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IES Grant

Title: Developing an Intervention to Foster Early Number Sense and Skill
Center: NCER Year: 2005
Principal Investigator: Baroody, Arthur Awardee: University of Illinois, Urbana-Champaign
Program: Science, Technology, Engineering, and Mathematics (STEM) Education      [Program Details]
Award Period: 3 years Award Amount: $1,499,965
Type: Development and Innovation Award Number: R305K050082

Purpose: The primary purpose of this project was to help children at risk for difficulties learning mathematics become fluent in basic addition and subtraction facts. In the classroom, students who fall behind in mathematics and are identified as having learning disabilities often lack fluency with basic mathematics facts. These skills are essential for many more-advanced aspects of school mathematics. To address this skill gap, the researchers developed three qualitatively different computer-aided pre-kindergarten to first-grade programs for helping children at risk of developing difficulties by learning basic addition facts (e.g., 8+6) and related subtraction facts (e.g., 14-8). They also evaluated the potential impact of the programs in a pilot study.

Structured Abstract


Setting: Three school districts serving a mid-sized urban/suburban area in the Midwest will participate in the project.

Population: About 550 students aged 4- to 7-years old who are at risk for difficulties learning mathematics (e.g., children from low-income families or racial, ethnic, or linguistic minority groups or with low mathematics achievement) from the 3 selected school districts will participate in the study. Approximately 50 percent of the students in these schools are White, 33 percent are Black, 6 percent are Hispanic, 1 percent are Asian, and 10 percent Other.

Intervention: Development of the programs will draw on existing theory, research, and curricula and will entail developing new manual and computer games. The indirect program is based on the assumptions that computational fluency (efficient and flexible computational skill) stems from number sense and that instruction should focus on constructing an explicit understanding of big ideas (concepts that are applicable across many topics and applications) and discovering relations among basic facts. For example, helping children understand the big idea of "decomposition" (a whole can be split up into parts often in different ways) may underlie spontaneously inventing a "decomposition-to-10" reasoning strategy (e.g., viewing 9+7 as 9+1+6 or the relatively easy fact 10+6), memorizing such facts, and making sense of missing-addend problems (e.g., recognizing that the unknown in 7+?=10 is a missing part and must be smaller than the whole 10). The semi-direct approach involves teaching reasoning strategies, such as decomposition-to-10 strategy. The direct ("controlled response time") approach entails well-designed and extensive fact drill (e.g., memorizing a few facts at a time by rote and providing immediate feedback).

Research Design and Methods: The focus of Year 1 will be the development and formative evaluation of the three programs for the pre-k and grade 1 components and the summative evaluation of the pre-k programs. The focus of Year 2 will be the summative evaluation of the grade 1 component and the development and formative evaluation of the kindergarten component. The summative evaluation of the kindergarten component will be completed in the third year of the project. The summative evaluation of each grade-level component will entail a training experiment. After screening and pre-testing of the participant pool, 162 students aged 4 through 7 years old will be randomly assigned to the treatments for the preschool, Kindergarten, and first grade study, respectively. The random assignment will be checked to ensure a balance of at-risk factors in each group. Participants will work in groups of three with the experimental and control programs. Training will last for 6 months in the case of the pre-k study and 7.5 months for the kindergarten and first grade studies.

Comparison Condition: In this project, the semi-direct instruction and direct instruction conditions serve as control or comparison conditions.

Key Measures: The computer program will automatically collect accuracy and response time data during the intervention in order to chart the on-going development of fact fluency. In addition, standardized, experimenter-designed and observational measures of computational estimation, computational fluency and addition and subtraction strategy choice will be collected.

Data Analytic Strategy: The analyses for comparing the potential efficacy of the three programs will typically entail a Kruskal-Wallis ANOVA if pre-testing does not reveal significant individual differences. If pre-testing reveals appreciable individual differences on a task, the posttest data will be analyzed using an ANCOVA with the pre-test score serving as the covariate.

Related IES Projects: Fostering Fluency with Basic Addition and Subtraction (R305A080479)

Products and Publications

ERIC Citations: Find available citations in ERIC for this award here.

WWC Review: Baroody, A. J., Eiland, M., & Thompson, B. (2009). Fostering at-risk preschoolers' number sense. Early Education and Development, 20(1), 80–128. [WWC Review]

Select Publications:


Baroody, A.J., Lai, M., and Mix, K.S. (2006). The Development of Young Children's Early Number and Operation Sense and its Implications for Early Childhood Education.(2nd ed.). Mahwah, NJ: Lawrence Erlbaum Associates Publishers.

Book chapters

Baroody, A.J. (2011). Learning: A Framework. In F. Fennell (Ed.), Special Education and Mathematics: Helping Children With Learning Difficulties Achieve Mathematical Proficiency (pp. 15–57). Reston, VA: National Council of Teachers of Mathematics.

Baroody, A.J., and Li, X. (2009). Mathematics Instruction That Makes Sense for 2 to 5 Year Olds. In E.L. Essa, and M.M. Burnham (Eds.), Informing Our Practice: Useful Research on Young Children's Development (pp. 119–135). Washington, DC: The National Association for the Education of Young Children.

Journal articles

Baroody, A.J. (2008). Fostering Early Numeracy in Preschool and Kindergarten. Encyclopedia of Language and Literacy Development: 1–10.

Baroody, A.J., Bajwa, N.P., and Eiland, M. (2009). Why Can't Johnny Remember the Basic Facts?. Developmental Disabilities Research Reviews, 15(1): 69–79.

Baroody, A.J., Eiland, M., and Thompson, B. (2009). Fostering At-Risk Preschoolers' Number Sense. Early Education and Development, 20(1): 80–128.

Baroody, A.J., Eiland, M.D., Purpura, D.J., and Reid, E.E. (2012). Fostering At-Risk Kindergarten Children's Number Sense. Cognition and Instruction, 30(4): 435–470.

Baroody, A.J., Feil, Y., and Johnson, A.R. (2007). An Alternative Reconceptualization of Procedural and Conceptual Knowledge. Journal for Research in Mathematics Education, 38(2): 115–131.