Developing Automaticity in Multiplication Facts: Integrating Strategy Instruction with Timed Practice Drills

Automaticity in math facts has been of considerable interest to special educators for decades. A review of the intervention literature suggests at least two common approaches to developing automaticity in facts. One is grounded in the use of strategies for teaching facts, the other emphasizes the use of timed practice drills. Recent research indicates that students might benefit from an integration of these two approaches. This experimental study contrasted an integrated approach (i.e., strategies and timed practice drills) with timed practice drills only for teaching multiplication facts. Participants were 58 fourth-grade students with a range of academic abilities. Fifteen of the students in the study had IEPs in math. Results indicated that both approaches were effective in helping students achieve automaticity in multiplication facts. However, students in the integrated approach generally performed better on posttest and maintenance test measures that assessed the application of facts to extended facts and approximation tasks. These results have implications for teaching a range of skills and concepts that are considered important to overall mathematical competence in the elementary grades.

[1]  Herbert P. Ginsburg,et al.  The development of mathematical thinking , 1983 .

[2]  S. Miller.  Promoting Strategic Math Performance among Students with Learning Disabilities. , 1996 .

[3]  Nancy C. Jordan,et al.  Performance across different areas of mathematical cognition in children with learning difficulties. , 2001 .

[4]  Mental Calculation Methods Used By 11-Year-Olds in Different Attainment Bands: a reanalysis of data from the 1987 APU survey in the UK , 2002 .

[5]  S R Goldman,et al.  Information Processing and Educational Microcomputer Technology , 1987, Journal of learning disabilities.

[6]  D. Kinder,et al.  Designing Effective Mathematics Instruction: A Direct Instruction Approach , 2005 .

[7]  J. Hiebert.  Conceptual and procedural knowledge : the case of mathematics , 1987 .

[8]  M. Burns.  Using incremental rehearsal to increase fluency of single-digit multiplication facts with children identified as learning disabled in mathematics computation , 2005 .

[9]  James M. Moser,et al.  The Acquisition of Addition and Subtraction Concepts in Grades One through Three. , 1984 .

[10]  William A. Brownell,et al.  The Effects of Premature Drill in Third-Grade Arithmetic , 1935 .

[11]  R. Siegler.  Emerging Minds: The Process of Change in Children's Thinking , 1996 .

[12]  Constance Kamii,et al.  Identification of Multiplicative Thinking in Children in Grades 1-5. , 1996 .

[13]  Edward C. Rathmell,et al.  Using Thinking Strategies to Teach the Basic Facts. , 1978 .

[14]  Karen S. Karp,et al.  Elementary and Middle School Mathematics , 1998 .

[15]  E. Kroesbergen,et al.  Mathematics Interventions for Children with Special Educational Needs , 2003 .

[16]  Donald L. Chambers.  Direct modeling and invented procedures: building on students' informal strategies , 1996 .

[17]  Bruce L Sherin,et al.  Multiplication Strategies and the Appropriation of Computational Resources , 2005 .

[18]  Nelly Tournaki,et al.  The Differential Effects of Teaching Addition Through Strategy Instruction Versus Drill and Practice to Students With and Without Learning Disabilities , 2003, Journal of learning disabilities.

[19]  Russell Gersten,et al.  Number Sense , 1999 .

[20]  R. Cheloha,et al.  The of a Development , 2004 .

[21]  James G. Greeno,et al.  Number sense as situated knowing in a conceptual domain , 1990 .

[22]  Eric A. Jenkins,et al.  How Children Discover New Strategies , 1989 .

[23]  John Wills Lloyd,et al.  Designing High-Quality Research in Special Education , 2000 .

[24]  J. Anghileri.  An investigation of young children's understanding of multiplication , 1989 .

[25]  Lauren B. Resnick,et al.  A Developmental Theory of Number Understanding. , 1984 .

[26]  Mark H. Ashcraft,et al.  THE FREQUENCY OF ARITHMETIC FACTS IN ELEMENTARY TEXTS: ADDITION AND MULTIPLICATION IN GRADES 1-6 , 1995 .

[27]  Ruth M. Steinberg.  Instruction on Derived Facts Strategies in Addition and Subtraction. , 1985 .

[28]  J. Elkins,et al.  Lack of Automaticity in the Basic Addition Facts as a Characteristic of Arithmetic Learning Problems and Instructional Needs , 1999 .

[29]  David C. Geary,et al.  Cognitive Addition: Strategy Choice and Speed-of-Processing Differences in Gifted, Normal, and Mathematically Disabled Children. , 1991 .

[30]  C. Thornton,et al.  Action Research: Strategies for Learning Subtraction Facts. , 1988 .

[31]  Ted S. Hasselbring,et al.  Developing Math Automaticity in Learning Handicapped Children: The Role of Computerized Drill and Practice. , 1988 .

[32]  James Hiebert.  Missing Links@@@Conceptual and Procedural Knowledge: The Case of Mathematics , 1987 .

[33]  Susan T. Koscinski,et al.  Use of Constant Time Delay in Teaching Multiplication Facts to Students with Learning Disabilities , 1993, Journal of learning disabilities.

[34]  Arthur J. Baroody,et al.  Fostering Children's Mathematical Power: An Investigative Approach To K-8 Mathematics Instruction , 1998 .

[35]  Ralph T. Putnam,et al.  Understanding of Derived-Fact Strategies in Addition and Subtraction , 1990 .

[36]  David C. Geary,et al.  The Problem-size Effect in Mental Addition: Developmental and Cross-national Trends , 1996 .

[37]  Susan R. Goldman,et al.  Information Processing and Elementary Mathematics , 1987, Journal of learning disabilities.

[38]  Katherine Garnett,et al.  Developing Fluency with Basic Number Facts: Intervention for Students with Learning Disabilities. , 1992 .

[39]  D. Geary.  Mathematical disabilities: cognitive, neuropsychological, and genetic components. , 1993, Psychological bulletin.

[40]  H. Simon,et al.  Situated Learning and Education1 , 1996 .

[41]  H. Lee Swanson,et al.  Interventions for Students with Learning Disabilities: A Meta-Analysis of Treatment Outcomes , 1999 .

[42]  Susan R. Goldman,et al.  Extended Practice of Basic Addition Facts: Strategy Changes in Learning-Disabled Students , 1988 .

[43]  Mary K. Hoard,et al.  Numerical and Arithmetical Cognition: Performance of Low- and Average-IQ Children , 1999 .

[44]  Joanne Mulligan,et al.  Young Children ’ s Intuitive Models of Multiplication and Division , 2001 .

[45]  Judith T. Sowder.  Making Sense of Numbers in School Mathematics , 1992 .

[46]  William M. Carroll,et al.  Strategies for Basic-Facts Instruction. , 1999 .

[47]  D. Wacker,et al.  Teaching multiplication facts to students with learning disabilities. , 1998, Journal of applied behavior analysis.

[48]  A. Baroody.  The roles of estimation and the commutativity principle in the development of third graders' mental multiplication. , 1999, Journal of experimental child psychology.