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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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/.
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.
Gick, M. L., & Holyoak, K. J. (1983). Schema induction and analogical transfer. Cognitive Pyschology, 15, 1–38.
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.
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).
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.
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.
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.
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.
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.
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.
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.
Milgram, R. J., & Wu, H. S. (2005). The key topics in a successful math curriculum. http://math.berkeley.edu/wu/.
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.
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.
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.
National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the national mathematics advisory panel. Washington, DC: U.S. Department of Education.
Parker, M., & Leinhardt, G. (1995). Percent: A privileged proportion. Review of Educational Research, 65, 421–481.
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.
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.
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.
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.
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.
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.
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer Science+Business Media New York
About this chapter
Cite this chapter
Jitendra, A., Dupuis, D. (2016). The Role of Tier I Mathematics Instruction in Elementary and Middle Schools: Promoting Mathematics Success. In: Jimerson, S., Burns, M., VanDerHeyden, A. (eds) Handbook of Response to Intervention. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7568-3_13
Download citation
DOI: https://doi.org/10.1007/978-1-4899-7568-3_13
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-7567-6
Online ISBN: 978-1-4899-7568-3
eBook Packages: Behavioral Science and PsychologyBehavioral Science and Psychology (R0)