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Journal of Behavioral Education

, Volume 17, Issue 3, pp 278–302 | Cite as

An Evaluation of Interventions to Facilitate Algebra Problem Solving

  • Kristin H. Mayfield
  • Irene M. Glenn
Original Paper

Abstract

Three participants were trained on 6 target algebra skills and subsequently received a series of 5 instructional interventions (cumulative practice, tiered feedback, feedback plus solution sequence instruction, review practice, and transfer training) in a multiple baseline across skills design. The effects of the interventions on the performance of 5 problem-solving tasks that required novel combinations of 2 or more of the target skills were evaluated. Results showed that cumulative practice of the skills and a combination of feedback with solution sequence instruction led to limited performance increases on some of the problem-solving tasks, with one task meeting the mastery criterion following the solution sequence intervention. The introduction of the transfer training resulted in more consistent improvements across tasks such that participants achieved the performance criterion on all remaining problem-solving tasks during a final baseline condition. The findings suggest that a structured intervention designed to transfer stimulus control from previously established discriminative stimuli to more complex, novel stimuli can facilitate problem solving without extensive direct instruction on the higher-level skills.

Keywords

Algebra Mathematics Novel behavior Problem solving Transfer 

References

  1. Atkinson, R. K., Renkl, A., & Merrill, M. M. (2003). Transitioning from studying examples to solving problems: Effects of self-explanation prompts and fading worked-out steps. Journal of Educational Psychology, 95(4), 774–783. doi: 10.1037/0022-0663.95.4.774.CrossRefGoogle Scholar
  2. Becker, W. C., Engelmann, S., & Thomas, D. R. (1975). Teaching 2: Cognitive learning and instruction. Chicago, IL: Science Research Associates.Google Scholar
  3. Chafouleas, S. M., Martens, B. K., Dobson, R. L., Weinstein, K. S., & Gardner, K. B. (2004). Fluent reading as the improvement of stimulus control: Additive effects of performance-based interventions to repeated readings on students’ reading and error rates. Journal of Behavioral Education, 13(2), 67–81. doi: 10.1023/B:JOBE.0000023656.45233.6f.CrossRefGoogle Scholar
  4. Fuchs, L. S., Fuchs, D., Prentice, K., Burch, M., Hamlett, C. L., Owen, R., et al. (2003). Explicitly teaching for transfer: Effects on third-grade students’ mathematical problem solving. Journal of Educational Psychology, 95(2), 293–304. doi: 10.1037/0022-0663.95.2.293.CrossRefGoogle Scholar
  5. Fuchs, L. S., Fuchs, D., & Tindal, G. (1986). Effects of mastery learning procedures on student achievement. The Journal of Educational Research, 79(5), 286–291.Google Scholar
  6. Grossen, B., & Ewing, S. (1994, Spring). Raising mathematics problem-solving performance: Do the NCTM teaching standards help? (Final report). Effective School Practices, 78–91.Google Scholar
  7. Heubusch, J. D., & Lloyd, J. W. (1998). Corrective feedback in oral reading. Journal of Behavioral Education, 8(1), 63–79. doi: 10.1023/A:1022864707734.CrossRefGoogle Scholar
  8. Hutchinson, N. L. (1993). Effects of cognitive strategy instruction on algebra problem solving of adolescents with learning disabilities. Learning Disability Quarterly, 16, 34–63. doi: 10.2307/1511158.CrossRefGoogle Scholar
  9. Jitendra, A., DiPipi, C. M., & Perron-Jones, N. (2002). An exploratory study of schema-based word problem-solving instruction for middle school students with learning disabilities: An emphasis on conceptual and procedural understanding. The Journal of Special Education, 36(1), 23–38.CrossRefGoogle Scholar
  10. Maccini, P., & Ruhl, K. L. (2000). Effects of a graduated instructional sequence on the algebraic subtraction of integers by secondary students with learning disabilities. Education & Treatment of Children, 23(4), 465–489.Google Scholar
  11. Mayfield, K. H., & Chase, P. N. (2002). The effect of cumulative practice on mathematics problem solving. Journal of Applied Behavior Analysis, 35, 105–123. doi: 10.1901/jaba.2002.35-105.PubMedCrossRefGoogle Scholar
  12. Neef, N. A., Nelles, D. E., Iwata, B. A., & Page, T. J. (2003). Analysis of precurrent skills in solving mathematics story problems. Journal of Applied Behavior Analysis, 36, 21–33. doi: 10.1901/jaba.2003.36-21.PubMedCrossRefGoogle Scholar
  13. Noell, G. H., Gansle, K. A., Witt, J. C., Whitmarsh, E. L., Freeland, J. T., LaFleur, L. H., et al. (1998). Effects of contingent reward and instructions on oral reading performance at differing levels of passage difficulty. Journal of Applied Behavior Analysis, 31, 659–663. doi: 10.1901/jaba.1998.31-659.PubMedCrossRefGoogle Scholar
  14. Paine, S. C., Carnine, D. W., White, W. A. T., & Walters, G. (1982). Effects of fading teacher presentation structure (covertization) on acquisition and maintenance of arithmetic problem-solving skills. Education & Treatment of Children, 5(2), 93–107.Google Scholar
  15. Renkl, A., Atkinson, R. K., Maier, U. H., & Staley, R. (2002). From example study to problem solving: Smooth transitions help learning. Journal of Experimental Education, 70(4), 293–315.CrossRefGoogle Scholar
  16. Rosenshine, B. (1983). Teaching functions in instructional programs. Elementary School Journal, 83(4), 335–351. doi: 10.1086/461321.CrossRefGoogle Scholar
  17. Rosenshine, B., & Stevens, R. (1986). Teaching functions. In M. C. Wittrock (Ed.), Handbook of research on teaching (3rd ed., pp. 376–391). New York: Macmillan.Google Scholar
  18. Skinner, B. F. (1984). An operant analysis of problem solving. The Behavioral and Brain Sciences, 7(4), 583–613.CrossRefGoogle Scholar
  19. Smeets, P. M., Lancioni, G. E., Striefel, S., & Willemsen, R. J. (1984). Training EMR children to solve missing minuend problems errorlessly: Acquisition, generalization, and maintenance. Analysis and Intervention in Developmental Disabilities, 4, 379–402. doi: 10.1016/0270-4684(84)90026-0.CrossRefGoogle Scholar
  20. Wood, D. K., Frank, A. R., & Wacker, D. P. (1998). Teaching multiplication facts to students with learning disabilities. Journal of Applied Behavior Analysis, 31, 323–338. doi: 10.1901/jaba.1998.31-323.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of PsychologyUniversity of FloridaGainesvilleUSA
  2. 2.The University of VirginiaCharlottesvilleUSA
  3. 3.GainesvilleUSA

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