# Research

We study cognitive development, with a primary focus on how children think, learn, and solve problems in mathematics. The development of mathematical thinking presents a paradox. On one hand, young children (and possibly even infants) have been shown to exhibit a fairly sophisticated understanding of fundamental math concepts. On the other hand, math is a notoriously difficult subject to learn in school, with many children (and adults) failing to achieve basic competence.

In our studies, we investigate cognitive processes that contribute to people's understanding (and misunderstanding) of math. Through this work, we seek to uncover mechanisms involved in the development of quantitative reasoning, symbolic understanding, and problem solving.

Our research has practical implications. For instance, it may help parents and teachers determine the best ways to structure the environment, so all children can be provided with the building blocks necessary for success in school and beyond. Our research is funded by Institute of Education Sciences and National Science Foundation.

We are proud members of the ManyNumbers network, a global research consortium of over 100 labs focused on studying the conceptual foundations of early numeracy. Our network's activities are supported by a grant from the National Science Foundation's Division on Research in Learning (DRL).

### Representative Publications

**(see McNeil's CV for longer list)**

Davenport, J., Kao, Y., Johannes, K., Hornburg, C. B., & McNeil, N. M. (2023). Improving children’s understanding of mathematical equivalence: An efficacy study. *Journal for Research on Educational Effectiveness. *DOI: 10.1080/19345747.2022.2144787

Hornburg, C. B., Devlin, B. L., & McNeil, N. M. (2022). Earlier understanding of mathematical equivalence in elementary school predicts algebra readiness in middle school. *Journal of Educational Psychology, 114*, 540-559.

Kirkland, P. K., & McNeil, N. M. (2021). Question design affects students' sense‐making on mathematics word problems. *Cognitive Science*, *45*(4), e12960.

O'Rear, C. D., McNeil, N. M., & Kirkland, P. K. (2020). Partial knowledge in the development of number word understanding. *Developmental Science*, *23*(5), e12944.

McNeil, N. M., Hornburg, C. B., Brletic-Shipley, H., & Matthews, J. M. (2019). Improving children's understanding of mathematical equivalence via an intervention that goes beyond nontraditional arithmetic practice. *Journal of Educational Psychology, 111*, 1023-1044.

Alibali, M. W., Crooks, N. M., & McNeil, N. M. (2018). Perceptual support promotes strategy generation: Evidence from equation solving. *British Journal of Developmental Psychology*, *36*(2), 153-168.

Hornburg, C. B., Wang, L., & McNeil, N. M. (2018). Comparing meta-analysis and individual person data analysis using raw data on children's understanding of equivalence. *Child Development, 89,* 1983-1995.

Fyfe, E. R., McNeil, N. M., & Rittle-Johnson, B. (2015). Easy as ABCABC: Abstract language facilitates performance on a concrete patterning task. *Child Development, 86*, 927-935.

McNeil, N. M. (2014). A change-resistance account of children's difficulties understanding mathematical equivalence. *Child Development Perspectives, 8*, 42-47.

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

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 Psychology, 104*, 1109-1121.

McNeil, N. M., Fyfe, E. R., Petersen, L. A., Dunwiddie, A. E., & Brletic-Shipley, H. (2011). Benefits of practicing 4 = 2 + 2: Nontraditional problem formats facilitate children's understanding of mathematical equivalence. *Child Development, 82*, 1620-1633.

Brown, M. C., McNeil, N. M., & Glenberg, A. M. (2009). Using concreteness in education: Real problems, potential solutions. *Child Development Perspectives, 3*, 160-164.

McNeil, N. M. (2008). Limitations to teaching children 2 + 2 = 4: Typical arithmetic problems can hinder learning of mathematical equivalence. *Child Development*,* 79*, 1524-1537.

McNeil, N. M. (2007). U-shaped development in math: 7-year-olds outperform 9-year-olds on equivalence problems. *Developmental Psychology, 43,* 687-695.

McNeil, N. M., Grandau, L., Knuth, E. J., Alibali, M. W., Stephens, A. S., Hattikudur, S., & Krill, D. E. (2006). Middle-school students’ understanding of the equal sign: The books they read can’t help. *Cognition and Instruction, 24,* 367-385.

McNeil, N. M., & Alibali, M. W. (2005b). Why won’t you change your mind? Knowledge of operational patterns hinders learning and performance on equations. *Child Development*, 76, 883-899.

McNeil, N. M., & Alibali, M. W. (2005a). Knowledge change as a function of mathematics experience: All contexts are not created equal. *Journal of Cognition and Development*, 6, 385-206.

McNeil, N. M., & Alibali, M. W. (2004). You’ll see what you mean: Students encode equations based on their knowledge of arithmetic. *Cognitive Science*, 28, 451-466.

### Sample Posters

O'Rear, C. D. & McNeil, N. M. (Oct, 2019). U-shaped development of spontaneous counting on tasks designed to assess children's number word knowledge. Poster presented at the Biennial Meeting of the Cognitive Development Society (CDS), Louisville, KY.

McNeil, N. M., Dunwiddie, A. E., Petersen, L. A., Fyfe, E. R., & Brletic-Shipley, H. (June, 2010). Arithmetic practice that promotes conceptual understanding and computational fluency: Year 3. Poster presented at the Annual Research Conference of the Institute of Education Sciences (IES), National Harbor, MD.

Fyfe, E. R., & McNeil, N. M. (October, 2009). Benefits of "concreteness fading" for children with low knowledge of mathematical equivalence. Poster presented at the Biennial Meeting of the Cognitive Development Society (CDS), San Antonio, TX.

McNeil, N. M., Dunwiddie, A. E., Petersen, L. A., Fyfe, E. R., & Brletic-Shipley, H. (June, 2009). Arithmetic practice that promotes conceptual understanding and computational fluency: Year 2. Poster presented at the Annual Research Conference of the Institute of Education Sciences (IES), Washington, DC.

Petersen, L. A., & McNeil, N. M. (July, 2008). Using perceptually rich objects to help children represent number: Established knowledge counts. Poster presented at the 30th Annual Meeting of the Cognitive Science Society, Washington, DC.

McNeil, N. M., Dunwiddie, A. E., Brletic-Shipley, H., Petersen, L. A., & Gibson, M. H. (June, 2008). Arithmetic practice that promotes conceptual understanding and computational fluency. Poster presented at the Annual Research Conference of the Institute of Education Sciences (IES), Washington, DC.

Petersen, L. A., & McNeil, N. M. (October, 2007). How do different types of concrete objects affect children's developing counting skill? Poster presented at the Biennial Meeting of the Cognitive Development Society (CDS), Sante Fe, NM.

McNeil, N. M., Jarvin, L., Sternberg, R. J., Uttal, D. H. (March, 2007). Trade-offs between more and less concrete manipulatives. In D. H. Uttal (Organizer), *Concreteness and cognitive development: New perspectives on a classic developmental issue*. Symposium presented at the Biennial Meeting of the Society for Research in Child Development (SRCD), Boston, MA.

### Relevant Professional Organizations

Association for Psychological Science

American Educational Research Association

Math Cognition and Learning Society

Mind Brain and Education Society

Society for Research in Child Development