be added to this page as the project continues.

See below for some studies on perceptual learning our team has published from this project

Closser, A, Purpura, D., & Ottmar, E. (accepted). From sight to insight: Perceptual cues in mathematics offer new directions for interdisciplinary research. Journal of Numerical Cognition. 

Lee, J.-E., Thorp, C.., Egorova, A., Kamberi, A., Bye, J. K., Closser, A.,, Hornburg, C. B., & Ottmar, E. (in press). Operator positions and perceptual cues: unpacking their effects on middle school students’ performance and errors in order of operations problems. Quarterly Journal of Experimental Psychology.

Zhang, P., Pradhan, S., Lee, M., Pei, Y., Sales, A., & Ottmar, E. (2026). Using Bayesian knowledge tracing to evaluate perceptual scaffolding and desirable difficulties in a math intervention. Journal of Educational Data Mining. 18(2), 88-114. https://doi.org/10.5281/zenodo.21443292

Ottmar, E. , Zhang, P., Lee, J., Bye, J., Colbert, M., Egorova, A., Yu, S., Closser, A, & Hornburg, C. B. (2025). Data from the Examining the Effects of Perceptual Cues on Middle School Students’ Online Mathematical Reasoning and Learning Study. Journal of Open Psychology Data, 13(1), 5. https://doi.org/10.5334/jopd.139.

Hornburg, C.., Lee, J., Closser, A., Bye, J.., Egorova, A., Colbert, M., Yu, S., Zhang, P., Valdivia, I., & Ottmar, E. (2025). Effects of spacing and color perceptual cues on middle schoolers’ order-of-operations performance. The Journal of Experimental Education. 1–22. https://doi.org/10.1080/00220973.2025.2528691

Other publications that are related to Perceptual Cues and Perceptual Learning in Math

Ferris, Z., Zhang, P., Zhong, Z., Rodriquez, H., & Ottmar, E. (in press). Perceptual Features of Arithmetic Expressions Bias Visual Attention: An Online Eye-tracking Study. Mind Brain and Education. 

Reid, K., Olson, S., Ferris, Z., Mathieu, M., Peloquin, V., Egorova, A., Zhang, P., & Ottmar, E. (in press). When Spacing Meets Color: How Executive Function Impacts the Use of Perceptual Cues During Arithmetic Problem Solving. Psychological Research.

Zhang, P., Wong, A., Mills, C., & Ottmar, E. (2026). Math structure biases attention during arithmetic problem solving: A webcam eye-tracking study. Journal of Numerical Cognition. https://doi.org/10.23668/psycharchives.21661

Bye, J., Chan, J. Y.-C., Closser, A., Lee, J., Shaw, S., & Ottmar, E. (2024). Perceiving precedence: Order of operations errors are predicted by perception of equivalent expressions. Journal of Numerical Cognition. 10, 1-23. https://doi.org/10.5964/jnc.14103

Ngo, V., Lacera, L. P., Closser, A. H., & Ottmar, E. (2023). The effects of operator position and superfluous brackets on student performance in simple arithmetic. Journal of Numerical Cognition, 9(1), 107-128. https://doi.org/10.5964/jnc.9535 

Lee, J. E., Hornburg, C. B., Chan, J. Y. C., & Ottmar, E. (2022). Perceptual and number effects on students’ initial solution strategies in an interactive online mathematics game. Journal of Numerical Cognition, 8(1), 166-182. https://doi.org/10.5964/jnc.8323 

Closser, A. H., Chan, J. Y.-C., Smith, H., & Ottmar, E. R. (2022). Perceptual learning in math: Implications for educational research, practice, and technology. Rapid Community Report Series. Digital Promise and the International Society of the Learning Sciences. https://repository.isls.org//handle/1/7668

Harrison, A., Smith, H., Hulse, T., & Ottmar, E. R. (2020). Spacing out! Manipulating spatial features in mathematical expressions affects performance. Journal of Numerical Cognition, 6(2), 186-203. https://doi.org/10.5964/jnc.v6i2.243