Selected Publications & Presentations


Viegut, A. A., Stephens, A. C., & Matthews, P. G. (2024). Unpacking the connections between fractions and algebra: The importance of fraction schemes and units coordination. Investigations in Mathematics Learning, 1-23.


Viegut, A. A., & Matthews, P. G. (2023). Building fraction magnitude knowledge with number lines: Partitioning versus analogy. Developmental Psychology59(10), 1757.

Park, Y., Kalra, P., Binzak, J., Matthews, P. G., & Hubbard, E. M. (2023). Developmental Changes in Nonsymbolic and Symbolic Fractions Processing: A Cross-Sectional fMRI study.


Donovan, A. M., Stephens, A., Alapala, B., Monday, A., Szkudlarek, E., Alibali, M. W., & Matthews, P. G. (2022). Is a substitute the same? Learning from lessons centering different relational conceptions of the equal sign. ZDM–Mathematics Education54(6), 1199-1213.


Park, Y. & Matthews, P.G. (2021). Revisiting and refining relations between nonsymbolic ratio processing and symbolic math achievement. Journal of Numerical Cognition, 7(3), 328-350.

Thompson, C.A…Matthews, P.G…(in press) Math matters: A novel, brief educational intervention decreases whole number bias when reasoning about COVID-19. Journal of Experimental Psychology: Applied

Hubbard, E.M. & Matthews, P.G. (in press) The Number Sense Represents (Rational) Numbers (commentary). Behavioral and Brain Sciences.

Park, Y., Viegut, A.A., & Matthews, P.G. (2021). More than the Sum of its Parts: Exploring the Development of Ratio Magnitude vs. Simple Magnitude Perception. Developmental Science, 24(3), e13043.


Fyfe, E. R., Matthews, P. G., & Amsel, E. (2020). College developmental math students’ knowledge of the equal sign. EDUCATIONAL STUDIES IN MATHEMATICS104(1), 65-85.

Kalra, P. B., Hubbard, E. M., & Matthews, P. G. (2020). Taking the relational structure of fractions seriously: Relational reasoning predicts fraction knowledge in elementary school children. Contemporary Educational Psychology62, 101896.

Kalra, P. B., Binzak, J. V., Matthews, P. G., & Hubbard, E. M. (2020). Symbolic fractions elicit an analog magnitude representation in school-age children. Journal of Experimental Child Psychology195, 104844.


Meng, R., Matthews, P. G., & Toomarian, E. Y. (2019). The relational SNARC: Spatial representation of nonsymbolic ratios. Cognitive science43(8), e12778.

Chesney, D. L., & Matthews, P. G. (2018). Task constraints affect mapping from approximate number system estimates to symbolic numbers. Frontiers in psychology9, 1801.

Matthews, P. G., & Fuchs, L. S. (2020). Keys to the gate? Equal sign knowledge at second grade predicts fourth‐grade algebra competence. Child Development91(1), e14-e28.


Matthews, P. G. & Ellis, A. B. (2018). Natural alternatives to natural number: The case of ratio. Journal of Numerical Cognition

Chesney, D. L., & Matthews, P. G. (2018). Task constraints affect mapping from approximate number system estimates to symbolic numbers. Frontiers in Psychology

Matthews, P. G. & Ellis, A. B. (2018). Natural Alternatives to Natural Number: The Case of Ratio. Journal of Numerical Cognition.

Fyfe, E. R., Matthews, P. G., Amsel, E., McEldoon, K. L., and McNeil, N. M. (2018). Knowledge of math equivalence beyond elementary school. Journal of Educational Psychology.


McCaffrey, T. & Matthews, P. G. (2017). An Emoji is Worth a Thousand Variables. The Mathematics Teacher.

Rau, M. A., & Matthews, P. G. (2017). How to make ‘more’ better? Principles for effective use of multiple representations to enhance students’ learning about fractions. ZDM, 1-14. doi: 10.1007/s11858-017-0846-8

Sidney, P. G., Thompson, C. A., Matthews, P. G. & Hubbard, E. M. (2017). From continuous magnitudes to symbolic numbers: The centrality of ratio. Behavioral and Brain Sciences.


Matthews, P. G., & Hubbard, E. M. (2017). Making space for spatial proportions. Journal of learning disabilities50(6), 644-647.

Hubbard, E., Matthews, P., & Samek, A. (2016). Using online compound interest tools to improve financial literacy. The Journal of Economic Education, 47(2), 106-120.

Lewis, M. R., & Matthews, P. G. Fractions we can’t ignore: The ratio congruity effect. Cognitive Science.

Matthews, P. G., Lewis, M. R., & Hubbard, E. M. (2016). Individual Differences in Nonsymbolic Ratio Processing Predict Symbolic Math Performance. Psychological science, 27(2), 191-202.


Matthews, P. G. & Chesney, D. L. (2015). Fractions as percepts? Exploring cross-format distance effects for fractional magnitudes. Cognitive Psychology.


Chesney, D. L., McNeil, N. M., Matthews, P. G., Byrd, C. E., Petersen, L. A., Wheeler, M. C, … & Dunwiddie, A. E. (2014). Organization matters: Mental organization to addition knowledge relates to understanding math equivalence in symbolic form. Cognitive Development, 30, 30-46.

Matthews, P.G., Chesney, D.L., McNeil, N.M. (2014). Are Fractions Natural Numbers Too? In M. Bello P., Guarini M., McShane M. & Scassellati B. (Eds.) Proceedings of the 26th Annual Conference of the Cognitive Science Society (pp. 982-987). Austin, TX: Cognitive Science Society


Chesney, D. L., & Matthews, P. G. (2013). Knowledge on the line: Manipulating beliefs about the magnitudes of symbolic numbers affects the linearity of line estimation tasks. Psychonomic Bulletin & Review, 1-8.


McNeil, N. M., Chesney, D. L., Matthews, P. G., Fyfe, E. R., Petersen, L. A., Dunwiddie, A. E., & Wheeler, M. C. (2012). It pays to be organized: Organizing arithmetic practice around equivalent values facilitates understanding of math equivalence. Journal of Educational Psychology104(4), 1109.

Matthews, P.G., Rittle-Johnson, B., McEldoon, K., & Taylor, R.T. (2012). Measure: What Combining Diverse Measures Reveals about Children’s Understanding of the Equal Sign as an Indicator of Mathematical Equality. Journal for Research in Mathematics Education, 43, 316-350


Rittle-Johnson, B., Matthews, P.G., Taylor, R.S., & McEldoon, K. (2011). Assessing Knowledge of Mathematical Equivalence: A Construct Modeling Approach. Journal of Educational Psychology, 103, 85-104.

Matthews, P.G. & Chesney, D.L. (2011) Straightening Up: Number Line Estimates Shift from Log to Linear with Additional Information. In L. Carlson, C. Hölscher, & T. Shipley (Eds.), Proceedings of the 33rd Annual Conference of the Cognitive Science Society (pp. 1936-1941). Boston, MA: Cognitive Science Society.


Matthews, P.G. & Rittle-Johnson, B. (2009). In Pursuit of Knowledge: Comparing Self-explanations, Concepts, and Procedures as Pedagogical Tools. Journal of Experimental Child Psychology, 104, 1-21.