• Namirah Fatmanissa Ms, Department of Mathematics and Science Education, Universitas Pendidikan Indonesia, Bandung, Indonesia-40154


calculus, word problem, schema, mathematics


The aim of this article is to provide literature review on why and how schema is used to help students solve calculus word problem. It starts with the description of typical difficulties found in common word problem, calculus, and both. Then, it continues with the explanation of what is schema and its advantages. The examples of promoting schema in classroom are also analyzed from several literatures. The strengths of schema are discussed yet some considerations on promoting it are also analyzed.


I. Baker, B., Cooley, L., Trigueros, M., & Trigueros, M. (2000). A Calculus Graphing Schema. Journal for Research in Mathematics Education, 31(5), 557.

II. Bremigan, E. G. (2005). An Analysis of Diagram Modification and Construction in Students’ Solutions to Applied Calculus Problems. Journal for Research in Mathematics Education, 36(3), 248–277.

III. Eisenberg, T. (2002). Advanced Mathematical Thinking. In D. Tall (Ed.) (p. 297). Netherlands: Kluwer Academic Publishers.

IV. Fuchs, L. S., Fuchs, D., Finelli, R., Courey, S. J., & Hamlett, C. L. (2004). Expanding Schema-Based Transfer Instruction to Help Third Graders Solve Real-Life Mathematical Problems. American Educational Research Journal, 41(2), 419–445.

V. Hegarty, M., & Kozhevnikov, M. (1999). Types of visual-spatial representations and mathematical problem solving. Journal of Educational Psychology, 91(4), 684–689.

VI. 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(3), 250–264.

VII. Klymchuk, S., Zverkova, T., Gruenwald, N., & Sauerbier, G. (2010). University students’ difficulties in solving application problems in calculus: Student perspectives. Mathematics Education Research Journal, 22(2), 81–91.

VIII. Marshall, S. P. (1995). Schemas in problem solving. Cambridge: Cambridge University Press.

IX. Powell, S. R. (2011). Solving word problems using schemas: A review of the literature. Learning Disabilities Research & Practice, 26(2), 94–108.

X. Presmeg, N. (2006). Research on visualization in learning an teaching mathematics. Handbook of Research on the Psychology of Mathematics Education, 205–235.

XI. Reys, R., Lindquist, M., Lambdin, D., & Smith, N. (2013). Helping Children Learn Mathematics (Vol. 53).

XII. Ryan, J., & Williams, J. (2007). Children ’ s Mathematics: Learning from Errors and Misconceptions. Berskhire: McGraw Hill.

XIII. Skemp, R. R. (1987). The Psychology of Learning Mathematics. New Jersey: Psychology Press.

XIV. Sofronas, K. S., DeFranco, T. C., Vinsonhaler, C., Gorgievski, N., Schroeder, L., & Hamelin, C. (2011). What does it mean for a student to understand the first-year calculus? Perspectives of 24 experts. Journal of Mathematical Behavior, 30(2), 131–148.

XV. Stillman, G. (2004). Strategies employed by upper secondary students for overcoming or exploiting conditions affecting accessibility of applications tasks. Mathematics Education Research Journal, 16(1), 41–70.

XVI. Stylianou, D. A., & Silver, E. A. (2009). The Role of Visual Representations in Advanced Mathematical Problem Solving : An Examination of Expert- Novice Similarities and Differences. Mathematical Thinking and Learning, 6(4), 353–387.

XVII. Verschaffel, L., van Dooren, W., Greer, B., & Mukhopadhyay, S. (2010). Die Rekonzeptualisierung von Textaufgaben als Übungen in mathematischer Modellierung. Journal Fur Mathematik-Didaktik, 31(1), 9–29.

Additional Files



How to Cite

Namirah Fatmanissa. (2018). SCHEMA AS VISUAL REPRESENTATION IN SOLVING CALCULUS WORD PROBLEMS: A LITERATURE REVIEW. International Education and Research Journal (IERJ), 4(4). Retrieved from