Abstract
A randomized controlled trial was used to evaluate the impact of a frequency-building curriculum to increase the fluency of component mathematics skills in a sample of 28 males aged 9–11 years. Assessments of mathematical ability were conducted before and after the training period to evaluate the impact of learning component skills fluently on endurance, stability and application of mathematical skills. Statistically significant differences between the experimental training group and treatment-as-usual control group were found on measures of fluency, endurance, stability and one subtest of the Wechsler Individual Achievement test of mathematical ability. Results indicate the efficacy of the frequency-building curriculum in promoting fluency with component skills. Results are discussed in light of research and theory in the area of instructional design and behavioral fluency enhancement.
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Billington, E. J., Skinner, C. H., & Cruchon, N. M. (2004). Improving sixth-grade students’ perceptions of high-effort assignments by assigning more work: Interaction of additive interspersal and assignment effort on assignment choice. Journal of School Psychology, 42(6), 477–490. doi:10.1016/j.jsp.2004.08.003.
Binder, C. (1996). Behavioral fluency: Evolution of a new paradigm. The Behavior Analyst, 19(2), 163.
Binder, C., Haughton, E., & Van Eyk, D. (1990). Precision teaching attention span. Teaching Exceptional Children, 22(3), 24–27.
Bliss, S. L., Skinner, C. H., McCallum, E., Saecker, L. B., Rowland-Bryant, E., & Brown, K. S. (2010). A comparison of taped problems with and without a brief post-treatment assessment on multiplication fluency. Journal of Behavioral Education, 19(2), 156–168. doi:10.1007/s10864-010-9106-5.
Brady, K. K., & Kubina, R. M. (2010). Endurance of multiplication fact fluency for students with attention deficit hyperactivity disorder. Behavior Modification, 34(2), 79–93. doi:10.1177/0145445510361331.
Bucklin, B. R., Dickinson, A. M., & Brethower, D. M. (2000). A comparison of the effects of fluency training and accuracy training on application and retention. Performance Improvement Quarterly, 13, 140–163. doi:10.1111/j.1937-8327.2000.tb00180.x.
Carr, M., & Alexeev, N. (2011). Fluency, accuracy, and gender predict developmental trajectories of arithmetic strategies. Journal of Educational Psychology, 103(3), 617. doi:10.1037/a0023864.
Carr, M., Steiner, H. H., Kyser, B., & Biddlecomb, B. (2008). A comparison of predictors of early emerging gender differences in mathematics competency. Learning and Individual Differences, 18(1), 61–75. doi:10.1016/j.lindif.2007.04.005.
Cavallini, F., & Perini, S. (2009). Comparison of teaching syllables or words on reading rate. European Journal of Behavior Analysis, 10, 225–263.
Chafouleas, S. M., Sanetti, L. M., Kilgus, S. P., & Maggin, D. M. (2012). Evaluating sensitivity to behavioral change using direct behavior rating single-item scales. Exceptional Children, 78(4), 491–505.
Chiesa, M., & Robertson, A. (2000). Precision teaching and fluency training: Making maths easier for pupils and teachers. Educational Psychology in Practice, 16(3), 297–310. doi:10.1080/713666088.
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(1), 93–105. doi:10.1007/s10864-010-9102-9.
Codding, R. S., Hilt-Panahon, A., Panahon, C. J., & Benson, J. L. (2009). Addressing mathematics computation problems: A review of simple and moderate intensity interventions. Education and Treatment of Children, 32(2), 279–312.
Cohen, J. D., Servan-Schreiber, D., & McClelland, J. C. (1992). A parallel distributed processing approach to automaticity. American Journal of Psychology, 2, 239–269.
Department of Education and Science (2000). Learning-support Guidelines. Retrieved from http://www.sess.ie/sites/default/files/Learning%20Support%20Guidelines.pdf.
Fabrizio, M. A., & Moors, A. L. (2003). Evaluating mastery: Measuring instructional outcomes for children with autism. European Journal of Behavior Analysis, 4(1/2), 23–36.
Geary, D. C., Hoard, M. K., Nugent, L., & Bailey, D. H. (2012). Mathematical cognition deficits in children with learning disabilities and persistent low achievement: A five-year prospective study. Journal of Educational Psychology, 104(1), 206. doi:10.1037/a0025398.
Gross, T. J., Duhon, G. J., Hansen, B., Rowland, J. E., Schutte, G., & Williams, J. (2013). The effect of goal-line presentation and goal selection on first-grader subtraction fluency. The Journal of Experimental Education, 81, 1–17. doi:10.1080/00220973.2013.813369.
Haring, N. G., & Eaton, M. D. (1978). Systematic instructional procedures: An instructional hierarchy. In N. G. Haring, T. C. Lovitt, M. D. Eaton, & C. L. Hansen (Eds.), The fourth R: Research in the classroom (pp. 23–40). Columbus: Charles E. Merrill Publishing Co.
Hartnedy, S. L., Mozzoni, M. P., & Fahoum, Y. (2005). The effect of fluency training on math and reading skills in neuropsychiatric diagnosis children: A multiple baseline design. Behavioral Interventions, 20(1), 27–36. doi:10.1002/bin.167.
Haughton, E. C. (1980). Practicing practices: Learning by activity. Journal of Precision Teaching, 1(3), 3–20.
Johnson, K. (2008). Morningside mathematics fluency: Math facts (Vols. 1–6; curriculum program). Seattle, WA: Morningside Press.
Johnson, K., & Layng, T. J. (1992). Breaking the structuralist barrier: Literacy and numeracy with fluency. American Psychologist, 47(11), 1475. doi:10.1037/0003-066X.47.11.1475.
Johnson, K., & Layng, T. J. (1994). The morningside model of generative instruction. In R. Gardner, D. Sainato, J. Cooper, T. Heron, W. Heward, J. Eshleman, & T. Grossi (Eds.), Behavior analysis in education: Focus on measurably superior instruction (pp. 173–197). Belmont, CA: Brooks/Cole.
Johnson, K., & Street, E. M. (2013). Response to intervention and precision teaching. NewYork: The Guilford Press.
Kubina, R. M., Young, A., & Kilwein, M. (2004). Examining an effect of fluency: Application of letter sound writing and oral word segmentation to spelling words. Learning Disabilities, 13, 17–23.
Kubina, R. M., & Yurich, K. K. L. (2012). The precision teaching book. Lemont, PA: Greatness Achieved Publishing Company.
Lin, F. Y., & Kubina, R. M, Jr. (2005). A preliminary investigation of the relationship between fluency and application for multiplication. Journal of Behavioral Education, 14(2), 73–87. doi:10.1007/s10864-005-2703-z.
Lipsey, M. W., & Hurley, S. M. (2009). Design sensitivity: Statistical power for applied experimental research. In L. Bickman & D. J. Rog (Eds.), The sage handbook of applied social research methods (pp. 44–76). Thousand Oaks: SAGE publications, Inc.
Logan, P., & Skinner, C. H. (1998). Improving students’ perceptions of a mathematics assignment by increasing problem completion rates: Is problem completion a reinforcing event? School Psychology Quarterly, 13(4), 322. doi:10.1037/h0088988.
Martens, B. K., & Witt, J. C. (2004). Competence, persistence, and success: The positive psychology of behavioral skill instruction. Psychology in the Schools, 41(1), 19–30. doi:10.1002/pits.10135.
McDowell, C., & Keenan, M. (2001). Developing fluency and endurance in a child diagnosed with attention deficit hyperactivity disorder. Journal of Applied Behavior Analysis, 34(3), 345–348. doi:10.1901/jaba.2001.34-345.
Organisation for Economic Co-operation and Development (2010). Programme for International Student Assessment 2009: What students know and can do—Student performance in reading, mathematics and science.
Organisation for Economic Co-operation and Development (2014). Programme for International Student Assessment 2012: Results in Focus: What 15 year-olds know and what they can do with what they know.
Poncy, B. C., Duhon, G. J., Lee, S. B., & Key, A. (2010). Evaluation of techniques to promote generalization with basic math fact skills. Journal of Behavioral Education, 19(1), 76–92. doi:10.1007/s10864-010-9101-x.
Poncy, B. C., Fontenelle, S. F, I. V., & Skinner, C. H. (2013). Using detect, practice, and repair (DPR) to differentiate and individualize math fact instruction in a class wide setting. Journal of Behavioral Education, 22(3), 211–228. doi:10.1007/s10864-013-9171-7.
Shapiro, E. S. (2004). Academic Skills Problems work-book (rev.). New York: Guilford Press.
Skinner, C. H. (2002). An empirical analysis of interspersal research: Evidence, implications, and applications of the discrete task completion hypothesis. Journal of School Psychology, 40(4), 347–368. doi:10.1016/s0022-4405(02)00101-2.
Skinner, C. H., Pappas, D. N., & Davis, K. A. (2005). Enhancing academic engagement: Providing opportunities for responding and influencing students to choose to respond. Psychology in the Schools, 42(4), 389–403. doi:10.1002/pits.20065.
Wechsler, D. (2005). The Wechsler individual achievement test (2nd ed.). London: Harcourt Assessment.
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Appendix
Appendix
Yes | No | |
---|---|---|
1. It is important to learn your math well | ||
2. I enjoyed practicing my math | ||
3. I learned my math well | ||
4. I liked trying to get my goal | ||
5. I am faster with addition and subtraction now | ||
6. I enjoyed working really fast and trying to beat the timer | ||
7. Getting faster with addition and subtraction has helped me with my math in class | ||
8. Getting my goals made me happy/feel confident | ||
9. It’s important to know addition and subtraction off by heart—it helps me answer my math better |
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McTiernan, A., Holloway, J., Healy, O. et al. A Randomized Controlled Trial of the Morningside Math Facts Curriculum on Fluency, Stability, Endurance and Application Outcomes. J Behav Educ 25, 49–68 (2016). https://doi.org/10.1007/s10864-015-9227-y
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DOI: https://doi.org/10.1007/s10864-015-9227-y