Arthur J Baroody

Professor Emeritus of Curriculum & Instruction

Personal profile

Personal profile

Art Baroody is a Professor Emeritus of Curriculum & Instruction (early childhood and elementary mathematics education) at the University of Illinois at Urbana-Champaign. His research focuses on the teaching and learning of basic counting, number, and arithmetic concepts and skills by young children and children with learning difficulties. He is currently the Principal Investigator for two National Science Foundation grants: (1) “Development of the Electronic Test of Early Numeracy” (9/15/2016–8/31/2022) and (2) “Completing the Development of the Electronic Test of Early Numeracy” (9/1/2022–8/31/2026). He was recently the Co-Principal Investigator for an Institute of Education Sciences grant ("Evaluating the Efficacy of Learning Trajectories in Early Mathematics"; 7/1/2015–6/30/2021) awarded to the University of Denver. Dr. Baroody is the author of a number of books on teaching children mathematics, including Fostering Children’s Mathematical Power: An Investigative Approach to K—8 Mathematics Instruction (published 1998 by Lawrence Erlbaum Associates), and is the co-author of the Test of Early Mathematics Ability (3rd edition; published 2003 by Pro-Ed). He co-edited a book with Ann Dowker (Cambridge University) on mathematical learning (The development of arithmetic concepts and skills: Constructing adaptive expertise), which part of the “Studies in Mathematics Thinking and Learning” series, edited by A. Schoenfeld and published by Erlbaum Associates in 2003.

Research Interests

My research has focused on the teaching and learning of the following basic number and arithmetic skills and concepts by young children and children with learning difficulties:
- Initial number concepts and skills
- Counting skills and principles
- Informal addition strategies
- Arithmetic concepts such as the principle of commutativity
- Number-fact mastery

Previous research grants include:

(a) “The Production of Background Research for the National Governors’ Association (NGA) Center Project on Early Mathematics,” Douglas Clements, Arthur J. Baroody (co-PI), and Julie Sarama; 7/19/13–11/31/13 (awarded to the University of Denver).

(b) “UIUC Postdoctoral Research Training Program in Mathematics Education” (R305B1000017), Sarah Lubienski, Arthur J. Baroody (co-PI), and Joseph Robinson, funded by IES/USDE; 3/1/2010–8/15/2016.

(c) "Fostering Fluency with Basic Addition and Subtraction” (R305A080479); funding from the Institute of Education Sciences, U.S. Department of Education, Arthur J. Baroody (PI), 7/1/2008–6/30/2012.

(d) "Developing an Intervention to Foster Early Number Sense and Skill" (R305K050082), funded by the Institute of Education Sciences, U.S. Department of Education, Arthur J. Baroody (PI), (6/16/2005–6/15/2009) and

(e) "Key Transitions in Preschoolers Number and Arithmetic Development: The Psychological Foundations of Early Childhood Mathematics Education"; (Kelly S. Mix, Michigan State University, co-PI), funded by the Spencer Foundation Major Grants Program, 7/03-12/08.

(f) Computer-guided Comprehensive Mathematics Assessment for Young Children"; funded by the Program in Early Learning and School Readiness, National Institutes of Health, Herbert P. Ginsburg (PI) & Arthur J. Baroody (co-PI), 10/1/2005–9/30/2010.

(g) "UIUC Postdoctoral Research Training Program in Mathematics Education"; (R305B1000017), Institute of Education Sciences, U.S. Department of Education, 3/1/2010-8/15/2014.

Recent publications in scholarly journals include (*indicates a refereed publication; † denotes an invited publication):

*Baroody, A. J., Mix, K.,  Kartal, G., & Lai, M-L. (in press). The development and assessment of early cardinal-number concepts. Journal of Numerical Cognition.

*O’Rear, C. D., Azar, J., Baroody, A. J., & McNeil, N. (in press). Features in children’s counting books that lead dyads to both count and label sets during shared book reading. Child Development.

*Baroody, A. J., & Lai, M-L. (2022). The development and assessment of counting-based cardinal-number concepts. Educational Studies in Mathematics.

†* Baroody, A. J., Clements, D. H., & Sarama, J. (2021). Lessons learned from 10 experiments that tested the efficacy and assumptions of hypothetical learning trajectories. Education Science, 12.

* Sarama, J., Clements, D. H., Baroody, A. J., Kutaka, T. S., Chernyavskiy, P., Shi, J., & Cong, M. (2020). Testing a theoretical assumption of a learning-trajectories approach in teaching length measurement to kindergartners. AERA Open.

†*Baroody, A. J., Yilmaz, N., Clements, D. H., & Sarama, J. (2021). Evaluating a basic assumption of learning trajectories: The case of early patterning learning. Journal of Mathematics Education, 13(2), 8–32

†*Clements, D. H., Sarama, J., Baroody, A. J., Joswick, C. (2020). Efficacy of a learning trajectory approach compared to a teach-to-target approach for addition and subtraction. ZDM Mathematics Education, 52(4) 637–649.

†*Clements, D. H., Sarama, J., Baroody, A. J., Kutaka, T. S., Chernyavskiy, P., Joswick, C., Cong, M., & Joseph, E. (2020). Comparing the efficacy of early arithmetic instruction based on a learning trajectory and teaching-to-a-target. Journal of Educational Psychology. https://doi: 10.1037/edu0000633 

†*Paliwal, V., & Baroody, A. J. (2020). Cardinality principle understanding: The role of focusing on the subitizing ability. ZDM Mathematics Education, 52(4) 649–661.

*Paliwal, V., & Baroody, A. J. (2020). Fostering the learning of subtraction concepts and the subtraction-as-addition reasoning strategy. Early Childhood Research Quarterly, 51, 403–415.

*Clements, D. H., Sarama, J., Baroody, A. J., Joswick, C., Wolfe, C. (2019). Evaluating the efficacy of a learning trajectory for early shape composition. American Educational Research Journal, 56(6), 2509–2530. https://doi: 10.3102/0002831219842788

†*Baroody, A. J. (2018). A commentary on Chen and Campbell (2017): Is there a clear case for addition fact recall? Psychonomic Bulletin & Review, 25, 2398–2405. https://doi: 10.3758/s13423-018-1440-y

*Paliwal, V., & Baroody, A. J. (2018). How best to teach the cardinality principle? Early Childhood Research Quarterly, 44, 152–160.

†*Baroody, A. J. (2016). Curricular approaches to introducing subtraction and fostering fluency with basic differences in grade 1. In R. Bracho (Ed.), The development of number sense: From theory to practice. Monograph of the Journal of Pensamiento Numérico y Algebraico (Numerical and Algebraic Thought) Vol. 10(3), 161–191. University of Granada. doi: 10.1080/17405629.2016.1147345

†Baroody, A. J., & Li, X. (2016). The construct and measurement of spontaneous attention to number. European Journal of Developmental Psychology, 10, 135–165. doi: 10.1080/17405629.2016.1147345

*Baroody, A. J., Purpura, D. J., Eiland, Reid, E. E., & Paliwal, V. (2016). Does fostering reasoning strategies for relatively difficult basic combinations promote transfer? Journal of Educational Psychology, 108, 576–591. doi: 10.17105/SPR44-1.41-59

*Purpura, D. J., Baroody, A. J., Eiland, M. D., & Reid, E. E. (2016). Fostering first-graders' reasoning strategies with basic sums: The value of guided-training. Elementary School Journal. 117, 72–100.doi: 10.1086/687809

*Reid, E. E., Baroody, A. J., & Purpura, D. J. (2016). Assessing young children’s number magnitude representation: a comparison between novel and conventional tasks. Journal of Cognition and Development, 16, 759–779. doi:10.1080/15248372.2014.920844

*Baroody, A. J., Purpura, D. J., Eiland, M. D., & Reid, E. E. (2015). The impact of highly and minimally guided discovery instruction on promoting the learning of reasoning strategies for basic add-1 and doubles combinations. Early Childhood Research Quarterly, 30, 93–105. doi: 10.1016/j.ecresq.2014.09.003

†*Li, X., Chi, L., DeBey, M., & Baroody, A. J. (2015). A study of early childhood mathematics teaching in the U.S. and China. Early Education and Development, 26. doi: 10.1080/10409289.2015.994464

*Purpura, D. J., Reid, E. E., Eiland, M. D., & Baroody, A. J. (2015). Using a brief preschool early numeracy skills screener to identify young children with mathematics difficulties. School Psychology Review, 44, 41–59.

*Baroody, A. J., Purpura, D. J., Eiland, M. D., & Reid, E. E. (2014). Fostering first-graders’ fluency with basic subtraction and larger addition combinations via computer-assisted instruction. Cognition and Instruction, 32, 159–197. doi: 10.1080/07370008.2014.887084

*Li, X., & Baroody, A. J. (2014). Young children's spontaneous attention to number and verbal quantification skills. European Journal of Developmental Psychology, 11(5), 608–623. doi: 10.1080/17405629.2014.896788

*Li, X., Sun, Y., Baroody, A. J., & Purpura, D. J. (2013). The effect of language on Chinese and American 2- and 3-Year olds’ small number identification. European Journal of Psychology of Education, 28(4), 1525–1542. doi: 10.1007/s10212-013-0180-7

*Baroody, A. J., Eiland, M. D., Purpura, D. J., & Reid, E. E. (2013). Can computer-assisted discovery learning foster first graders’ fluency with the most basic addition combinations? American Educational Research Journal, 50, 533–573. doi: 10.3102/0002831212473349

*Purpura, D. J., Baroody, A. J., & Lonigan, C. J. (2013). The transition from informal to formal mathematical knowledge: Mediation by numerical knowledge. Journal of Educational Psychology, 105, 453–464. doi: 10.1037/a0031753

*Baroody, A. J., Eiland, M. D., Purpura, D. J., & Reid, E. E. (2012). Fostering kindergarten children’s number sense. Cognition and Instruction, 30(4), 435–470. doi: 10.1080/07370008.2012.720152

*Palmer, A., & Baroody, A. J. (2011). Blake’s development of the number words “one,” “two,” and “three.” Cognition & Instruction, 29(3), 265–296. doi: 10.1080/07370008.2011.583370

Recent book chapters include:

†Baroody, A. J., Clements, D. H., & Sarama, J. (2019). Teaching and learning mathematics in early childhood programs. In C. Brown, M. McMullen, & N. K. File (Eds.), Handbook of early childhood care and education (Section III of Curriculum in Early Childhood Care and Education; pp. 329–353). Hoboken, NJ: Wiley Blackwell Publishing.

†Baroody, A. J. (2018). Commentary: Using meaningful analogies to reflect on and make sense of integers. In L. Bofferding & N. M. Wessman-Enzinger (Eds.), Exploring the integer addition and subtraction landscape: Perspectives on integer thinking (pp. 259–268). (Research in Mathematics Education series.) New York, NY: Springer International Publishing.

†Brownell, J. O., Hynes-Berry, M., & Baroody, A. J. (2018). Pathways to basic combination fluency in the primary grades. In J. S. McCray, J-Q Chen, & J. E. Sorkin (Eds.), Growing mathematical minds (pp. 139–171). New York, NY: Routledge.

†Baroody, A. J. (2017). The use of concrete experiences in early childhood mathematics instruction? In D. Clements & Julie Sarama (with Drs. Carrie Germeroth and Crystal Day-Hess; Guest Eds.), Interventions in Early Childhood Mathematics Education, Volume 53 of Advances in Child Development and Behavior. Kidlington, Oxford, U.K.: Elsevier.

†*Baroody, A. J., with Purpura, D. J. (2017). Early number and operations: Whole numbers. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 308–354). Reston, VA: National Council of Teachers of Mathematics.

†*Baroody, A. J.  (2016). Using number and arithmetic instruction as a basis for fostering mathematical reasoning. In M. T. Battista (Ed.), Reasoning and sense making in the mathematics classroom: Pre-K—Grade 2 (pp. 27–69). Reston, VA: National Council of Teachers of Mathematics.

Recent books include:

Frye, D., Baroody, A. J., Burchinal, M., Carver, S. M., Jordan, N. C., & McDowell, J. (2013). Teaching math to young children: A practice guide. Washington, DC: National Center for Education Evaluation and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education. <>.

Education/Academic qualification

Educational and developmental psychology , Ph>d>, Cornell University

Award Date: Jan 12 1979


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