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IES Grant

Title: Fostering Fluency With Basic Addition and Subtraction
Center: NCER Year: 2008
Principal Investigator: Baroody, Arthur Awardee: University of Illinois, Urbana-Champaign
Program: Science, Technology, Engineering, and Mathematics (STEM) Education      [Program Details]
Award Period: 4 years Award Amount: $3,099,995
Type: Efficacy and Replication Award Number: R305A080479

Purpose: Children at risk for academic failure frequently have difficulty achieving fluency in basic addition and subtraction facts. Many at-risk first and second graders have difficulty with even the simplest addition facts, such as 6 + 0 = 6 and 7 + 1 = 8. Although early intervention might prevent these deficiencies and learning difficulties, little research has rigorously examined how to best promote fact fluency among young at-risk children. The purpose of this study is to evaluate the efficacy of a set of computer-based activities, developed under a previous Institute of Education Sciences development grant, designed to foster children's fluency with single digit, basic addition and subtraction facts.

Project: The theory- and research-based computer activities incorporate different features that may promote fact fluency. The four features that will be systematically compared are: unstructured discovery learning, structured discovery learning, structured discovery learning plus active modeling reasoning strategies, and structured discovery learning plus active modeling and decomposition training. These program features will be evaluated against each other, along with a control condition, to determine which features or blend of features work and which work best.

Products: The expected outcomes of this research include published reports on the relative efficacy of the computer-based activities for fostering fluency in single digit, basic addition and subtraction facts.

Structured Abstract

Setting: Six diverse medium-size urban and suburban elementary schools in Illinois will participate in the study.

Population: The sample consists of kindergarten through second grade students who have been identified as having mathematical learning difficulties and who are at-risk for academic failure. The ethnic composition of the schools serving at-risk children in the participating schools districts is approximately 50% White, 33% Black, and 17% other. All the school districts serve children from families representing a wide range of socioeconomic backgrounds. The minimum sample size for each training study will be 120 students at each grade level resulting in 24 students per experimental or control condition at each grade level.

Intervention: The interventions to be tested are computer-based activities that focus on various blends of direct and indirect instructional approaches. In the first version, unstructured discovery learning, students are provided with haphazard practice of basic addition and subtraction facts. In the second version, passive structured discovery learning, students are first encouraged to self-discover a pattern or relation followed by explicit instruction of basic addition and subtraction facts. In the active structured discovery learning version, the guided discovery approach is similar to that used in the second experimental version except that passive feedback or modeling of the reasoning strategies by the computer will be intermixed with active feedback in which the student interacts with the computer. The fourth version, active structured discovery learning plus decomposition training, is similar to the third experimental version except it will include decomposition training to facilitate the efficient mastery of such strategies as "n+1" or "1+n" equals the number after n, and make-ten strategies.

Research Design and Methods: Children will be initially tested with the Test of Early Mathematics Ability—Third Edition (TEMA-3) to gauge mathematical achievement and diagnose specific deficiencies that might affect mental-addition performance. Based on their score on the TEMA-3, students will be assigned to take part in one of five training studies for 30-minutes twice a week. Well-qualified and trained project personnel will oversee the students' use of the computer-based activities during the training study on a one-to-one basis. The training studies consist of computer-based games that encourage students to respond quickly and accurately to the computation questions so that they can maximize the number of reward points earned in the game. Within each of the five training studies, students will be randomly assigned to one of the four experimental computer activity conditions described above-unstructured discovery learning, passive structured discovery learning, active structured discovery, active structured discovery learning plus decomposition training—or the control condition. Year 1 of the study will focus on students in first grade, Year 2 will focus on students in kindergarten, and Year 3 will focus on students in second grade.

Control Condition: The control condition for the study will be identical to the fourth experimental condition (active structured discovery learning plus decomposition training), except that the training and practice students receive in the control condition will be on a different set of basic addition and subtraction facts.

Key Measures: Students will receive a pre-test, mid-training test, immediate post-test, and delayed post-test on the TEMA-3, a mental arithmetic task, and a mental computational shortcut task.

Data Analytic Strategy: Analyses of covariance and multiple regression analyses will be conducted to determine the efficacy of the four versions of the computer activities in fostering fluency with single digit, basic addition and subtraction facts.

Related IES Projects: Developing an Intervention to Foster Early Number Sense and Skill (R305K050082)

Products and Publications

Book chapter

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 Varma, S. (2006). The Active Construction View of Basic Number Fact Knowledge: New Directions for Cognitive Neuroscience. In J. Baek, A.E. Kelly, and L. Kalbfleisch (Eds.), Neuropsychology and Mathematics Education.

Baroody, A.J., Purpura, D.J., and Reid, E.E. (2012). Comments on Learning and Teaching Early and Elementary Mathematics. In J. Carlson, and J. Levin (Eds.), Psychological Perspectives on Contemporary Educational Issues, Volume 3 (pp. 163–175). Charlotte, NC: Information Age Publishing.

Baroody, A.J., Purpura, D.J., Reid, E.E., Paliwal, V., and Bajwa, N.P. (2013). Early Childhood Mathematics Education. In L. Meyer (Ed.), Oxford Bibliographies Online. New York: Oxford University Press.

Journal article, monograph, or newsletter

Baroody, A.J. (2016). Curricular Approaches to Connecting Subtraction to Addition and Fostering Fluency With Basic Differences in Grade 1. PNA, 10(3): 161–190.

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.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., Eiland, M.D., Purpura, D.J., and Reid, E.E. (2013). Can Computer-Assisted Discovery Learning Foster First Graders' Fluency With the Most Basic Addition Combinations?. American Educational Research Journal, 50(13): 533–573.

Baroody, A.J., Purpura, D.J., Eiland, M.D., Reid, E.E., and 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.

Baroody, A.J., Purpura, D.J., Eiland, M.M., and 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.

Baroody, A.J., Reid, E.E., and Purpura, D.J. (2013). An Example of a Hypothetical Learning Progression: The Successor Principle and Emergence of Informal Mathematical Induction. WISDOMe Monograph 3.

lmer, A., and Baroody, A.J. (2011). Blake's Development of the Number Words "One," "Two," and "Three". Cognition and Instruction, 29(3): 265–296.

Purpura, D.J., Baroody, A.J., and Lonigan, C.J. (2013). The Transition From Informal to Formal Mathematical Knowledge: Mediation by Numeral Knowledge. Journal of Educational Psychology, 105(2): 453–464.

Purpura, D.J., Baroody, A.J., Eiland, M.D., and Reid, E.E. (2016). Fostering First Graders' Reasoning Strategies with Basic Sums: The Value of Guided Instruction. Elementary School Journal, 117(1): 72–100.

Reid, E.E., Baroody, A.J., and 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.