Below is a list of publications published by SCIL scholars. 


Braithwaite, D. W., & Siegler, R. S. (2020). Putting fractions together. Journal of Educational Psychology. doi: 10.1037/edu0000477

Mcmullen, J., Hannula-Sormunen, M. M., Lehtinen, E., & Siegler, R. S. (2020). Distinguishing adaptive from routine expertise with rational number arithmetic. Learning and Instruction, 68, 101347. doi: 10.1016/j.learninstruc.2020.101347

Tian, J., Braithwaite, D. W., & Siegler, R. S. (2020). Distributions of textbook problems predict student learning: Data from decimal arithmetic. Journal of Educational Psychology. doi:10.1037/edu0000618

Tian, J., Braithwaite, D. W., & Siegler, R. S. (2020). How do people choose among rational number notations? Cognitive Psychology, 123, 101333. doi:10.1016/j.cogpsych.2020.101333

Siegler, R. S., Im, S., & Braithwaite, D. (2020). Understanding development requires assessing the relevant environment: Examples from mathematics learning. New Directions for Child and Adolescent Development. doi:10.1002/cad.20372

Siegler, R. S., Im, S,. Schiller, L., Tian, J., Braithwaite, D. W. (In press). The sleep of reason produces monsters: how and when biased input shapes mathematics learning. Annual Review of Developmental Psychology.


Braithwaite, D. W., Lieb, E., Siegler, R. S., & McMullen, J. (2019). Individual differences in fraction arithmetic learning. Cognitive Psychology. doi:


Braithwaite, D. W., & Siegler, R. S. (2018, April 26). Children learn spurious associations in their math textbooks: Examples from fraction arithmetic. Journal of Experimental Psychology: Learning, Memory, and Cognition. Advance online publication. doi: 10.1037/xlm0000546

Braithwaite, D. W., & Siegler, R. S. (2018). Developmental changes in whole number bias. Developmental Science, 21(2), e12541. doi: 10.1111/desc.12541

Braithwaite, D. W., Tian, J., & Siegler, R. S. (2018). Do children understand fraction addition? Developmental Science, 21(4), e12601. doi: 10.1111/desc.12601

Cheng, D., Xiao, Q., Chen, Q., Cui, J., & Zhou, X. (2018). Dyslexia and dyscalculia are characterized by common visual perception deficits. Developmental Neuropsychology, 43(6), 497-507.

Tian, J., & Siegler, R. S. (2018). Which type of rational numbers should students learn first? Educational Psychology Review, 30, 351-372. doi: 10.1007/s10648-017-9417-3


Braithwaite, D. W., Pyke, A. A., & Siegler, R. S. (2017). A computational model of fraction arithmetic. Psychological Review, 124(5), 603-625. doi: 10.1037/rev0000072

Cheng, D., Wu, H., Yuan, L., Xu, R., Chen, Q., & Zhou, X. (2017). Modality-dependent or modality-independent processing in mental arithmetic: Evidence from unimpaired auditory multiplication for a patient with left frontotemporal stroke. Journal of the International Neuropsychologi, 23(8), 692-699.

Cui, J., Georgiou, G. K., Zhang, Y., Li, Y., Shu, H., & Zhou, X. (2017). Examining the relationship between rapid automatized naming and arithmetic fluency in Chinese kindergarten children. Journal of Experimental Child Psychology, 154, 146-163.

Lortie-Forgues, H., & Siegler, R. S. (2017). Conceptual knowledge of decimal arithmetic. Journal of Educational Psychology, 109(3), 374-386. doi: 10.1037/edu0000148

Siegler, R. S. (2017). Fractions: Where it all goes wrong. Why do Americans have such trouble with fractions — and what can be done? Scientific American [November 28 blog post]. Retrieved from

Siegler, R. S., & Braithwaite, D. W. (2017). Numerical development. Annual Review of Psychology, 68, 187-213. doi: 10.1146/annurev-psych-010416-044101

Siegler, R. S., & Lortie-Forgues, H. (2017). Hard lessons: Why rational number arithmetic is so difficult for so many people. Current Directions in Psychological Science, 26(4), 346-351. doi: 10.1177/0963721417700129

Tian, J., & Siegler, R. S. (2017). Fractions learning in children with mathematics difficulties. Journal of Learning Disabilities, 50(6), 614-620.doi: 10.1177/0022219416662032

Zhou, X., Li, M., Li, L., Zhang, Y., Cui, J., & Liu, J., et al. (2017). The semantic system is involved in mathematical problem solving. Neuroimage, 166, 360-370.


Fazio, L. K., DeWolf, M., & Siegler, R. S. (2016). Strategy use and strategy choice in fraction magnitude comparison. Journal of Experimental Psychology: Learning, Memory, and Cognition, 42, 1-16, doi: 10.1037/xlm0000153

Fazio, L. K., Kennedy, C., & Siegler, R. S. (2016). Improving children’s knowledge of fraction magnitudes. PLOS ONE. doi: 10.1371/journal.pone.0165243

Liu, J., Zhang, H., Chen, C., Hui, C., Cui, J., & Zhou, X. (2016). The neural circuits for arithmetic principles. Neuroimage, 147, 432-446.

Siegler, R. S. (2016). Continuity and change in the field of cognitive development and in the perspectives of one cognitive developmentalist. Child Development Perspectives, 10(2), 128-133. doi: 10.1111/cdep.12173

Siegler, R. S. (2016). Magnitude knowledge: The common core of numerical development. Developmental Science, 19, 341-361. doi: 10.1111/desc.12395

Yu, X., Liu, J., Li, D., Liu, H., Cui, J., & Zhou, X. (2016). Dynamic mental number line in simple arithmetic. Psychological Research, 80(3), 410-421.

Wang, L., Sun, Y., & Zhou, X. (2016). Relation between approximate number system acuity and mathematical achievement: The influence of fluency. Frontiers in Psychology, 7(1966), 1-9.

Wei, W., Chen, C., & Zhou, X. (2016). Spatial ability explains the male advantage in approximate arithmetic. Frontiers in Psychology, 7(306), 1-9.

Zhang, Y., Chen, C., Liu, H., Cui, J., & Zhou, X. (2016). Both non-symbolic and symbolic quantity processing are important for arithmetical computation but not for mathematical reasoning. Journal of Cognitive Psychology, 28(7), 807-824.

Zhang, H., Chen, C., Sun, Z., Lin, J., Zhou, W., & Zhou, X. (2016). Early occipital injury affects numerosity counting but not simple arithmetic. Neurocase, 22(1), 12-21.

Zhang, Y., & Zhou, X. (2016). Building knowledge structures by testing helps children with mathmatical learning difficulty. Journal of Learning Disabilities, 49(2), 166-175. doi: 10.1177/0022219414538515

Zhou, X., Shen, C., Li, L., Li, D., & Cui, J. (2016). Mental numerosity line in the human’s approximate number system. Experimental Psychology, 63(3), 169-179.


Bailey, D. H., Zhou, X., Zhang, Y., Cui, J., Fuchs, L. S., Jordan, N. C., Gersten, R., & Siegler, R. S. (2015). Development of fraction concepts and procedures in U.S. and Chinese children. Journal of Experimental Psychology, 129, 68-83. doi: 10.1016/j.jecp.2014.08.006

Lortie-Forgues, H., Tian, J., & Siegler, R. S. (2015). Why is learning fraction and decimal arithmetic so difficult? Developmental Review, 38, 201-221, doi: 10.1016/j.dr.2015.07.008

Torbeyns, J., Schneider, M., Xin, Z. & Siegler, R. S. (2015). Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents. Learning and Instruction, 37, 5-13. doi: 10.1016/j.learninstruc. 2014.03.002

Zhou, X., Wei, W., Zhang, Y., Cui, J., & Chen, C. (2015). Visual perception can account for the close relation between numerosity processing and computational fluency. Frontiers in Psychology, 6, 1364.


Bailey, D. H., Siegler, R. S., & Geary, D. C. (2014). Early predictors of middle school fraction knowledge. Developmental Science, 17, 775-785. doi: 10.1111/desc.12155

Fazio, L. K., Bailey, D. H., Thompson, C. A., & Siegler, R. S. (2014). Relations of different types of numerical magnitude representations to each other and to mathematics achievement. Journal of Experimental Child Psychology, 123, 53-72. doi: 10.1016/j.jecp.2014.01.01

Fuchs, L. S., Schumacher, R. F., Sterba, S. K., Long, J., Namkung, J., Malone, A. Hamlett, C. L., Jordan, N. C., Gersten, R., Siegler, R. S., & Changas, P. (2014). Does working memory moderate the effects of fraction intervention? An aptitude-treatament interaction. Journal of Educational Psychology, 106, 499-514. doi: 10.1037/a0034341

Laski, E. V., & Siegler, R. S. (2014). Learning from number board games: You learn what you encode. Developmental Psychology, 50, 853-864. doi: 10.1037/a0034321

Siegler, R. S. & Lortie-Forgues, H. (2014). An integrative theory of numerical development. Child Development Perspectives, 8, 144-150. doi: 10.1111/cdep.12077

Vukovic, R. K., Fuchs, L. S., Geary, D. C., Jordan, N. C., Gersten, R., & Siegler, R. S. (2014). Sources of individual differences in children’s understanding of fractions. Child Development, 85, 1461-1476. doi: 10.1111/cdev.12218


Cui, J., Yu, X., Yang, H., Chen, C. Kiang, P., & Zhou, X. (2013). Neural correlates of quantity processing of numeral classifiers. Neuropsychology, 27, 583-594. doi: 10.1037/a0033630

Fuchs, L. S., Schumacher, R. F., Long, J., Namkung, J., Hamlett, C. L., Cirino, P. T., Jordan N. C., Siegler, R., Gersten R., & Changas, P. (2013). Improving at-risk learners’ understanding of fractions. Journal of Educational Psychology, 105, 683-700.doi: 10.1037/a0032446

Jordan N. C., Hansen, N., Fuchs, L. S., Siegler, R. S., Gersten, R., & Micklos, D. (2013). Developmental predictors of fraction concepts and procedures. Journal of Experimental Child Psychology, 116, 45-58. doi: 10.1016/j.jecp.2013.02.001

Siegler, R. S., Fazio, L. K., Bailey, D. H., & Zhou, X. (2013). Fractions: The new frontier for theories of numerical development. Trends in Cognitive Science, 17, 13-19. doi: 10.1016/j.tics.2012.11.004

Siegler, R. S., & Pyke, A. A. (2013). Developmental and individual differences in understanding fractions. Developmental Psychology, 49, 1994-2004.doi: 10.1037/a0031200

Wang, Y., & Siegler, R. S. (2013). Representations of and translation between common fractions and decimal fractions. Chinese Science Bulletin, 58, 4630-4640.doi:10.1007/s11434-013-6035-4


Siegler, R. S., Duncan, G. J., Davis-Kean, P. E., Duckworth, K., Claessens, A., Engel, M., Susperreguy, M. I., & Chen, M. (2012). Early predictors of high school mathematics achievement. Psychological Science, 23, 691-697. doi: 10.1177/0956797612440101