- Initial number concepts and skills
- Counting skills and principles
- Informal addition strategies
- Arithmetic concepts such as the principle of commutativity (a + b = b + a)
- Number-fact mastery

I am currently the Principal Investigator for three research projects:

(a) Fostering Fluency with Basic Addition and Subtraction”; funding from the Institute of Education Sciences, U.S. Department of Education pending, 7/1/2008–6/30/2012. 

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

(c) 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.

I am also a co-PI on a third project:  Computer-guided Comprehensive Mathematics Assessment for Young Children funded by the Program in Early Learning and School Readiness, National Institutes of Health; 10/1/2005–9/30/2010.

Recent scholarly publications include:

Baroody, A. J., Lai, M.-L., Li, X., & Baroody, A. E. (in press). Preschoolers’ understanding of subtraction-related principles. Mathematics Thinking and Learning,

Baroody, A. J., Li, X., & Lai, M.-L. (in press). Toddlers’ spontaneous attention to number. Mathematics Thinking and Learning, 10, 51–58.

Lai, M.-L., Baroody, A. J., & Johnson, A. R. (in press). Fostering Taiwanese preschoolers’ understanding of the addition-subtraction inverse principle. Cognitive Development.
 

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..

Baroody, A. J., & Lai, M.-L. (2007). Preschoolers’ understanding of the addition-subtraction inverse principle: A Taiwanese sample. Mathematics Thinking and Learning, 9, 131–171.

Baroody, A. J., Tiilikainen, S. H., & Tai, Y. (2006).  The application and development of an addition goal sketch. Cognition and Instruction, 24, 123–170.

Baroody, A. J., Lai, M.-L., & Mix, K. S. (2006).  The development of young children’s number and operation sense and its implications for early childhood education. In B. Spodek & O. Saracho (Eds.) Handbook of Research on the Education of Young Children (pp. 187–221). Mahwah, NJ: Lawrence Erlbaum Associates.

Mix, K. S., Sandhofer, C. M., & Baroody, A. J.  (2005). Number words and number concepts: The interplay of verbal and nonverbal processes in early quantitative development. In R. Kail (Ed.), Advances in Child Development and Behavior, Vol. 33 (pp. 305–346). New York: Academic Press.

Baroody, A. J., Cibulskis, M., Lai, M.-L., & Li, X.  (2004). Comments on the use of learning trajectories in curriculum development and research. Mathematical Thinking and Learning, 6, 227–260.

Baroody, A. J., & Dowker, A. (2003).  The development of arithmetic concepts and skills:  Constructing adaptive expertise.  “Studies in Mathematics Thinking and Learning” series, edited by A. Schoenfeld.  Mahwah, NJ: Lawrence Erlbaum Associates.

As an educational and developmental psychologist, I am particularly interested in applying developmental theory and research to improving instruction, especially in the areas of early childhood and elementary mathematics education. Some of my recent work in this area include the following:

(1) Co-writer for the number and operation standards for early childhood mathematics (in D. Clements, J., & Sarama, J. (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education. Mahwah, NJ: Lawrence Erlbaum Associates.

(2) Co-author with Herbert P. Ginsburg, Test of Early Mathematics Ability (3rd ed.), published in 2003 by Pro-Ed, Austin, TX.

(3) Author of Fostering children's mathematical power: An investigative approach to K-8 mathematics instruction, published in (1998) by Lawrence Erlbaum Associates.

(4) Author of Baroody, A. J., with Johnson, A. R. (in preparation). Helping struggling learners achieve mathematical proficiency. Norwood, MA: Christopher-Gordon Publishers Inc. 

Recent articles for teachers include:

(a) Baroody, A. J. (2006). Why children have difficulties mastering the basic number facts and how to help them. Teaching Children Mathematics, 13, 22–31.

(b) Baroody, A. J., & Wilkins, J. L. M. (2004). The inverting-a triangular array problem: An opportunity to involve students in the processes of mathematical inquiry. Mathematics Teaching in the Middle School, 9(6), 306–313.

(c) Baroody, A. J., & Benson. A. P. (2001).  Early number instruction.  Teaching Children Mathematics, 8(3), 154–158.

(d)Baroody, A. J., & Bartels, B. H. (2001). Assessing understanding in mathematics with concept mapping. Mathematics in School, 30(3), 24–27.

(e) Isenbarger, L. M., & Baroody, A. J. (2001).  Fostering the mathematical power of children with behavioral difficulties: The case of Carter. Teaching Children Mathematics, 7(8), 468–471.

(f) Baroody, A. J. (2000).  Does mathematics instruction for 3- to 5-year olds really make sense?  Young Children, 55(4), 61–67.

(g) Baroody, A. J., & Bartels, B. H. (2000).  Using concept maps to link mathematical ideas.  Mathematics Teaching in the Middle School, 5(9), 604–609.