Concept Mapping as a Means to Develop and Assess Conceptual Understanding in Primary Mathematics Teacher Education

  • Jean Schmittau
  • James J. Vagliardo

Psychologists such as Vygotsky and Skemp indicate that as a superordinate concept the understanding of positional system requires knowledge of several bases for its adequate development. However, current elementary mathematics curricula fail to adequately develop the concept of positional system, attempting instead to teach operations in base ten in isolation. This paper exhibits the power of concept mapping to reveal to teachers the centrality of this concept in elementary mathematics. The map presented here, constructed by Maryanne, a pre-service teacher, also features the pedagogical content knowledge required to successfully teach the concept of positional system and the other mathematics concepts to which it is related. Maryanne’s pedagogical treatment is neither simplistic nor reductionist, but reveals the conceptual essence of the concepts in question and the complexity of their relationships within elementary mathematics when taught as a conceptual system.


Pedagogical Content Knowledge Positional System Elementary Mathematics Multiple Basis Decimal System 
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.



Our special thanks to the pre-service student who graciously provided the concept map discussed in this chapter.


  1. Burris, A. (2005). Understanding the math you teach. Upper Saddle River, NJ: Prentice Hall.Google Scholar
  2. Davidson, P. S., Galton, G. K., & Fair, A. W. (1975). Chip trading activities. Fort Collins, CO: Scott Resources.Google Scholar
  3. Lesar, T. S. (2003). Tenfold medication dose prescribing errors. The American Journal for Nurse Practictioners, 7(2), 31–32, 34–38, 43.Google Scholar
  4. National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.Google Scholar
  5. National Council of Teachers of Mathematics. (1998). The teaching and learning of algorithms in school mathematics. Reston, VA: Author.Google Scholar
  6. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.Google Scholar
  7. Pirie, S. (1987). Nurses and mathematics: Deficiences in basic mathematical skills among nurses. London: Royal College of Nursing.Google Scholar
  8. Prairie Rainbow Blocks. Oakland, CA: Prairie Rainbow Company.Google Scholar
  9. Przybycien, P. (2005). Safe meds: An interactive guide to safe medication practice. St. Louis: Elsevier Mosby.Google Scholar
  10. Skemp, R. (1987). The psychology of learning mathematics. Mahwah, NJ: Lawrence Erlbaum.Google Scholar
  11. Vygotsky, L. S. (1962). Thought and language. Cambridge, MA: MIT Press.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.State University of New York at BinghamtonBinghamtonUSA

Personalised recommendations