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The Role of Tier I Mathematics Instruction in Elementary and Middle Schools: Promoting Mathematics Success

  • Asha K. JitendraEmail author
  • Danielle N. Dupuis
Chapter

Abstract

The purpose of this chapter is to describe effective mathematics instructional programs delivered in general education settings by elementary classroom and middle school mathematics teachers. Following a discussion of critical mathematical concepts and skills and the role of instructional practices in enhancing learning for all students and in preventing mathematics difficulties before they become intractable, instructional design features that promote the mathematical development of struggling students are highlighted. This chapter also describes the nature and results of specific mathematics instructional programs in elementary and middle schools to understand the instructional conditions that need to be in place to promote mathematics success. Finally, study limitations and recommendations for future research are discussed.

Keywords

Minority Student Mathematics Achievement English Language Learner Instructional Program Special Education Service 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Baker, S., Gersten, R., & Lee, D. (2002). A synthesis of empirical research on teaching mathematics to low-achieving students. The Elementary School Journal, 103, 51–73.CrossRefGoogle Scholar
  2. Bryant, B., Bryant, D. P., Kethley, C., Kim, S. A., Pool, C., & You-Jin, S. (2008). Preventing mathematics difficulties in the primary grades: The critical features of instruction in textbooks as part of the equation. Learning Disabilities Quarterly, 31, 21–35.Google Scholar
  3. Chard, D. J., Baker, S. K., Clarke, B., Jungjohann, K., Davis, K., & Smolkowski, K. (2008). Preventing early mathematics difficulties: The feasibility of a rigorous kindergarten mathematics curriculum. Learning Disability Quarterly, 31, 11–20.Google Scholar
  4. Clarke, B., Baker, S. K., & Chard, D. (2008). Best practices in mathematics assessment and intervention with elementary students. In A. Thomas & J. Grimes (Eds.), Best practices in school psychology (Vol. 5, pp. 453–464). Bethesda: National Association of School Psychologists.Google Scholar
  5. Clarke, B., Gersten, R., & Newman-Gonchar, R. (2010). RTI in mathematics: Beginnings of a knowledge base. In T. A. Glover & S. Vaughn (Eds.), The promise of response to intervention: Evaluating current science and practice (pp. 187–202). New York: Guilford.Google Scholar
  6. Clarke, B., Smolkowski, K., Baker, S. K., Hank, F., Doabler, C. T., & Chard, D. J. (2011). The impact of a comprehensive tier I core kindergarten program on the achievement of students at risk in mathematics. The Elementary School Journal, 111, 561–584.CrossRefGoogle Scholar
  7. Clarke, B., Doabler, C. T., Smolkowski, K., Baker, S. K., & Fien, H. (2013, February). Evaluating the value of a tier 2 intervention in kindergarten mathematics. Paper presented at the Pacific Coast Research Conference. San Diego, CA.Google Scholar
  8. Codding, R. S., Chan-Iannetta, L., George, S., Ferreira, K., & Volpe, R. (2011). Early number skills: Examining the effects of class-wide interventions on kindergarten performance. School Psychology Quarterly, 26, 85–96.CrossRefGoogle Scholar
  9. Crawford, L., & Ketterlin-Geller, L. R. (2008). Improving math programming for students at risk: Introduction to the special topic issue. Remedial and Special Education, 29, 5–8.CrossRefGoogle Scholar
  10. Doabler, C. T., Fien, H., Nelson-Walker, N. J., & Baker, S. K. (2012). Evaluating three elementary mathematics programs for presence of eight research-based instructional design principles. Learning Disability Quarterly, 35, 200–211.CrossRefGoogle Scholar
  11. Flynn, L. J., Zheng, X., & Swanson, H. L. (2012). Instructing struggling older readers: A selective meta-analysis of intervention research. Learning Disabilities Research & Practice, 27, 21–32.CrossRefGoogle Scholar
  12. Fuchs, L. S., Fuchs, D., Phillips, N. B., Hamlett, C. L., & Karns, K. (1995). Acquisition and transfer effects of classwide peer-assisted learning strategies in mathematics for students with varying learning histories. School Psychology Review, 24, 604–20.Google Scholar
  13. Fuchs, L. S., Fuchs, D., & Karns, K. (2001). Enhancing kindergartners’ mathematical development: Effects of peer-assisted learning strategies. The Elementary School Journal, 101, 495–510.CrossRefGoogle Scholar
  14. Fuchs, L. S., Fuchs, D., Yazdian, L., & Powell, S. R. (2002). Enhancing first-grade children’s mathematical development with peer-assisted learning strategies. School Psychology Review, 31, 569–583.Google Scholar
  15. Fuchs, L. S., Fuchs, D., Prentice, K., Burch, M., Hamlett, C. L., Owen, R., & Jancek, D. (2003a). Explicitly teaching for transfer: Effects on third-grade students’ mathematical problem solving. Journal of Educational Psychology, 95, 293–305.CrossRefGoogle Scholar
  16. Fuchs, L. S., Fuchs, D., Prentice, K., Burch, M., Hamlett, C. L., Owen, R., & Schroeter, K. (2003b). Enhancing third-grade students’ mathematical problem solving with self-regulated learning strategies. Journal of Educational Psychology, 95, 306–315.CrossRefGoogle Scholar
  17. Fuchs, L. S., Fuchs, D., Finelli, R., Courey, S. J., & Hamlett, C. L. (2004a). Expanding schema-based transfer instruction to help third graders solve real-life mathematical problems. American Educational Research Journal, 41, 419–445.CrossRefGoogle Scholar
  18. Fuchs, L. S., Fuchs, D., Prentice, K., Hamlett, C. L., Finelli, R., & Courey, S. J. (2004b). Enhancing mathematical problem solving among third-grade students with schema-based instruction. Journal of Educational Psychology, 96, 635–647.CrossRefGoogle Scholar
  19. Fuchs, L. S., Fuchs, D., Craddock, C., Schatschneider, C., Hollenbeck, K. N., & Hamlett, C. L. (2008). Effects of small-group tutoring with and without validated classroom instruction on at-risk students’ math problem solving: Are two tiers of prevention better than one? Journal of Educational Psychology, 100, 491–509.PubMedCentralCrossRefPubMedGoogle Scholar
  20. Fuchs, L., Powell, S., Seethaler, P., Cirino, P., Fletcher, J., Fuchs, D., & Zumeta, R. (2009). Remediating number combination and word problem deficits among students with mathematics difficulties: A randomized control trial. Journal of Educational Psychology, 101, 561–576.PubMedCentralCrossRefPubMedGoogle Scholar
  21. Fuchs, L. S., Zumeta, R. O., Schumacher, R. F., Powell, S. R., Seethaler, P. M., Hamlett, C. L, & Fuchs, D. (2010). The effects of schema-broadening instruction on second graders’ word-problem performance and their ability to represent word problems with algebraic equations: A randomized control study. The Elementary School Journal, 110, 440–463.CrossRefGoogle Scholar
  22. Gersten, R., Beckmann, S., Clarke, B., Foegen, A., Marsh, L., Star, J. R., & Witzel, B. (2009a). Assisting students struggling with mathematics: Response to intervention (RTI) for elementary and middle schools (NCEE 2009–4060). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. http://ies.ed.gov/ncee/wwc/publications/practiceguides/.
  23. Gersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morphy, P., & Flojo, J. (2009b). Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79, 1202–1242.CrossRefGoogle Scholar
  24. Gick, M. L., & Holyoak, K. J. (1983). Schema induction and analogical transfer. Cognitive Pyschology, 15, 1–38.CrossRefGoogle Scholar
  25. Griffin, S. A., Case, R., & Siegler, R. S. (1994). Rightstart: Providing the central conceptual prerequisites for first formal learning of arithmetic to students at risk for school failure. In K. McGilly (Ed.), Classroom lessons: Integrating cognitive theory and classroom practice (pp. 25–50). Cambridge: MIT Press.Google Scholar
  26. Jayanthi, M., & Gersten, R. (2011). Effective instructional practices in mathematics for tier 2 and tier 3 instruction. In R. Gersten & R. Newman-Gonchar (Eds.), Understanding RTI in mathematics: Proven methods and applications (pp. 109–125). Baltimore: Paul H. Brookes. (Copyright by Paul H. Brookes).Google Scholar
  27. Jitendra, A. K., & Star, J. R. (2012). An exploratory study contrasting high- and low-achieving students’ percent word problem solving. Learning and Individual Differences, 22, 151–158.CrossRefGoogle Scholar
  28. Jitendra, A. K., Griffin, C. C., Haria, P., Leh, J., Adams, A., & Kaduvettoor, A. (2007). A comparison of single and multiple strategy instruction on third-grade students’ mathematical problem solving. Journal of Educational Psychology, 99, 115–127.CrossRefGoogle Scholar
  29. Jitendra, A. K., Star, J. R., Starosta, K., Leh, J. M., Sood, S., Caskie, G., & Mack, T. R. (2009). Improving seventh grade students’ learning of ratio and proportion: The role of schema-based instruction. Contemporary Educational Psychology, 34, 250–264.CrossRefGoogle Scholar
  30. Jitendra, A. K., Star, J. R., Rodriguez, M., Lindell, M., & Someki, F. (2011). Improving students’ proportional thinking using schema-based instruction. Learning and Instruction, 21, 731–745.CrossRefGoogle Scholar
  31. Jitendra, A. K., Dupuis, D. N., Rodriguez, M., Zaslofsky, A. F., Slater, S., Corroy, K. C., & Church, C. (2013a). A randomized controlled trial of the impact of schema-based instruction on mathematical outcomes for third grade students with mathematics difficulties. The Elementary School Journal, 114, 252–276.CrossRefGoogle Scholar
  32. Jitendra, A. K., Rodriguez, M., Kanive, R. G., Huang, J. P., Church, C., Corroy, K. C., & Zaslofsky, A. F. (2013b). The impact of small-group tutoring interventions on the mathematical problem solving and achievement of third grade students with mathematics difficulties. Learning Disability Quarterly, 36, 21–35.CrossRefGoogle Scholar
  33. Kroesbergen, E. H., & Van Luit, J. H. (2003). Mathematics interventions for children with special educational needs: A meta-analysis. Remedial and Special Education, 24, 97–114.CrossRefGoogle Scholar
  34. Milgram, R. J., & Wu, H. S. (2005). The key topics in a successful math curriculum. http://math.berkeley.edu/wu/.
  35. National Center on Response to Intervention. (n.d.). RtI practices glossary. www.rti4success.org/index.php?option=com_content&task=view&id=634&Itemid=2.
  36. National Council of Teachers of Mathematics. (2006). Curriculum focal points for prekindergarten through grade 8 mathematics: A quest for coherence. http://www.nctm.org/standards/focalpoints.aspx?id_282.
  37. National Governors Association Center for Best Practices, Council of Chief State School Officers (2010). Common core state standards. Washington, DC: National Governors Association Center for Best Practices, Council of Chief State School Officers.Google Scholar
  38. 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
  39. Parker, M., & Leinhardt, G. (1995). Percent: A privileged proportion. Review of Educational Research, 65, 421–481.CrossRefGoogle Scholar
  40. Schmidt, W. H., & Houang, R. T. (2007). Lack of focus in the mathematics curriculum: Symptom or cause? In T. Loveless (Ed.), Lessons learned: What international assessments tell us about math achievement (pp. 65–44). Washington, DC: Brookings Institution Press.Google Scholar
  41. Schumacher, R. F., & Fuchs, L. S. (2012). Does understanding relational terminology mediate effects of intervention on compare word problems? Journal of Experimental Child Psychology, 111, 607–628.PubMedCentralCrossRefPubMedGoogle Scholar
  42. Sood, S., & Jitendra, A. K. (2007). A comparative analysis of number sense instruction in reform-based and traditional mathematics textbooks. Journal of Special Education, 41, 145–157.CrossRefGoogle Scholar
  43. Swanson, H., & Hoskyn, M. (1998). Experimental intervention research on students with learning disabilities: A meta-analysis of treatment outcomes. Review of Educational Research, 68, 277–321.CrossRefGoogle Scholar
  44. VanDerHeyden, A. M., Witt, J. C., & Gilbertson, D. (2007). A multi-year evaluation of the effects of a response to intervention (RTI) model on identification of children for special education. Journal of School Psychology, 45, 225–256.CrossRefGoogle Scholar
  45. VanDerHeyden, A. M., McLaughlin, T., Algina, J., & Synder, P. (2012). Randomized evaluation of a supplememtal grade-wide mathematics intervention. American Educational Research Journal, 49, 1251–1284.CrossRefGoogle Scholar
  46. Xin, Y. P., & Jitendra, A. K. (1999). The effects of instruction in solving mathematical word problems for students with learning problems: A meta-analysis. Journal of Special Education, 32, 207–225.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Educational PsychologyUniversity of MinnesotaMinneapolisUSA

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