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.
Keywords
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Burris, A. (2005). Understanding the math you teach. Upper Saddle River, NJ: Prentice Hall.
Davidson, P. S., Galton, G. K., & Fair, A. W. (1975). Chip trading activities. Fort Collins, CO: Scott Resources.
Lesar, T. S. (2003). Tenfold medication dose prescribing errors. The American Journal for Nurse Practictioners, 7(2), 31–32, 34–38, 43.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics. (1998). The teaching and learning of algorithms in school mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
Pirie, S. (1987). Nurses and mathematics: Deficiences in basic mathematical skills among nurses. London: Royal College of Nursing.
Prairie Rainbow Blocks. Oakland, CA: Prairie Rainbow Company.
Przybycien, P. (2005). Safe meds: An interactive guide to safe medication practice. St. Louis: Elsevier Mosby.
Skemp, R. (1987). The psychology of learning mathematics. Mahwah, NJ: Lawrence Erlbaum.
Vygotsky, L. S. (1962). Thought and language. Cambridge, MA: MIT Press.
Acknowledgement
Our special thanks to the pre-service student who graciously provided the concept map discussed in this chapter.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Schmittau, J., Vagliardo, J.J. (2009). Concept Mapping as a Means to Develop and Assess Conceptual Understanding in Primary Mathematics Teacher Education. In: Afamasaga-Fuata'i, K. (eds) Concept Mapping in Mathematics. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-89194-1_3
Download citation
DOI: https://doi.org/10.1007/978-0-387-89194-1_3
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-89193-4
Online ISBN: 978-0-387-89194-1
eBook Packages: Humanities, Social Sciences and LawEducation (R0)