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Abstract
Incremental rehearsal (IR) has consistently led to effective retention of newly learned material, including math facts. The number of new items taught during one intervention session, called the intervention set, could be used to individualize the intervention. The appropriate amount of information that a student can rehearse and later recall during one intervention session is called the acquisition rate (AR). The current study taught single-digit multiplication facts with factors of 6, 7, and 8 to 55 third- and fourth-grade students. Each student was randomly assigned to be taught two multiplication math facts, eight multiplication math facts, or a set size determined by each student’s AR. The average AR was 4.05 (SD = 0.71). Set size led to a significant and large effect on retention, percentage of multiplication math facts retained, and efficiency as computed by math facts retained per minute of intervention time. IR appeared to be an effective intervention when AR data were used to determine the intervention set size, and it was more efficient to do so.
Keywords curriculum-based assessment, math
References
Section:
|
Burns, M. K. (2001). Measuring acquisition and retention rates with curriculum-based assessment. Journal of Psychoeducational Assessment, 19, 148–157. Google Scholar | SAGE Journals | ISI | |
|
Burns, M. K. (2004a). Age as a predictor of acquisition rates as measured by curriculum-based assessment: Evidence of consistency with cognitive research. Assessment for Effective Intervention, 29, 31–38. doi:10.1177/073724770402900203 Google Scholar | Crossref | |
|
Burns, M. K. (2004b). Empirical analysis of drill ratio research: Refining the instructional level for drill tasks. Remedial and Special Education, 25, 167–175. doi:10.1177/07419325040250030401 Google Scholar | SAGE Journals | ISI | |
|
Burns, M. K. (2005). Using incremental rehearsal to practice multiplication facts with children identified as learning disabled in mathematics computation. Education & Treatment of Children, 28, 237–249. Google Scholar | |
|
Burns, M. K. (2007). Comparison of drill ratio and opportunities to respond when rehearsing sight words with a child with mental retardation. School Psychology Quarterly, 22, 250–263. Google Scholar | Crossref | ISI | |
|
Burns, M. K., Dean, V. J. (2005). Effect of acquisition rates on off-task behavior with children identified as learning disabled. Learning Disability Quarterly, 28, 273–281. Google Scholar | SAGE Journals | ISI | |
|
Burns, M. K., Mosack, J. (2005). Criterion-referenced validity of measuring acquisition rates with curriculum-based assessment. Journal of Psychoeducational Assessment, 25, 216–224. Google Scholar | SAGE Journals | ISI | |
|
Burns, M. K., Parker, D. C. (2014). Curriculum-based assessment for instructional design: Using data to design instruction and intervention. New York, NY: Guilford Press. Google Scholar | |
|
Burns, M. K., Sterling-Turner, H. (2010). Comparison of efficiency measures for academic interventions based on acquisition and maintenance of the skill. Psychology in the Schools, 47, 126–134. Google Scholar | ISI | |
|
Burns, M. K., Ysseldyke, J., Nelson, P., Kanive, R. (2014). Number of repetitions required to retain single-digit multiplication math facts for elementary students. School Psychology Quarterly. Advance online publication. doi:10.1037/spq0000097 Google Scholar | Crossref | Medline | ISI | |
|
Burns, M. K., Zaslofsky, A. F., Kanive, R., Parker, D. C. (2012). Meta-analysis of incremental rehearsal: Using phi coefficients to compare single-case and group designs. Journal of Behavioral Education, 21, 185–202. doi:10.1007/s10864-012-9160-2 Google Scholar | Crossref | |
|
Cates, G. L., Skinner, C. H., Watson, T. S., Meadows, T. J., Weaver, A., Jackson, B. (2003). Instructional effectiveness and instructional efficiency as considerations for data-based decision making: An evaluation of interspersing procedures. School Psychology Review, 32, 601–616. Google Scholar | ISI | |
|
Cepeda, N. J., Pashler, H., Vul, E., Wixted, J. T., Rohrer, D. (2006). Distributed practice in verbal recall tasks: A review and quantitative synthesis. Psychological Bulletin, 132, 354–380. doi:10.1037/0033-2909.132.3.354 Google Scholar | Crossref | Medline | ISI | |
|
Ceraso, J. (1967). The interference theory of forgetting. Scientific American, 217, 117–124. doi:10.1038/scientificamerican1067-117 Google Scholar | Crossref | Medline | ISI | |
|
Codding, R. S., Archer, J., Connell, J. (2010). A systematic replication and extension of using incremental rehearsal to improve multiplication skills: An investigation of generalization. Journal of Behavioral Education, 19, 93–105. doi:10.1007/s10864-010-9102-9 Google Scholar | Crossref | |
|
Codding, R. S., Burns, M. K., Lukito, G. (2011). Meta-analysis of mathematic basic-factfluency interventions: A component analysis. Learning Disabilities Research & Practice, 26, 36–47. Google Scholar | Crossref | ISI | |
|
Cohen, J. (1988). Statistical power analyses for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum. Google Scholar | |
|
Fuchs, L. S., Fuchs, D. (2001). Principles for the prevention and intervention of mathematics difficulties. Learning Disabilities Research & Practice, 16, 85–95. Google Scholar | Crossref | |
|
Fuchs, L. S., Fuchs, D., Powell, S. R., Seethaler, P. M., Cirino, P. T., Fletcher, J. M. (2008). Intensive intervention for students with mathematics disabilities: Seven principles of effective practice. Learning Disability Quarterly, 31, 79–92. Google Scholar | SAGE Journals | ISI | |
|
Geary, D. C., Hoard, M. K., Byrd-Craven, J., Nugent, L., Numtee, C. (2007). Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child Development, 78, 1343–1359. doi:10.1111/j.1467-8624.2007.01069.x Google Scholar | Crossref | Medline | ISI | |
|
Gersten, R., Chard, D. (1999). Number sense rethinking arithmetic instruction for students with mathematical disabilities. The Journal of Special Education, 33, 18–28. doi:10.1177/002246699903300102 Google Scholar | SAGE Journals | ISI | |
|
Gersten, R., Jordan, N. C., Flojo, J. R. (2005). Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities, 38, 293–304. doi:10.1177/00222194050380040301 Google Scholar | SAGE Journals | ISI | |
|
Gravois, T. A., Gickling, E. (2002). Best practices in curriculum-based assessment. In Thomas, A., Grimes, J. (Eds.), Best practices in school psychology IV (pp. 885–898). Bethesda, MD: National Association of School Psychologists. Google Scholar | |
|
Greenwood, C. R., Delquadri, J., Hall, R. V. (1984). Opportunity to respond and student academic performance. In Heward, W., Heron, T., Hill, D., Trap-Porter, J. (Eds.), Focus on behavior analysis in education (pp. 58–88). Columbus, OH: Charles E. Merrill. Google Scholar | |
|
Haegele, K., Burns, M. K. (2015). The effect of modifying instructional set size based on the acquisition rate among students identified with a learning disability. Journal of Behavioral Education, 24, 33–50. Google Scholar | Crossref | ISI | |
|
Hanich, L. B., Jordan, N. C., Kaplan, D., Dick, J. (2001). Performance across different areas of mathematical cognition in children with learning difficulties. Journal of Educational Psychology, 93, 615–626. doi:10.1037//0022-0663.93.3.615 Google Scholar | Crossref | ISI | |
|
Hargis, C. H., Terhaar-Yonkers, M., Williams, P. C., Reed, M. T. (1988). Repetition requirements for word recognition. Journal of Reading, 31, 320–327. Google Scholar | |
|
Howell, D. C. (2002). Statistical methods for psychology (5th ed.). Pacific Grove, CA: Duxbury. Google Scholar | |
|
Hulac, D. M., Dejong, K., Benson, N. (2012). Can students run their own interventions? A self-administered math fluency intervention. Psychology in the Schools, 49, 526–538. Google Scholar | Crossref | ISI | |
|
Kanive, R., Nelson, P., Burns, M. K., Ysseldyke, J. (2014). Comparison of computer-based practice and conceptual understanding interventions on math fact fluency. Journal of Educational Research, 107, 83–89. Google Scholar | Crossref | ISI | |
|
Kilpatrick, J., Swafford, J., Finell, B. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press. Google Scholar | |
|
Logan, G. D., Taylor, S. E., Etherton, J. L. (1996). Attention in the acquisition and expression of automaticity. Journal of Experimental Psychology: Learning, Memory, and Cognition, 22, 620–638. doi:10.1037//0278-7393.22.3.620 Google Scholar | Crossref | ISI | |
|
Minnesota Department of Education . (2013). Summary of Optional Local Purpose Assessment (OLPA) mathematics in grades 3–8. St. Paul, MN: Author. Google Scholar | |
|
National Council of Teachers of Mathematics . (2000). Principles and standards for school mathematics (Vol. 1). Reston, VA: Author. Google Scholar | |
|
National Mathematics Advisory Panel . (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education. Google Scholar | |
|
Patton, J. R., Cronin, M. E., Bassett, D. S., Koppel, A. E. (1997). A life skills approach to mathematics instruction preparing students with learning disabilities for the real-life math demands of adulthood. Journal of Learning Disabilities, 30, 178–187. Google Scholar | SAGE Journals | ISI | |
|
Samuels, S. J. (1987). Information processing abilities and reading. Journal of Learning Disabilities, 20, 18–22. doi:10.1177/002221948702000104 Google Scholar | SAGE Journals | ISI | |
|
Singer-Dudek, J., Greer, R. D. (2005). A long-term analysis of the relationship between fluency and the training and maintenance of complex math skills. The Psychological Record, 55, 361–376. Google Scholar | Crossref | ISI | |
|
Skinner, C. H., Belfiore, P. J., Watson, T. S. (1995). Assessing the relative effects of interventions in students with mild disabilities: Assessing instructional time. Assessments in Rehabilitation and Exceptionality, 20, 207–220. doi:10.1177/073428290202000403 Google Scholar | SAGE Journals | ISI | |
|
Szadokierski, I., Burns, M. K. (2008). Analogue evaluation of the effects of opportunities to respond and ratios of known items within drill rehearsal of Esperanto words. Journal of School Psychology, 46, 593–609. doi:10.1016/j.jsp.2008.06.004 Google Scholar | Crossref | Medline | ISI | |
|
Tucker, J. A. (1988). Basic flashcard technique when vocabulary is the goal. Unpublished teaching materials, School of Education, University of Chattanooga, Chattanooga, TN. Google Scholar | |
|
Winick, D. M., Avallone, A. P., Smith, C. E., Crovo, M., Martin, W., Olson, J., Wilson, L. (2008). Mathematics framework for the 2009 National Assessment of Educational Progress. Washington, DC: U.S. Department of Education, National Assessment Governing Board. Google Scholar | |
|
Woodward, J. (2006). Developing automaticity in multiplication facts: Integrating strategy instruction timed practice drills. Learning Disability Quarterly, 29, 269–289. Google Scholar | SAGE Journals | ISI | |
|
Zheng, X., Flynn, L. J., Swanson, H. L. (2013). Experimental intervention studies on word problem-solving and math disabilities: A selective analysis of the literature. Learning Disability Quarterly, 36, 97–111. Google Scholar | SAGE Journals | ISI |
