Journal of Behavioral Education

, Volume 14, Issue 2, pp 73–87 | Cite as

A Preliminary Investigation of the Relationship Between Fluency and Application for Multiplication

  • Fan-Yu Lin
  • Richard M. KubinaJr.


Research suggests component skill performance has a strong positive relationship with composite skill performance. This study examined the association between accuracy and fluency for the component-composite relationship within multiplication. One hundred and fifty-seven fifth-graders did one-minute assessments for single-digit, and multi-digit multiplication problems. The results demonstrated the students achieved high levels of accuracy but low levels of fluency. Strong correlations between the component-composite skill fluency suggest that fluent component skills may have a significant role in composite skill performance. Moderate/low correlations between component and composite skill accuracy indicate that more than one skill component may contribute to composite skill acquisition.


fluency application component and composite performance 


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  1. Barrett, B. (1979). Communitization and the measured message of normal behavior. In R. York & E. Edgar (Eds.), Teaching the Severely Handicapped (Vol. 4, pp. 301–318). Columbus, OH: Special Press.Google Scholar
  2. Berens, K., Boyce, T. E., Berens, N. M., Doney, J. K., & Kenzer, A. L. (2003). A technology for evaluation relations between response frequency and academic performance outcomes. Journal of Precision teaching and Celeration, 19(1), 20–34.Google Scholar
  3. Carnine, C. W., Silbert, J., Kameenui, E. J., & Tarver, S. G. (2004). Direct instruction reading (4th ed.). Upper Saddle River, NJ: Prentice Hall/Merrill.Google Scholar
  4. Binder, C. (1996). Behavioral fluency: Evolution of a new paradigm. The Behavior Analyst, 19, 163–197.Google Scholar
  5. 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(3), 140–163.Google Scholar
  6. Carnine, D. (1980). Preteaching versus concurrent teaching of the component skills of a multiplication algorithm. Journal for Research in Mathematics Education, 11, 375–378.Google Scholar
  7. Christenson, S. L., Ysseldyke, J. E., & Thurlow, M. L. (1989). Critical instructional factors for students with mild handicaps: An integrative review. Remedial and Special Education, 10(5), 21–31.Google Scholar
  8. Eaton, M. D. (1978). Data decisions and evaluation. In N. G. Haring, T. C. Lovitt, M. D. Eaton, & C. L. Hansen (Eds.), The forth R: Research in the classroom (pp. 167–190). Columbus, Oh: Merrill.Google Scholar
  9. Evans, S. S., & Evans, W. H. (1985). Frequencies that ensure skill competency. Journal of Precision Teaching, 6(2), 25–30.Google Scholar
  10. Evans, S. S., Mercer, C. D., & Evans, W. H. (1983). The relationship of frequency to subsequent skill acquisition. Journal of Precision Teaching, 4(2), 28–34.Google Scholar
  11. Hanushek, E. A., & Kimko, D. (2000). Schooling, labor-force quality, and the growth of nations. American Economic Review, 90(5), 1184–1208.Google Scholar
  12. Haughton, E. C. (1980). Practicing practices: Learning by activity. Journal of Precision Teaching, 1(3), 3–20.Google Scholar
  13. Johnson, K. R. (1996). Morningside mathematics fluency: Math facts (3rd ed.). Seattle, WA: Morningside Press.Google Scholar
  14. Johnson, K. R., & Layng, T. J. (1992). Breaking the structuralist barrier: Literacy and numeracy with fluency. American Psychologist, 47(11), 1475–1490.Google Scholar
  15. Johnson, K. R., & Layng, T. V. 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.Google Scholar
  16. Kamii, C., & Joseph, L. (1988). Teaching place value and double-column addition. Arithmetic Teacher, 35(6), 48–52.Google Scholar
  17. Koorland, M. A., Keel, M. C., & Ueberhorst, P. (1990). Setting aims for precision learning. Teaching Exceptional Children, 22(3), 64–66.Google Scholar
  18. Kubina, R. M., Young, A. E., & Kilwein, M. (2004). Examining an effect of fluency: Application of oral word segmentation and letters sounds for spelling. Learning Disabilities: A Multidisciplinary Journal, 13(1), 17–23.Google Scholar
  19. Kubina, R. M., & Lin, F. (2003). [College student performance in multi-digit multiplication]. Unpublished raw data.Google Scholar
  20. Kubina, R. M., & Morrison, R. (2000). Fluency education. Behavior and Social Issues, 10, 83–99.Google Scholar
  21. Lorenz, J, H. (1982). On some psychological aspects of mathematics achievement assessment and classroom interaction. Educational Studies in Mathematics, 13(1), 1–19.Google Scholar
  22. Lovitt, T. C. (1978). Arithmetic. In N. G. Haring, T. C. Lovitt, M. D. Eaton, & C. L. Hansen (Eds.), The forth R: Research in the classroom (pp. 127–166). Columbus, Oh: Merrill.Google Scholar
  23. McDowell, C., & Keenan, M. (2001). Cumulative dysfluency: Still evident in our classrooms, despite what we know. Journal of Precision Teaching and Celeration, 17(2), 1–6.Google Scholar
  24. McDowell, C., & Keenan, M. (2002). Comparison of two teaching structures examining the effects of component fluency on the performance of related skills. Journal of Precision Teaching and Celeration, 18(2), 16–29.Google Scholar
  25. McDowell, C., Keenan, M., & Kerr, K. P. (2002). Comparing levels of dysfluency among students with mild learning difficulties and typical students. Journal of Precision Teaching and Celeration, 18(2), 37–48.Google Scholar
  26. McDowell, C., McIntyre, C., Bones, R., & Keenan, M. (2002). Teaching component skills to improve golf swing. Journal of Precision Teaching and Celeration, 18(2), 61–66.Google Scholar
  27. Mercer, C. D., Campbell, K. U., Miller, M. D., Mercer, K. D., & Lane, H. B. (2000). Reading fluency intervention for middle schools with specific learning disabilities. Learning Disabilities: Research & Practice, 15(4), 179–189.Google Scholar
  28. Mercer, C. D., & Mercer, A. R. (2001). Teaching students with learning problems (6th ed.). Upper Saddle River, NJ: Prentice Hall/Merrill.Google Scholar
  29. Mercer, C. D., Mercer, A. R., & Evans, S. (1982). The use of frequency in establishing instructional aims. Journal of Precision Teaching, 3(3), 57–63.Google Scholar
  30. McIntyre, S. B., Test, D. W., Cooke, N. L., & Beattie, J. (1991). Using count-bys to increase multiplication facts fluency. Learning Disability Quarterly, 14(2), 82–88.Google Scholar
  31. National Center for Education Statistics (2000). National Assessment of Educational Progress (NAEP) Mathematics 2000 major reports. Retrieved January 29, 2003, from
  32. New York City Board of Education (2000a). Impact of teacher certification on reading and mathematics performance in elementary and middle schools in New York City. Flash research report &2. (ERIC Document Reproduction Service No. ED451315).Google Scholar
  33. New York City Board of Education (2000b). Analyses of performance of extended-time and non-extended time SURR school. Flash research report &1. (ERIC Document Reproduction Service No. ED451314).Google Scholar
  34. Pennsylvania Department of Education (2004). Data file documentation: Pennsylvania system of school assessment–school and district report cards. Retrieved March 30, 2004, from
  35. Rhymer, K. N., Skinner, C. H., Henington, C., D’Reaux, R. A., & Sims S. (1998). Effects of explicit timing on mathematics problem completion rates in African-American third-grade elementary students. Journal of Applied Behavior Analysis, 31(4), 673–677.Google Scholar
  36. Rosenshine, B., & Stevens, R. (1986). Teaching functions. In M. C. Wittrock, (Ed.) The handbook of research on teaching (pp. 376–391). New York: Macmillan.Google Scholar
  37. Shapiro, E. S. (1996). Academic skills problems: Direct assessment and intervention (2nd ed.). New York: Guilford.Google Scholar
  38. Smith, D. D. (1981). Teaching the learning disabled. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
  39. Smyth, P., & Keenan, M. (2002). Compound performance: The role of free and controlled operant components. Journal of Precision Teaching and Celeration, 18(2), 3–15.Google Scholar
  40. Stein, M., Silbert, J., & Carnine, D. (1997). Designing effect mathematics instruction: A direct instruction approach (3rd ed.). Upper Saddle River, NJ: Prentice-Hall.Google Scholar
  41. Trends in International Mathematics and Science Study (TIMSS) (1999). TIMSS 1999 International Mathematics Report. Retrieved February 10, 2003 from
  42. US Department of Education (2003). No child left behind. Retrieved May 16, 2003, from
  43. Van de Walle, J. A. (1990). Elementary school mathematics: Teaching developmentally. White Plains, NY: Longman.Google Scholar
  44. Van Houten, R., & Thompson, C. (1976). The effects of explicit timing on math performance. Journal of Applied Behavior Analysis, 9, 227–230.Google Scholar
  45. Wood, S., Burke, L., Kunzelmann, H., & Koenig, C. (1978). Functional criteria in basic math skill proficiency. Journal of Special Education Technology, 2(2), 29–36.Google Scholar
  46. Wu, H. (1999). Basic skills versus conceptual understanding: A bogus dichotomy in mathematics education. American Educator, 23(3), 14–19, 50–52.Google Scholar
  47. Zhang, Y., & Zhang, L. (2002). Modeling school and district effects in the math achievement of Delaware students measured by DSTP: A preliminary application of hierarchal linear modeling in accountability study. (ERIC Document Reproduction Service No. ED468962).Google Scholar
  48. Zaner-Bloser . (1999). Handwriting with continuous-stroke alphabet. Columbus, OH: Zaner-Bloser.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Special Education at California State UniversityStanislaus
  2. 2.The Pennsylvania State University, University Park
  3. 3.Department of Educational and School Psychology and Special EducationThe Pennsylvania State University

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