Arthur Baroody

Arthur "Art" J. Baroody (born August 15, 1947) is an educational psychologist, academic, and an expert in mathematics education research.

He is a Professor Emeritus of Curriculum and Instruction at the University of Illinois at Urbana-Champaign, and a Senior Research Fellow in Morgridge College of Education (COE) at the University of Denver.

Baroody attended Cornell University and earned a B.S. in science education in 1969 and a Ph.D. in educational and developmental psychology in 1979.

For the latter degree, he was mentored by Herbert P. Ginsburg.

Baroody began his academic career as an Assistant Professor of Developmental Psychology at Keuka College in 1978.

He joined the University of Rochester’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).

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 was promoted to Associate Professor of Curriculum and Instruction in 1989, and to Professor of Curriculum and Instruction in 1994.

Since 2000, Baroody has been the Principal Investigator or Co-PI on 12 grants from the National Science Foundation, Institute of Education Sciences, Spencer Foundation, National Institutes of Health, and National Governors’ Association.

Baroody’s early research focused on the development of informal mathematical 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 [is one more], 7 [is two more]).

Subsequent 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.

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 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).

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 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.

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; 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.

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 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.

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 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.

Later research efforts focused on how instruction could promote meaningful number, counting and arithmetic learning by fostering both conceptual and procedural knowledge.

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.