Using Schema-Based Instruction to Improve Students’ Mathematical Word Problem Solving Performance

  • Asha K. JitendraEmail author


The purpose of this chapter is to describe an evidence-based instructional program, schema-based instruction (SBI), which provides support in word problem solving for students who have difficulties in mathematics (MD). First, I describe mathematical word problem solving and the critical components linked to the ability to understand and solve word problems. Second, I describe the theoretical framework for SBI, including a discussion of its unique features and how SBI contributes to word problem solving performance. Third, I summarize previous research on SBI to understand the instructional conditions that need to be in place to support mathematical word problem solving for students with MD. Last, I conclude with a discussion of challenges yet to be addressed.


Word problem solving Schema-based instruction Mathematics difficulties 


  1. Andersson, U. (2008). Mathematical competencies in children with different types of learning difficulties. Journal of Educational Psychology, 100, 48–66. CrossRefGoogle Scholar
  2. Boonen, A. J. H., van der Schoot, M., van Wesel, F., de Vries, M. H., & Jolles, J. (2013). What underlies successful word problem solving? A path analysis in sixth grade students. Contemporary Educational Psychology, 38(2013), 271–279. CrossRefGoogle Scholar
  3. Briars, D. J., & Larkin, J. H. (1984). An integrated model of skill in solving elementary word problems. Cognition and Instruction, 1, 245–296.CrossRefGoogle Scholar
  4. Bush, S. B., & Karp, K. S. (2013). Prerequisite algebra skills and associated misconceptions of middle grade students: A review. Journal of Mathematical Behavior, 32(3), 613–632.CrossRefGoogle Scholar
  5. Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (2015). Children’s mathematics: Cognitively guided instruction (2nd ed.). Portsmouth, N.H.: Heinemann.Google Scholar
  6. Carpenter, T. P., & Moser, J. M. (1984). The acquisition of addition and subtraction concepts in grades one through three. Journal for Research in Mathematics Education, 15, 179–202.CrossRefGoogle Scholar
  7. Carpraro, M. M., & Joffrion, H. (2006). Algebraic equations: Can middle school students meaningfully translate from words to mathematical symbols? Reading Psychology, 27(2), 147–164.CrossRefGoogle Scholar
  8. Christou, C., & Philippou, G. (2001). Mapping and development of intuitive proportional thinking. The Journal of Mathematical Behavior, 20, 321–336. CrossRefGoogle Scholar
  9. 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
  10. De Corte, E., Verschaffel, L., & Masui, C. (2004). The CLIA-model: A framework for designing powerful learning environments for thinking and problem solving. European Journal of Psychology of Education, 19, 365–384.CrossRefGoogle Scholar
  11. Depaepe, F., De Corte, E., & Verschaffel, L. (2010). Teachers’ approaches towards word problem solving: Elaborating or restricting the problem context. Teaching and Teacher Education: An International Journal of Research and Studies, 26(2), 152–160.CrossRefGoogle Scholar
  12. Desoete, A. (2009). Metacognitive prediction and evaluation skills and mathematical learning in third-grade students. Educational Research and Evaluation, 15, 435–446.CrossRefGoogle Scholar
  13. Diezmann, C. M., & English, L. D. (2001). Promoting the use of diagrams as tools for thinking. In A. A. Cuoco & F. R. Curcio (Eds.), The roles of representation in school mathematics: 2001 yearbook (pp. 77–89). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  14. EACEA/Eurydice. (2011). Mathematics education in Europe: Common challenges and national policies. Brussels: Eurydice [Online] Available at: Accessed 9 July 2017Google Scholar
  15. Fuchs, L. S., Geary, D. C., Compton, D. L., Fuchs, D., Hamlett, C. L., Seethaler, P. M., … Schatschneider, C. (2010). Do different types of school mathematics development depend on different constellations of numerical versus general cognitive abilities? Developmental Psychology, 46, 1731–1746. doi: Scholar
  16. Fuchs, L. S., Fuchs, D., Prentice, K., Burch, M., Hamlett, C. L., Owen, R., & Schroeter, K. (2003). 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., Seethaler, P. M., Powell, S. R., Fuchs, D., Hamlett, C. L., & Fletcher, J. M. (2008). Effects of preventative tutoring on the mathematical problem solving of third- grade students with math and reading difficulties. Exceptional Children, 74, 155–173.CrossRefGoogle Scholar
  18. Fuson, K. C., & Willis, G. B. (1989). Second graders’ use of schematic drawings in solving addition and subtraction word problems. Journal of Educational Psychology, 81, 514–520. CrossRefGoogle Scholar
  19. Gersten, R., Beckmann, S., Clarke, B., Foegen, A., Marsh, L., Star, J. R., & Witzel, B. (2009). 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 Retrieved from Google Scholar
  20. Gersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morphy, P., & Flojo, J. (2009). Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79, 1202–1242. CrossRefGoogle Scholar
  21. Goldin, G. (2002). Representation in mathematical learning and problem solving. In L. English (Ed.), Handbook of research in mathematics education (pp. 197–218). Mahwah: Lawrence Erlbaum.Google Scholar
  22. Greer, B. (1994). Extending the meaning of multiplication and division. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 61–85). Albany: State University of New York Press.Google Scholar
  23. Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77, 81–112.CrossRefGoogle Scholar
  24. Hegarty, M., & Kozhevnikov, M. (1999). Types of visual-spatial representations and mathematical problem solving. Journal of Educational Psychology, 91, 684–689. CrossRefGoogle Scholar
  25. Hegarty, M., Mayer, R. E., & Monk, C. A. (1995). Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers. Journal of Educational Psychology, 87, 18–32.CrossRefGoogle Scholar
  26. Jitendra, A. K. (2007). Solving math word problems: Teaching students with learning disabilities using schema-based instruction. Austin, TX: Pro-Ed.Google Scholar
  27. Jitendra, A. K., Dupuis, D. N., & Zaslofsky, A. (2014). Curriculum-based measurement and standards-based mathematics: Monitoring the arithmetic word problem-solving performance of third-grade students at risk for mathematics difficulties. Learning Disability Quarterly, 37(4), 241–251.CrossRefGoogle Scholar
  28. Jitendra, A. K., Griffin, C., Haria, P., Leh, J., Adams, A., & Kaduvetoor, 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., Griffin, C., McGoey, K., Gardill, C., Bhat, P., & Riley, T. (1998). Effects of mathematical word problem solving by students at risk or with mild disabilities. Journal of Educational Research, 91, 345–356.CrossRefGoogle Scholar
  30. Jitendra, A. K., Rodriguez, M., Kanive, R. G., Huang, J.-P., Church, C., Corroy, K. C., & Zaslofsky, A. F. (2013). 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
  31. Jitendra, A. K., Sczesniak, E., & Deatline-Buchman, A. (2005). Validation of curriculum-based mathematical word problem solving tasks as indicators of mathematics proficiency for third graders. School Psychology Review, 34, 358–371.Google Scholar
  32. Jupri, A., & Drijvers, P. (2016). Student difficulties in mathematizing word problems in algebra. EURASIA Journal of Mathematics, Science, & Technology Education, 12(9), 2481–2502. CrossRefGoogle Scholar
  33. Kalyuga, S. (2006). Rapid cognitive assessment of learners’ knowledge structures. Learning and Instruction, 16, 1–11. CrossRefGoogle Scholar
  34. Kintsch, W., & Greeno, J. G. (1985). Understanding and solving word arithmetic problems. Psychological Review, 92, 109–129. CrossRefGoogle Scholar
  35. Leh, J., Jitendra, A. K., Caskie, G., & Griffin, C. (2007). An evaluation of CBM mathematics word problem solving measures for monitoring third grade students’ mathematics competence. Assessment for Effective Intervention, 32, 90–99.CrossRefGoogle Scholar
  36. Lesh, R., & Zawojewski, J. (2007). Problem solving and modeling. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning. National Council of Teachers of Mathematics (pp. 763–804). Charlotte, NC: Information Age Publishing.Google Scholar
  37. Marshall, S. P. (1995). Schemas in problem solving. New York: Cambridge University Press.CrossRefGoogle Scholar
  38. Mayer, R. E. (1999). The promise of educational psychology Vol. I: Learning in the content areas. Upper Saddle River, NJ: Merrill Prentice Hall.Google Scholar
  39. Mayer, R. E., & Hegarty, M. (1996). The process of understanding mathematics problems. In R. J. Sternberg & T. Ben-Zeev (Eds.), The nature of mathematical thinking (pp. 29–53). Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  40. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.Google Scholar
  41. OECD. (2010). PISA 2009 results: What students know and can do – Student performance in reading, mathematics, and science (volume 1). Paris: OECD Publishing.Google Scholar
  42. Pólya, G. (1990). How to solve it. London: Penguin (Originally published in 1945).Google Scholar
  43. Presmeg, N. (2006). Research on visualization in learning and teaching mathematics. In Á. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 205–236). Rotterdam: Sense.Google Scholar
  44. Riley, M. S., Greeno, J. G., & Heller, J. I. (1983). Development of children’s problem–solving ability in arithmetic. In H. P. Ginsburg (Ed.), The development of mathematical thinking (pp. 153–196). New York: Academic Press.Google Scholar
  45. Rosenzweig, C., Krawec, J., & Montague, M. (2011). Metacognitive strategy use of eighth-grade students with and without learning disabilities during mathematical problem solving: A think-aloud analysis. Journal of Learning Disabilities, 44, 508–520. CrossRefGoogle Scholar
  46. Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334–370). New York: McMillan.Google Scholar
  47. 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. CrossRefGoogle Scholar
  48. Van Amerom, B. A. (2003). Focusing on informal strategies when linking arithmetic to early algebra. Educational Studies in Mathematics, 54(1), 63–75.CrossRefGoogle Scholar
  49. Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). New York: Pearson.Google Scholar
  50. Van Dooren, W., de Bock, D., Vleugels, K., & Verschaffel, L. (2010). Just answering…or thinking? Contrasting pupils’ solutions and classifications of missing-value word problems. Mathematical Thinking and Learning, 12, 20–35. CrossRefGoogle Scholar
  51. van Garderen, D. (2006). Spatial visualization, visual imagery, and mathematical problem solving of students with varying abilities. Journal of Learning Disabilities, 39, 496–506 CrossRefGoogle Scholar
  52. van Garderen, D., & Montague, M. (2003). Visual–spatial representation, mathematical problem solving, and students of varying abilities. Learning Disabilities Research & Practice, 18, 246–254. CrossRefGoogle Scholar
  53. Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse, The Netherlands: Swets & Zeitlinger.Google Scholar
  54. Woodward, J., Beckmann, S., Driscoll, M., Franke, M., Herzig, P., Jitendra, A., et al. (2012). Improving mathematical problem solving in grades 4 through 8: A practice guide (NCEE 2012-4055). Washington, DC: Institute of Education Sciences, U.S. Department of Education Retrieved from Google Scholar
  55. Xin, Y. P., Zhang, D., Park, J. Y., Tom, K., Whipple, A., & Si, L. (2011). A comparison of two mathematics problem-solving strategies: Facilitate algebra-readiness. Journal of Educational Research, 104(6), 381–395. CrossRefGoogle Scholar
  56. Yancey, A. V., Thompson, C. S., & Yancey, J. S. (1989). Children must learn to draw diagrams. Arithmetic Teacher, 36(7), 15–23.Google Scholar
  57. Zahner, D., & Corter, J. E. (2010). The process of probability problem solving: Use of external visual representations. Mathematical Thinking and Learning, 12, 177–204. CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Graduate School of EducationUniversity of CaliforniaRiversideUSA

Personalised recommendations