The Effects of Strategic Counting Instruction, with and without Deliberate Practice, on Number Combination Skill among Students with Mathematics Difficulties.

The primary purpose of this study was to assess the effects of strategic counting instruction, with and without deliberate practice with those counting strategies, on number combination (NC) skill among students with mathematics difficulties (MD). Students (n = 150) were stratified on MD status (i.e., MD alone vs. MD with reading difficulty) and site (proximal vs. distal to the intervention developer) and then randomly assigned to control (no tutoring) or 1 of 2 variants of NC remediation. Both remediations were embedded in the same validated word-problem tutoring protocol (i.e., Pirate Math). In 1 variant, the focus on NCs was limited to a single lesson that taught strategic counting. In the other variant, 4-6 min of practice per session was added to the other variant. Tutoring occurred for 16 weeks, 3 sessions per week for 20-30 min per session. Strategic counting without deliberate practice produced superior NC fluency compared to control; however, strategic counting with deliberate practice effected superior NC fluency and transfer to procedural calculations compared with both competing conditions. Also, the efficacy of Pirate Math word-problem tutoring was replicated.

[1]  Paul J. Feltovich,et al.  Categorization and Representation of Physics Problems by Experts and Novices , 1981, Cogn. Sci..

[2]  Houghton Mifflin math , 2005 .

[3]  Nancy C. Jordan,et al.  Cognitive Arithmetic and Problem Solving , 1997, Journal of learning disabilities.

[4]  Nancy C. Jordan,et al.  Journal of Experimental , 2002 .

[5]  F. Rivera-batiz,et al.  Quantitative Literacy and the Likelihood of Employment among Young Adults in the United States , 1992 .

[6]  R. Siegler.  The perils of averaging data over strategies: An example from children's addition. , 1987 .

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

[8]  Nancy C. Jordan,et al.  Mathematical Thinking in Second-Grade Children with Different Forms of LD , 2000, Journal of learning disabilities.

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

[10]  An introduction to the special issue: pathways to mathematical learning difficulties and disabilities. , 2009, Developmental disabilities research reviews.

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

[12]  Michael D. Coyne,et al.  Direct Instruction of Comprehension: Instructional Examples From Intervention Research on Listening and Reading Comprehension , 2009 .

[13]  D. Geary,et al.  Cognitive Addition: Comparison of Learning Disabled and Academically Normal Elementary School Children , 1987 .

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

[15]  G. Groen,et al.  A chronometric analysis of simple addition. , 1972 .

[16]  M. Barnes,et al.  Cognitive Arithmetic Differences in Learning Difficulty Groups and the Role of Behavioral Inattention , 2007 .

[17]  R. Shalev,et al.  Developmental dyscalculia: prevalence and prognosis , 2009, European Child & Adolescent Psychiatry.

[18]  Mary K. Hoard,et al.  Numerical and arithmetical cognition: patterns of functions and deficits in children at risk for a mathematical disability. , 1999, Journal of experimental child psychology.

[19]  Douglas Fuchs,et al.  Effects of Preventative Tutoring on the Mathematical Problem Solving of Third-Grade Students with Math and Reading Difficulties , 2008, Exceptional children.

[20]  H. Swanson,et al.  The Relationship Between Working Memory and Mathematical Problem Solving in Children at Risk and Not at Risk for Serious Math Difficulties , 2004 .

[21]  Neet Priya Bajwa,et al.  Why can't Johnny remember the basic facts? , 2009, Developmental disabilities research reviews.

[22]  Ann L. Brown,et al.  Interactive Learning Environments: A New Look at Assessment and Instruction , 1992 .

[23]  S. Miller,et al.  Using Evidence‐Based Practices to Build Mathematics Competence Related to Conceptual, Procedural, and Declarative Knowledge , 2007 .

[24]  Ulf Andersson,et al.  Working memory deficit in children with mathematical difficulties: a general or specific deficit? , 2007, Journal of experimental child psychology.

[25]  Lynn S. Fuchs,et al.  The Prevention, Identification, and Cognitive Determinants of Math Difficulty. , 2005 .

[26]  T. Conway,et al.  Intensive Remedial Instruction for Children with Severe Reading Disabilities , 2001, Journal of learning disabilities.

[27]  Gary J. Robertson,et al.  Wide‐Range Achievement Test , 2010 .

[28]  M. Ashcraft,et al.  Menatal addition: A test of three verification models , 1981, Memory & cognition.

[29]  Silvana Micallef,et al.  Arithmetic learning difficulties in children , 2004 .

[30]  D. Geary,et al.  Counting Knowledge and Skill in Cognitive Addition: a Comparison of Normal and Mathematically Disabled Children , 2022 .

[31]  L. Fuchs,et al.  Explicitly Teaching for Transfer: Effects on the Mathematical Problem–Solving Performance of Students with Mathematics Disabilities , 2002 .

[32]  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.

[33]  Jill L. Quilici,et al.  Role of examples in how students learn to categorize statistics word problems. , 1996 .

[34]  H. Lee Swanson,et al.  Cross-Sectional and Incremental Changes in Working Memory and Mathematical Problem Solving. , 2006 .

[35]  Snorre A. Ostad,et al.  Developmental differences in addition strategies: a comparison of mathematically disabled and mathematically normal children. , 1997, The British journal of educational psychology.

[36]  Lynn S. Fuchs,et al.  Remediating Computational Deficits at Third Grade: A Randomized Field Trial , 2008, Journal of research on educational effectiveness.

[37]  Elin Reikerås.  Performance in solving arithmetic problems: a comparison of children with different levels of achievement in mathematics and reading , 2006 .

[38]  R. Dykman,et al.  Arithmetic Automatization Failure in Children with Attention and Reading Disorders: Associations and Sequela , 1986, Journal of learning disabilities.

[39]  D. Carnine,et al.  Instructional Design in Mathematics for Students with Learning Disabilities , 1997, Journal of learning disabilities.

[40]  M. Bruck.  Persistence of dyslexics' phonological awareness deficits. , 1992 .

[41]  Arthur J. Baroody,et al.  Children's Relational Knowledge of Addition and Subtraction , 1999 .

[42]  Cynthia M. Okolo,et al.  The Effect of Computer-Assisted Instruction Format and Initial Attitude on the Arithmetic Facts Proficiency and Continuing Motivation of Students with Learning Disabilities. , 1992 .

[43]  Jack M. Fletcher,et al.  Effects of Intensive Reading Remediation for Second and Third Graders and a 1-Year Follow-Up. , 2004 .

[44]  Helmer R. Myklebust.  Progress in Learning Disabilities , 1982 .

[45]  M. O’Connor,et al.  Changing assessments : alternative views of aptitude, achievement and instruction , 1994 .

[46]  David C. Geary,et al.  Cognitive addition: A short longitudinal study of strategy choice and speed-of-processing differences in normal and mathematically disabled children. , 1991 .

[47]  Lynn S. Fuchs,et al.  The cognitive correlates of third-grade skill in arithmetic, algorithmic computation, and arithmetic word problems , 2006 .

[48]  L. Fuchs,et al.  Problem Solving and Computational Skill: Are They Shared or Distinct Aspects of Mathematical Cognition? , 2008, Journal of educational psychology.

[49]  Mary K. Hoard,et al.  Numerical and arithmetical cognition: a longitudinal study of process and concept deficits in children with learning disability. , 2000, Journal of experimental child psychology.

[50]  Douglas Fuchs,et al.  Remediating Number Combination and Word Problem Deficits Among Students With Mathematics Difficulties: A Randomized Control Trial. , 2009, Journal of educational psychology.

[51]  L. Hedges,et al.  Statistical Methods for Meta-Analysis , 1987 .

[52]  Arthur J. Baroody,et al.  Children's Use of Mathematical Structure. , 1983 .

[53]  Asha K. Jitendra,et al.  AN ANALYSIS OF MIDDLE SCHOOL GEOGRAPHY TEXTBOOKS: IMPLICATIONS FOR STUDENTS WITH LEARNING PROBLEMS , 2001 .

[54]  Arthur J. Baroody,et al.  The Role of the Number-After Rule in the Invention of Computational Shortcuts , 1995 .

[55]  J. Sweller,et al.  Effects of schema acquisition and rule automation on mathematical problem-solving transfer. , 1987 .

[56]  C. Christensen,et al.  Effectiveness of computerized drill and practice games in teaching basic math facts , 1990 .

[57]  J. Fletcher.  Learning Disabilities : From Identification to Intervention , 2006 .

[58]  Douglas Fuchs,et al.  Effects of Fact Retrieval Tutoring on Third–Grade Students with Math Difficulties with and without Reading Difficulties , 2009, Learning disabilities research & practice : a publication of the Division for Learning Disabilities, Council for Exceptional Children.

[59]  Mary K. Hoard,et al.  Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. , 2007, Child development.