# Arthur Baroody

**Professor Emeritus**, Curriculum & Instruction

## Contact

Department of Curriculum & Instruction

College of Education (mail code 708)

(UIUC Campus Mail) Champaign, IL 61820

# Arthur Baroody

## Biography

Art Baroody is a Professor 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 a National Science Foundation grant (“Development of the Electronic Test of Early Numeracy”; 9/15/2016–8/31/2021). He is also the Co- Principal Investigator for an Institute of Education Sciences grant ("Evaluating the Efficacy of Learning Trajectories in Early Mathematics"; 7/1/2015–6/30/2019) 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.

## Key Professional Appointments

Professor Emeritus, Curriculum and Instruction, University of Illinois, Urbana-Champaign

## Research & Service

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

†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

## Publications

Baroody, A. J., Clements, D. H., & Sarama, J. (2022). Lessons Learned from 10 Experiments That Tested the Efficacy and Assumptions of Hypothetical Learning Trajectories. *Education Sciences*, *12*(3), [195].
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Clements, D. H., Sarama, J., Baroody, A. J., Kutaka, T. S., Chernyavskiy, P., Joswick, C., Cong, M., & Joseph, E. (2021). Comparing the Efficacy of Early Arithmetic Instruction Based on a Learning Trajectory and Teaching-to-a-Target. *Journal of Educational Psychology*, *113*(7), 1323–1337.
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Sarama, J., Clements, D. H., Baroody, A. J., Kutaka, T. S., Chernyavskiy, P., Shi, J., & Cong, M. (2021). Testing a Theoretical Assumption of a Learning-Trajectories Approach in Teaching Length Measurement to Kindergartners. *AERA Open*, *7*.
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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), 637-648.
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Paliwal, V., & Baroody, A. J. (2020). Cardinality principle understanding: the role of focusing on the subitizing ability. *ZDM - Mathematics Education*, *52*(4), 649-661.
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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.
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Baroody, A. J., Clements, D. H., & Sarama, J. (2019). Teaching and Learning Mathematics in Early Childhood Programs. In C. P. Brown, M. B. McMullen, & N. File (Eds.), *The Wiley Handbook of Early Childhood Care and Education *(pp. 329-353). John Wiley & Sons, Ltd..
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Clements, D. H., Sarama, J., Baroody, A. J., Joswick, C., & Wolfe, C. B. (2019). Evaluating the Efficacy of a Learning Trajectory for Early Shape Composition. *American Educational Research Journal*, *56*(6), 2509-2530.
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Baroody, A. J. (2018). A commentary on Chen and Campbell (2017): Is there a clear case for addition fact recall? *Psychonomic Bulletin and Review*, *25*(6), 2398-2405.
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Baroody, A. J. (2018). Commentary on Chapters 1 to 3: 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 *(pp. 259-268). (Research in Mathematics Education). Springer.
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Brownell, J. ON., 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: Conversations Between Developmental Psychologists and Early Childhood Teachers *(pp. 139-171). Routledge.
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Paliwal, V., & Baroody, A. J. (2018). How best to teach the cardinality principle? *Early Childhood Research Quarterly*, *44*, 152-160.
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Baroody, A. J. (2017). The Use of Concrete Experiences in Early Childhood Mathematics Instruction. In J. Sarama, D. H. Clements, C. Germeroth, & C. Day-Hess (Eds.), *Advances in Child Development and Behavior *(pp. 43-94). (Advances in Child Development and Behavior; Vol. 53). Academic Press Inc..
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Baroody, A. J., Purpura, D. J., Eiland, M. D., Reid, E. E., & Paliwal, V. (2016). Does fostering reasoning strategies for relatively difficult basic combinations promote transfer by K-3 students? *Journal of Educational Psychology*, *108*(4), 576-591.
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Baroody, A. J., & Li, X. (2016). The construct and measurement of spontaneous attention to a number. *European Journal of Developmental Psychology*, *13*(2), 170-178.
link >

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 instruction. *Elementary School Journal*, *117*(1), 72-100.
link >

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*(PA), 93-105.
link >

Li, X., Chi, L., DeBey, M., & Baroody, A. J. (2015). A Study of Early Childhood Mathematics Teaching in the United States and China. *Early Education and Development*, *26*(3), 450-478.
link >

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*(1), 41-59.
link >

Reid, E. E., Baroody, A. J., & Purpura, D. J. (2015). Assessing Young Children's Number Magnitude Representation: A Comparison Between Novel and Conventional Tasks. *Journal of Cognition and Development*, *16*(5), 759-779.
link >

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*(2), 159-197.
link >

Li, X., & Baroody, A. J. (2014). Young children's spontaneous attention to exact quantity and verbal quantification skills. *European Journal of Developmental Psychology*, *11*(5), 608-623.
link >

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*(3), 533-573.
link >

Li, X., Sun, Y., Baroody, A. J., & Purpura, D. (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.
link >

Purpura, D. J., Baroody, A. J., & Lonigan, C. J. (2013). The transition from informal to formal mathematical knowledge: Mediation by numeral knowledge. *Journal of Educational Psychology*, *105*(2), 453-464.
link >

Baroody, A. J., Eiland, M. D., Purpura, D. J., & Reid, E. E. (2012). Fostering At-Risk Kindergarten Children's Number Sense. *Cognition and Instruction*, *30*(4), 435-470.
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Palmer, A., & Baroody, A. J. (2011). Blake's development of the number words "one," "two," and "three". *Cognition and Instruction*, *29*(3), 265-296.
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Baroody, A. J., Eiland, M., & Thompson, B. (2009). Fostering at-risk preschoolers' number sense. *Early Education and Development*, *20*(1), 80-128.
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Baroody, A. J., Lai, M. L., Li, X., & Baroody, A. E. (2009). Preschoolers' understanding of subtraction-related principles. *Mathematical Thinking and Learning*, *11*(1-2), 41-60.
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Baroody, A. J., Bajwa, N. P., & Eiland, M. (2009). Why can't johnny remember the basic facts? *Developmental Disabilities Research Reviews*, *15*(1), 69-79.
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Baroody, A. J., Torbeyns, J., & Verschaffel, L. (2009). Young children's understanding and application of subtraction-related principles. *Mathematical Thinking and Learning*, *11*(1-2), 2-9.
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Baroody, A. J., Li, X., & Lai, M. (2008). Toddlers' Spontaneous Attention to Number. *Mathematical Thinking and Learning*, *10*(3), 240-270.
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Lai, M. L., Baroody, A. J., & Johnson, A. R. (2008). Fostering Taiwanese preschoolers' understanding of the addition-subtraction inverse principle. *Cognitive Development*, *23*(1), 216-235.
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Baroody, A. J., Feil, Y., & Johnson, A. R. (2007). An alternative reconceptualization of procedural and conceptual knowledge. *Journal for Research in Mathematics Education*, *38*(2), 115-131.
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Baroody, A. J., & Lai, M. (2007). Preschoolers' Understanding of the Addition–Subtraction Inverse Principle: A Taiwanese Sample. *Mathematical Thinking and Learning*, *9*(2), 131-171.
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Baroody, A. J., Tiilikainen, S. H., & Tai, Y. C. (2006). The application and development of an addition goal sketch. *Cognition and Instruction*, *24*(1), 123-170.
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Baroody, A. J. (2006). Why Children Have Difficulties Mastering the Basic Number Combinations and How to Help Them. *Teaching Children Mathematics*, *13*(1), 22-31.

Mix, K. S., Sandhofer, C. M., & Baroody, A. J. (2005). Number words and number concepts: The interplay of verbal and nonverbal quantification in early childhood. In R. Kail (Ed.), *Advances in Child Development and Behavior *(pp. 305-346). (Advances in Child Development and Behavior; Vol. 33).
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Baroody, A. J., Cibulskis, M., Lai, M., & Li, X. (2004). Comments on the Use of Learning Trajectories in Curriculum Development and Research. *Mathematical Thinking and Learning*, *6*(2), 227-260.
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Baroody, A. J., & Wilkins, J. L. M. (2004). Inverting a Triangular Array: Involving Students in Mathematical Inquiry. *Mathematics Teaching in the Middle School*, *9*(6), 306-313.

Baroody, A. J., & Dowker, A. (2003). Preface. In *The Development of Arithmetic Concepts and Skills: Constructive Adaptive Expertise *(pp. xv-xxi). Lawrence Erlbaum Associates.
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Baroody, A. J. (2003). The developmental bases for early childhood number and operations standards. In D. H. Clements, & J. Sarama (Eds.), *Engaging Young Children in Mathematics: Standards for Early Childhood Mathematics Education *(pp. 173-220). Taylor and Francis.

Baroody, A. J. (2003). The development of adaptive expertise and flexibility: The integration of conceptual and procedural knowledge. In A. J. Baroody, & A. Dowker (Eds.), *The Development of Arithmetic Concepts and Skills: Constructive Adaptive Expertise *(pp. 1-33). Lawrence Erlbaum Associates.
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Baroody, A. J., & Dowker, A. (Eds.) (2003). *The Development of Arithmetic Concepts and Skills: Constructive Adaptive Expertise*. Lawrence Erlbaum Associates.
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Baroody, A. J., Wilkins, J. L. M., & Tiilikainen, S. H. (2003). The development of children's understanding of additive commutativity: From protoquantitive concept to general concept? In A. J. Baroody, & A. Dowker (Eds.), *The Development of Arithmetic Concepts and Skills: Constructive Adaptive Expertise *(pp. 127-160). Lawrence Erlbaum Associates.
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Baroody, A. J. (2003). The role of psychological research in the development of early childhood mathematics standards. In D. H. Clements, & J. Sarama (Eds.), *Engaging Young Children in Mathematics: Standards for Early Childhood Mathematics Education *(pp. 149-171). Taylor and Francis.

Baroody, A. J., & Tiilikainen, S. H. (2003). Two perspectives on addition development. In A. J. Baroody, & A. Dowker (Eds.), *The Development of Arithmetic Concepts and Skills: Constructive Adaptive Expertise *(pp. 75-125). Lawrence Erlbaum Associates.
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Wilkins, J. L. M., Baroody, A. J., & Tiilikainen, S. (2001). Kindergartners' Understanding of Additive Commutativity within the Context of Word Problems. *Journal of Experimental Child Psychology*, *79*(1), 23-36.
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Baroody, A. J. (2000). Does mathematics instruction for three- to five-year-olds really make sense? *Young Children*, *55*(4), 61-67.

Baroody, A. J., & Bartels, B. H. (2000). Using Concept Maps to Link Mathematical Ideas. *Mathematics Teaching in the Middle School*, *5*(9), 604-609.

Baroody, A. J. (1999). Children's relational knowledge of addition and subtraction. *Cognition and Instruction*, *17*(2), 137-175.
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Baroody, A. J. (1999). The Development of Basic Counting, Number, and Arithmetic Knowledge among Children Classified as Mentally Handicapped. In L. M. Glidden (Ed.), *International Review of Research in Mental Retardation *(Vol. 22, pp. 51-103). Academic Press Inc..
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Baroody, A. J. (1999). The Roles of Estimation and the Commutativity Principle in the Development of Third Graders' Mental Multiplication. *Journal of Experimental Child Psychology*, *74*(3), 157-193.
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Baroody, A. J., & Coslick, R. T. (1998). *Fostering children's mathematical power: an investigative approach to K-8 mathematics instruction*. Lawrence Erlbaum Associates, Inc.

Baroody, A. J. (1996). Self-invented addition strategies by children with mental retardation. *American Journal on Mental Retardation*, *101*(1), 72-89.

Baroody, A. J. (1995). The Role of the Number-After Rule in the Invention of Computational Shortcuts. *Cognition and Instruction*, *13*(2), 189-219.
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Baroody, A. J. (1994). An evaluation of evidence supporting fact-retrieval models. *Learning and Individual Differences*, *6*(1), 1-36.
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Baroody, A. J. (1993). Early mental multiplication performance and the role of relational knowledge in mastering combinations involving "two". *Learning and Instruction*, *3*(2), 93-111.
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Baroody, A. J., & Coslick, R. T. (1993). *Problem solving, reasoning, and communicating, K-8: helping children think mathematically*. Merrill.

Baroody, A. J. (1993). The Relationship between the Order-Irrelevance Principle and Counting Skill. *Journal for Research in Mathematics Education*, *24*(5), 415-427.

Baroody, A. J. (1992). The development of kindergartners' mental-addition strategies. *Learning and Individual Differences*, *4*(3), 215-235.
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Baroody, A. J., & Hume, J. (1991). Meaningful Mathematics Instruction: The Case of Fractions. *Remedial and Special Education*, *12*(3), 54-68.
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Baroody, A. J., & Gatzke, M. R. (1991). The Estimation of Set Size by Potentially Gifted Kindergarten-Age Children. *Journal for Research in Mathematics Education*, *22*(1), 59-68.

Baroody, A. J. (1990). How and When Should Place-Value Concepts and Skills Be Taught? *Journal for Research in Mathematics Education*, *21*(4), 281-286.

Baroody, A. J. (1989). Kindergartners' Mental Addition with Single-Digit Combinations. *Journal for Research in Mathematics Education*, *20*(2), 159-172.

Baroody, A. J. (1988). Mental-addition development of children classified as mentally handicapped. *Educational Studies in Mathematics*, *19*(3), 369-388.
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Baroody, A. J. (1988). Number-comparison learning by children classified as mentally retarded. *American Journal on Mental Retardation*, *92*(5), 461-471.

Baroody, A. J. (1987). *Children's mathematical thinking: A developmental framework for preschool, primary, and special education teachers*. Teachers College Press.

Baroody, A. J. (1987). Problem size and mentally retarded children's judgment of commutativity. *American Journal of Mental Deficiency*, *91*(4), 439-442.

Baroody, A. J. (1987). The Development of Counting Strategies for Single-Digit Addition. *Journal for Research in Mathematics Education*, *18*(2), 141-157.

Baroody, A. J. (1986). Basic Counting Principles Used by Mentally Retarded Children. *Journal for Research in Mathematics Education*, *17*(5), 382-389.

Baroody, A. J., & Ginsburg, H. P. (1986). The relationship between initial meaningful and mechanical knowledge of arithmetic. In J. Hiebert (Ed.), *Conceptual and Procedural Knowledge: The Case of Mathematics *(pp. 75-112). Taylor and Francis.
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Baroody, A. J. (1985). Mastery of Basic Number Combinations: Internalization of Relationships or Facts? *Journal for Research in Mathematics Education*, *16*(2), 83-98.

Baroody, A. J. (1985). Pitfalls in Equating Informal Arithmetic Procedures with Specific Mathematical Conceptions. *Journal for Research in Mathematics Education*, *16*(3), 233-236.

Baroody, A. J. (1984). A reexamination of mental arithmetic models and data: A reply to Ashcraft. *Developmental Review*, *4*(2), 148-156.
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Baroody, A. J. (1984). Children's Difficulties in Subtraction: Some Causes and Questions. *Journal for Research in Mathematics Education*, *15*(3), 203-213.

Baroody, A. J. (1984). More precisely defining and measuring the order-irrelevance principle. *Journal of Experimental Child Psychology*, *38*(1), 33-41.
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Baroody, A. J. (1984). The Case of Felicia: A Young Child’s Strategies for Reducing Memory Demands During Mental Addition. *Cognition and Instruction*, *1*(1), 109-116.
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Baroody, A. J., & Gannon, K. E. (1984). The Development of the Commutativity Principle and Economical Addition Strategies. *Cognition and Instruction*, *1*(3), 321-339.
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Baroody, A. J., Ginsburg, H. P., & Waxman, B. (1983). Children's Use of Mathematical Structure. *Journal for Research in Mathematics Education*, *14*(3), 156-168.

Baroody, A. J. (1983). The development of procedural knowledge: An alternative explanation for chronometric trends of mental arithmetic. *Developmental Review*, *3*(2), 225-230.
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Baroody, A. J., & Price, J. (1983). The Development of the Number-Word Sequence in the Counting of Three-Year-Olds. *Journal for Research in Mathematics Education*, *14*(5), 361-368.

Baroody, A. J., & Ginsburg, H. P. (1983). The Effects of Instruction on Children's Understanding of the "Equals" Sign. *Elementary School Journal*, *84*(2), 199-212.
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Ginsburg, H., & Baroody, A. J. (1983). *Test of Early Mathematics Ability: TEMA*. Pro Ed.

Baroody, A. J., & Ginsburg, H. P. (1982). Preschoolers’ Informal Mathematical Skills: Research and Diagnosis. *American Journal of Diseases of Children*, *136*(3), 195-197.
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Posner, J. K., & Baroody, A. J. (1979). Number conservation in two west African societies. *Journal of Cross-Cultural Psychology*, *10*(4), 479-496.
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