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An eighth-grade student, was able to memorize multiplication facts (0 to 10) for the zeroes to fives with 100% accuracy. In a previous study  the student used skip counting and her hands to recall all the facts for the ones to fives. The overall goal of the current study was to improve the student’s automaticity of multiplication facts (0-10) for the ones through fives, such as 4 x 6 = 24. The student had been taught multiplication concepts in her elementary years and she did have a basic understanding of the meaning of multiplication facts as shown in the previous study. She understood that 4 x 6 is a representation of four sets of six or 6 + 6 + 6 + 6 = 24. The student had used skip counting and flash cards with illustrations of the multiplication facts to memorize the multiplication facts. In the current study a multiple baseline design was used to measure the acquisition of fluency of multiplication facts over time. The student was able to develop automaticity with 80% accuracy by giving the solution within 3 seconds for all of the facts (0-10) for the ones through fives.
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De Los Santos, E, “Helping a Student with Learning Disabilities Memorize Multiplication Facts”, International Journal for Innovation Education and Research, Vol. 7 No. 7, 2019, pp. 133-146.
National Council of Teachers of Mathematics, Principles and Standards for School Mathematics, NCTM, Reston, Va, 2000, p. 148, 153.
Common Core State Standards Initiative, Preparing America’s Students for College & Career, Mathematics Standards, 2014, Grade 3, p. 23.
Agaliotis, I. and A. Teli, “Teaching arithmetic combinations of multiplication and division to students with learning disabilities or mild intellectual disability: The impact of alternative fact grouping and the role of cognitive and learning factors”, Journal of Education and Learning, Vol. 5 No. 4, 2016, pp. 90-103.
Baroody, A.J., N.P. Bajwa, and M. Eiland, “Why can’t Johnny remember the basic facts? Developmental Disabilities Research Reviews, Vol. 15 No. 1, 2009, pp. 69-
Baroody, A.J. “Mastering the basic number combinations”, Teaching Children Mathematics, Aug. 2006, pp. 22-31.
Crawford, D.B., “The third stage of learning math facts: Developing automaticity”, R&D Instructional Solutions, pp. 2003, pp. 1-40. https://www.rocketmath.com/wp-content/uploads/2016/03/Math-Facts-research.1.pdf
Woodward, J, “Developing automaticity in multiplication facts: Integrating strategy instruction with timed practice drills”, Learning Disability Quarterly, Vol. 29, No. 4, 2006, pp. 269-289.
Baker, A.T. and J. Cuevas, “The importance of automaticity development in mathematics”, Georgia Educational Researcher, Vol. 14 No. 2, 2018, pp. 11-23.
Bouck, E.C., L. Bassette, T. Taber-Doughty, L.M. Flanagan, and K. Szwed, “Pentop computers as tools for teaching multiplication to students with mild intellectual disabilities”, Education and Training in Developmental Disabilities, Vol. 44 No. 3, 2009, pp. 367-380.
Geary, D.C., M.K. Hoard, J. Byrd-Craven, L. Nugent, and C. Numtee, “Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability”, Child Development, Vol. 78 No. 4, 2007, pp. 1343-1359.
Gersten, R., N.C. Jordan, and J.R. Flojo, “Early identification and interventions for students with mathematical difficulties”, Journal of Learning Disabilities, Vol. 38 No. 4, 2005, 293-304.
Van De Walle, J.A., K.S. Karp, and J.M. Bay-Williams, Elementary and Middle School Mathematics: Teaching Developmentally, Allyn & Bacon, Boston, MA, 2010.
Miller, S.P. and P.J. Hudson, “Helping Students with Disabilities Understand What Mathematics Means”, Teaching Exceptional Children, Vol. 39 No. 1, 2006, pp. 28-35.
Hinton, V., S.D. Strozier, and M.M. Flores, “Building Mathematical Fluency for Students with Disabilities or Students At-Risk for Mathematics Failure”, International Journal of Education in Mathematics, Science and Technology, Vol. 2 No. 4, Oct. 2014, pp. 257-265.
Mudaly, V. and J. Naidoo, “The concrete-representational-abstract Sequence of Instruction in Mathematics Classrooms”, Perspectives in Education, Vol. 33 No. 1, 2015, pp. 42-56.
Stroizer, S., V. Hinton, M. Flores, and L. Terry, “An Investigation of the Effects of CRA Instruction and Students with Autism Spectrum Disorder”, Education and Training in Autism and Developmental Disabilities, Vol. 50 No. 2, 2015, pp. 223-236.
Flores, M.M., V.M. Hinton, S.D. Strozier, and S.L. Terry, “Using the Concrete-representational-abstract Sequence and the Strategic Instruction Model to Teach Computation to Students with Autism Spectrum Disorders and Developmental Disabilities”, Education and Training in Autism and Developmental Disabilities, Vol. 49 No. 4, 2014, pp. 547-554.
Miller, S.P., C.D. Mercer, and A.S. Dillon, “CSA: Acquiring and Retaining Math Skills”, Intervention in School and Clinic, Vol. 28 No. 2, 1992, pp. 105-110.
Morin, V.A. and S.P. Miller, “Teaching multiplication to middle school students with mild intellectual disabilities, Education and Treatment of Children, Vol. 21 No. 1, 1998, pp. 22-36.
Parmar, R.S., J.F. Cawley, and J.H. Miller, “Differences in mathematics performance between students with learning disabilities and students with mild intellectual disabilities”, Exceptional Children, Vol. 60 No. 6, 1994, pp. 549-563.
Thorton, C.A. and M.A. Toohey, “Basic Math Facts: Guidelines for Teaching and Learning”, Learning Disabilities Focus, Vol. 1 No. 1, 1985, pp. 44-57. [***Was  ***]
ASCD Express, “Teaching Students with Learning Disabilities in the Regular classroom”, Learning with Disabilities, Vol. 7 No. 7, 2012, pp. 1-6.
Wood, D.K., A.R. Frank, and D.P. Wacker, “Teaching Multiplication Facts to Students with Learning Disabilities, Journal of Applied Behavior Analysis, Vol. 31 No. 3, 1998, pp. 323-338.
Codding, R.S., M. Shiyko, M. Russo, S. Birch, S., E. Fanning, and D. Jaspen, “Comparing mathematics interventions: Does initial level of fluency predict intervention effectiveness?”, Journal of School Psychology, Vol. 45 No. 6, 2007, pp. 603-617.
Skinner, C.H., T.F. McLaughlin, and P. Logan, “Cover-Copy, and Compare: A self-managed academic intervention effective across skills, students, and settings”, Journal of Behavioral Education, Vol. 7 No. 3, 1997, pp. 295-306.
Morton, R.C. and D.L. Gadke, “A comparison of Math Cover, Copy, Compare intervention procedures for children with Autism Spectrum Disorder”, Behavior Analysis in Practice, Vol. 11 No. 1, 2018, pp. 80-84.
Burns, M.K., “Using Incremental Rehearsal to Increase fluency of single-digit multiplication facts with children identified as learning disabled in mathematics computation”, Education and Treatment of Children, Vol. 28 No. 3, 2005, 237-249.
Cravalho, C.J., T.F. McLaughlin, K.M. Derby and T. Waco, “The effects of Direct Instruction Flashcards on Math Performance with Measures of Generalization across Elementary Students with Learning Disabilities and Autism Spectrum Disorder”, International Journal of Basic and Applied Science, Vol. 2 No. 4, 2014, pp. 16-31.
Lund, K., T.F. McLaughlin, J. Neyman, and M. Everson, “The Effects of DI Flashcards and Math Racetrack on Multiplication Facts for Two Elementary Students with Learning Disabilities”, Journal of Special Education Apprenticeship, Vol. 1 No. 1, 2012, pp. 1-15.
Mattingly, J.C. and D.A. Bott, “Teaching multiplication facts to students with learning problems”, Exceptional Children, Vol. 56 No. 5, 1990, pp. 438-449.
Glover, P., T. McLaughlin, K.M. Derby, and J. Gower, “Using a Direct Instruction Flashcard System with Two Students with Learning Disabilities”, Electronic Journal of Research in Educational Psychology, Vol. 8 No. 2, 2010, pp. 457-472.
Parmar, R.S., R. Frazita, and J.F. Cawley, “Mathematics Assessment for Students with Mild Disabilities: An Exploration of Content Validity”, Learning Disability Quarterly, Vol. 19 No. 2, 1996, pp. 127-136.
Tawney, J.W. and D.L. Gast, Eds., Single Subject Research in Special Education, Charles Merrill, Columbus, OH, 1984.
Barlow, D.H., M.K. Nock, and M. Hersen, Single case experimental designs: Strategies for studying behavior change, 3rd ed., Pearson, Boston, MA, 2009.
Kazdin, A.E., Single Case Research Designs: Methods for clinical and applied settings, 2th ed, Oxford University Press, New York, NY, 2011.
Individual with Disabilities Education Act 2004, Statute Chapter 33, Subchapter I (Part A), Section 1401- Definitions.
De Los Santos, E. and B. Patton, “Making Mathematical Place Value Meaningful for a Special Needs Student”, International Journal of Technology and Inclusive Education, Vol. 1 No. 2, 2014, pp. 455-458.
De Los Santos, E. and B. Patton, “Using Concrete and Abstract Models to Help a Special Needs Third Grader Master Whole Number Addition”, International Journal of Technology and Inclusive Education, Vol. 5 No. 1, 2016, pp. 787-793.
De Los Santos, E., “Helping a Special Needs Student Learn Place Value in the Hundreds”, International Journal of Technology and Inclusive Education, Vol. 6 No. 2, 2017, pp. 1108-1116.