220:’s Graduate School of Education and Human Development in 1980 as a Research Associate for H. P. Ginsburg’s NIE Research Grant: "Cognitive Development Approach to Mathematics Learning Difficulties". From 1983 till 1986, he served as the Principal Investigator for a NIH Research Grant: "Basic Mathematics Learning in TMR and EMR Children." His next appointment was at the University of Illinois Urbana-Champaign as an Assistant Professor of Elementary and Early Childhood Education (1986-1989). He was promoted to Associate Professor of Curriculum and Instruction in 1989, and to Professor of Curriculum and Instruction in 1994. During this time, he also held a concurrent appointment with the Bureau of Educational Research from 1987 to 1990, and then again from 1999 to 2001. He retired in 2009 and was made an emeritus professor of Curriculum and Instruction. Since 2013, he has also been serving as Senior Research Fellow of Morgridge College of Education at the University of Denver.
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child realized she could use her existing knowledge of the counting sequence to determine add-1 sums—that adding one to a number such as six resulted in a sum equal to the next number in the count sequence: seven (the number-after rule for adding one). In addition to serving as a basis for fluency with add-1 sums and doubles-plus-1 reasoning strategy, the number-after rule appears to serve as basis for inventing counting-on from the larger (MIN). The key educational implication is that instruction should focus on meaningful memorization of basic facts—help children discover patterns and relations and use these arithmetic regularities to invent reasoning strategies, not the memorization of basic facts by rote via drill and practice. A theoretical implication is that mental-arithmetic experts may rely on multiple strategies that become automatic.
256:
guided the learning of verbal-based counting knowledge. Baroody proposed an iterative view of conceptual and procedural development view—a middle ground perspective between the skills-first view and the some-concepts-first view. According to the iterative view, children gradually construct an understanding of small numbers by seeing examples of a number labeled with a particular number word and nonexamples of the number labeled with other number words. Small-number concepts provide a meaningful basis for the skill of subitizing small numbers. Subitizing, in turn, serves to promote number, counting, and arithmetic development. For instance, contrary to conventional wisdom, subitizing-based number recognition of small numbers appears to develop before and serve as a basis for creating small collections.
264:
this is useful in determining the total (cardinal value) of a collection. A child may count five blocks accurately, but when asked how many blocks there are, guess incorrectly or recount the collection. Basically, such children do not understand the cardinality principle—that the last number word used in one-to-one counting has special meaning because it represents the total. Modeling the cardinal principle with small subitizable collections can help children see that the last number word in the one-to-one counting process is the total and discover the principle.
268:
amount of drill and practice and significantly more successful than drill and practice in promoting transfer to unpracticed but related facts. He also helped provide the first controlled experiments on the use of learning progression as an important tool in improving instruction. This research also indicated that in some domain such as patterning, further work is needed to define the learning progression or that lower levels in a progression serve only to facilitate (rather than as necessary prerequisites for) higher levels.
288:’ Compendium for Research in Mathematics Education, Baroody reviewed the research on whole-number operations in early childhood. The theme was the interconnectedness of learning, including how early (informal) learning in the domain provides a foundation for school (formal) learning. As an example, he outlined a number-sense view of basic number-fact learning—how fluency with basic sums and differences in the primary grades depends on development in the preschool starting with subitizing.
260:
deep conceptual knowledge or vice versa. The depth of knowledge depends on its number of connections to other knowledge, accuracy, degree of organization, and generality or breadth. Another difference with other views is that big idea—overarching concepts that connect multiple concepts, procedures, or problems within or even across domains or topics—facilitate the construction of both deep conceptual and procedural knowledge.
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could learn to determine which number is larger; invent more efficient counting strategies to determine sums; and discover basic arithmetic regularities such as additive commutativity, the number-after rule for adding one, and the zero rule. He found that developmental level or readiness, not IQ, was predictive of learning success.
240:
research confirmed that
Felicia’s strategy is the primary transition between more basic informal addition strategies and the advanced strategy of counting-on from the larger addend—sometimes called the MIN strategy because counting is minimized by counting on a number of times equal to the smaller added.
263:
Later research efforts focused on how instruction could promote meaningful number, counting and arithmetic learning by fostering both conceptual and procedural knowledge. In terms of counting development, children initially learn to count collections in a one-to-one fashion but do not understand that
251:
Baroody found that, contrary to the conventional wisdom at the time, children with serious learning difficulties could benefit from formal mathematics instruction if general cognitive principle of learning were honored. Children with IQs of less than 75 or even 50, could self-correct counting errors;
295:
Baroody served as the co-author of the
Institute of Education Science’s early numeracy practice guide. This publication represented an effort to review the evidence and recommend best practices regarding early childhood mathematics education. Recommendations included using developmental progressions
280:
In 2003, Baroody helped edit a book on adaptive expertise—conceptually based knowledge that can be applied to new tasks or situations as well familiar ones. Contributions to the book underscore the advantages of fostering adaptive expertise as opposed to routine expertise: procedures learned by rote
267:
In a series of experiments, Baroody found that promoting the discovering of arithmetic relations could promote the invention of various arithmetic reasoning strategies and fluency with basic sums and differences. This approach was as efficacious in promoting fluency with practiced facts as the same
247:
Baroody challenged the conventional wisdom in psychology at the time by arguing that children may use relational knowledge to learn and represent the basic arithmetic facts. He overheard a kindergartner comment: Six and one more "is an easy one, because it’s just the number after six." That is, the
243:
Baroody contributed to a balanced view of children’s informal mathematical knowledge by exploring both its strengths and limitations. He found that children’s informal view of addition as making a collection larger is a barrier to their recognizing the commutative property of the operation—that the
259:
Baroody’s view of the interdependence of conceptual and procedural knowledge differs from others in some key respects. One is that, although relatively superficial procedural and conceptual knowledge may exist independently, relatively deep procedural knowledge cannot not exist without relatively
255:
Proponents of the skills-first view argued that subitizing, verbal counting, and one-to-one counting by preschoolers were not meaningful but merely skills learned by rote. In contrast, nativists proposed a some-concepts-first view—that subitizing does not exists and that innate counting concepts
291:
Baroody has written over 30 practitioner-oriented books, chapters, and articles on teaching mathematics to preschool, primary, and special-education children. He was an early proponent that using manipulatives does not guarantee meaningful learning. The effective use of manipulatives depends on
239:
knowledge of children in early childhood and those with learning difficulties. He discovered a previously unrecognized counting-based mental-addition strategy, namely
Felicia’s strategy of counting-all from the larger addend (solving, e.g., 2 + 5 by counting “1, 2, 3, 4, 5; 6 , 7 ). Subsequent
244:
order in which two addends are added does not matter. His studies also indicated that an understanding of additive commutativity is not necessary for inventing strategies that disregard addend order (i.e., Felicia’s and the MIN strategies).
281:
memorization, which can usually be applied only to familiar tasks or situations. A key educational implication is that promoting meaningful learning is more powerful in promoting appropriate use of knowledge, including transfer.
276:
In 1983, Baroody helped
Ginsburg develop a novel early mathematical achievement test that assessed children’s informal, as well as their formal, mathematical knowledge, namely the Test of Early Mathematics Achievement (TEMA).
502:
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.
296:
and progress monitoring to ensure that math instruction builds on what each child knows and dedicate time each day to teaching math and integrate such instruction throughout the school day.
499:
Baroody, A. J., Yilmaz, N., Clements, D. H., & Sarama, J. (2021). Evaluating a basic assumption of learning trajectories: The case of early patterning learning. J. Math. Educ, 13, 8-32.
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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.
508:
Baroody, A. J., Mix, K., Kartal, G., & Lai, M-L. (2023). The development and assessment of early cardinal-number concepts. Journal of
Numerical Cognition, 9(1).
1388:
1551:
285:
1003:
Baroody, A. (December 29, 1999). "The
Development of Basic Counting, Number, and Arithmetic Knowledge among Children Classified as Mentally Handicapped".
505:
Baroody, A. J., & Lai, M. (2022). The development and assessment of counting-based cardinal number concepts. Educational
Studies in Mathematics, 1-21.
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141:
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Baroody, Arthur J. (2016). "Using number and arithmetic instruction as a basis for fostering mathematical reasoning". In
Battista, M.T. (ed.).
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1987 – 1990 & 1999-2001 - Awarded a UIUC College of Education faculty fellowship (appointment to the Bureau of Educational Research)
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227:, Institute of Education Sciences, Spencer Foundation, National Institutes of Health, and National Governors’ Association.
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1244:"Teaching and learning mathematics in early childhood programs | Development and Research in Early Math Education"
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224:
1230:"Curricular approaches to connecting subtraction to addition and fostering fluency with basic differences in grade 1"
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169:
1320:"Lessons Learned from 10 Experiments That Tested the Efficacy and Assumptions of Hypothetical Learning Trajectories"
553:"Children's mathematical thinking: A developmental framework for preschool, primary, and special education teachers"
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821:"The development of procedural knowledge: An alternative explanation for chronometric trends of mental arithmetic"
472:
Children’s mathematical thinking: A developmental framework for preschool, primary, and special education teachers
442:
Children's Mathematical Thinking: A Developmental Framework for Preschool, Primary, and Special Education Teachers
327:
988:
Baroody, Arthur J.; Purpura, David J. (2017). "Early number and operations: Whole numbers". In Cai, Jinfa (ed.).
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carefully considering a learning goal, a child’s developmental level, and how the manipulatives are used.
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568:"The Case of Felicia: A Young Child's Strategies for Reducing Memory Demands during Mental Addition"
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Fostering children's mathematical power: an investigative approach to K-8 mathematics instruction
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Fostering Children's Mathematical Power: An Investigative Approach To K-8 Mathematics Instruction
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Engaging Young Children in Mathematics: Standards for Early Childhood Mathematics Education
212:
Baroody began his academic career as an Assistant Professor of Developmental Psychology at
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1523:"Teaching Math to Young Children | Frank Porter Graham Child Development Institute"
54:
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Since 2000, Baroody has been the Principal Investigator or Co-PI on 12 grants from the
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1263:"Cardinality principle understanding: the role of focusing on the subitizing ability"
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552:
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213:
790:"The Development of the Commutativity Principle and Economical Addition Strategies"
478:
The development of arithmetic concepts and skills: Constructing adaptive expertise.
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Baroody, Arthur J.; Mix, Kelly; Kartal, Gamze; Lai, Meng-lung (December 5, 2022).
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905:"The Role of the Number-after Rule in the Invention of Computational Shortcuts"
337:. Contentious material about living people that is unsourced or poorly sourced
164:, academic, and an expert in mathematics education research. He is a Professor
920:
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121:
1464:"The developmental bases for early childhood number and operations standards"
1448:
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1319:
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Baroody, Arthur J.; Bajwa, Neet Priya; Eiland, Michael (December 29, 2009).
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Wilkins, Jesse L. M.; Baroody, Arthur J.; Tiilikainen, Sirpa (May 1, 2001).
44:
1200:"An Alternative Reconceptualization of Procedural and Conceptual Knowledge"
969:
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Baroody, Arthur J.; Clements, Douglas H.; Sarama, Julie (March 29, 2022).
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in 1979. For the latter degree, he was mentored by Herbert P. Ginsburg.
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Reasoning and sense making in the mathematics classroom: Pre-K—Grade 2
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450:. (Spanish translation of Children’s Mathematical Thinking.) (1988)
1181:"The Development and Assessment of Early Cardinal-Number Concepts"
671:
Baroody, Arthur J.; Ginsburg, Herbert P.; Waxman, Barbara (1983).
607:"The Development of Counting Strategies for Single-Digit Addition"
890:"Fostering At-Risk Preschoolers' Number Sense | Request PDF"
462:: Helping children think mathematically (1992) ISBN 9780023064883
992:. National Council of Teachers of Mathematics. pp. 308–354.
852:"Kindergartners' Mental Addition with Single-Digit Combinations"
417:
1997-98 - UIUC College of Education Distinguished Senior Scholar
1198:
Baroody, Arthur J.; Feil, Yingying; Johnson, Amanda R. (2007).
712:"Children's Difficulties in Subtraction: Some Causes and Cures"
1426:. National Council of Teachers of Mathematics. pp. 27–69.
474:. (Chinese edition of Children’s Mathematical Thinking) (2000)
303:
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and earned a B.S. in science education in 1969 and a Ph.D. in
18:
1493:"One Point of View: Manipulatives Don't Come with Guarantees"
460:
Problem Solving, Reasoning, and Communicating, Grades K to 8
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Ginsburg, Herbert; Baroody, Arthur J. (December 29, 1983).
1437:
Baroody, Arthur J.; Coslick, Ronald T. (March 9, 1998).
788:
Baroody, Arthur J.; Gannon, Kathleen E. (June 1, 1984).
454:
Elementary Mathematics Activities: A Teacher's Guidebook
235:
Baroody’s early research focused on the development of
49:
39:
1005:
International Review of Research in Mental Retardation
644:
Siegler, Robert; Jenkins, Eric A. (January 14, 2014).
1261:
Paliwal, Veena; Baroody, Arthur J. (August 1, 2020).
1451:– via University of Illinois Urbana-Champaign.
484:
IES Practice Guide: Teaching Math to Young Children
137:
132:
120:
115:
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82:
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423:2011 - Recognized as AERJ-THLD Excellent Reviewer
990:Compendium for research in mathematics education
1577:University of Illinois Urbana-Champaign faculty
1112:"The notion of principle: The case of counting"
1387:Baroody, Arthur J.; Dowker, Ann, eds. (2013).
426:2020 - Recognized as JRME Outstanding Reviewer
414:1990 – UIUC College of Education Scholar Award
1204:Journal for Research in Mathematics Education
856:Journal for Research in Mathematics Education
677:Journal for Research in Mathematics Education
611:Journal for Research in Mathematics Education
8:
944:"Why can't Johnny remember the basic facts?"
107:, academic, mathematics education researcher
948:Developmental Disabilities Research Reviews
286:National Council of Teachers of Mathematics
1355:. Pro Ed – via experts.illinois.edu.
673:"Children's Use of Mathematical Structure"
174:University of Illinois at Urbana-Champaign
142:University of Illinois at Urbana-Champaign
72:
1353:"Test of Early Mathematics Ability: TEMA"
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959:
401:Learn how and when to remove this message
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755:Journal of Experimental Child Psychology
1462:Baroody, Arthur J. (October 17, 2003).
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1491:Baroody, Arthur J. (October 1, 1989).
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448:El pensamiento matemático de los niños
526:
524:
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7:
1443:. Lawrence Erlbaum Associates, Inc.
808:– via Taylor and Francis+NEJM.
647:How Children Discover New Strategies
819:Baroody, Arthur J. (June 1, 1983).
1552:American educational psychologists
1187:– via www.psycharchives.org.
1066:Piaget, Jean (December 29, 1997).
176:, and a Senior Research Fellow in
14:
1480:– via experts.illinois.edu.
1289:– via experts.illinois.edu.
1069:The Child's Conception of Number
308:
23:
1390:Constructive Adaptive Expertise
1185:Journal of Numerical Cognition
178:Morgridge College of Education
1:
1017:10.1016/S0074-7750(08)60131-7
160:(born August 15, 1947) is an
1572:University of Denver faculty
837:10.1016/0273-2297(83)90031-X
319:biography of a living person
903:Baroody, Arthur J. (1995).
850:Baroody, Arthur J. (1989).
710:Baroody, Arthur J. (1984).
605:Baroody, Arthur J. (1987).
566:Baroody, Arthur J. (1984).
339:must be removed immediately
225:National Science Foundation
1593:
1511:– via pubs.nctm.org.
1279:10.1007/s11858-020-01150-0
839:– via ScienceDirect.
777:– via ScienceDirect.
468:(1998) ISBN 978-0805831054
170:Curriculum and Instruction
1562:Cornell University alumni
1267:ZDM Mathematics Education
1082:– via Google Books.
921:10.1207/s1532690xci1302_2
909:Cognition and Instruction
806:10.1207/s1532690xci0103_3
794:Cognition and Instruction
660:– via Google Books.
584:10.1207/s1532690xci0101_5
572:Cognition and Instruction
480:(2003) ISBN 0-8058-3155-X
456:(1989) ISBN 9780205118311
444:(1987) ISBN 9780807728376
284:In a 2017 chapter of the
151:
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202:developmental psychology
162:educational psychologist
105:Educational psychologist
16:Educational psychologist
1337:10.3390/educsci12030195
486:. (2013) NCEE 2014-4005
218:University of Rochester
216:in 1978. He joined the
158:Arthur "Art" J. Baroody
38:, as no other articles
1497:The Arithmetic Teacher
1368:Cite journal requires
767:10.1006/jecp.2000.2580
716:The Arithmetic Teacher
333:Please help by adding
1399:10.4324/9781410607218
328:references or sources
237:informal mathematical
1509:10.5951/AT.37.2.0004
1072:. Psychology Press.
825:Developmental Review
728:10.5951/AT.32.3.0014
650:. Psychology Press.
536:College of Education
182:University of Denver
146:University of Denver
350:"Arthur J. Baroody"
116:Academic background
1557:American educators
1324:Education Sciences
1248:dreme.stanford.edu
1218:– via JSTOR.
931:– via JSTOR.
878:– via JSTOR.
738:– via JSTOR.
699:– via JSTOR.
633:– via JSTOR.
594:– via JSTOR.
532:"Faculty Profiles"
317:This section of a
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47:to this page from
491:Selected articles
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300:Awards and honors
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