Concept Mapping in Mathematics pp 137-147 | Cite as

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

A case study of the concept maps of two pre-service teachers illustrates the potential of concept mapping to the teacher educator. The maps reveal much about whether future secondary teachers grasp the nature of mathematics as a conceptual system, understand the conceptual content of mathematical procedures, and possess the requisite pedagogical content knowledge to mediate such understandings to future learners. The map of one of the two teachers reveals that she possesses these understandings. The map of the other shows a formalistic understanding of mathematics. Concept mapping also functions as an epistemological heuristic for pre- and in-service teachers.

## Keywords

Concept Mapping Conceptual Understanding Pedagogical Content Knowledge Conceptual System Class Discussion## Notes

### Acknowledgements

My thanks to James J. Vagliardo for his expert assistance in digitizing the concept mapping sections, and to the two pre-service teachers who graciously provided the concept maps discussed in this chapter.

## References

- Davydov, V. V. (1990).
*Types of generalization in instruction: Logical and psychological problems in the structuring of school curricula*. Reston, VA: National Council of Teachers of Mathematics.Google Scholar - Davydov, V. V. (1992). The psychological analysis of multiplication procedures.
*Focus on Learning Problems in Mathematics, 14*(1), 3–67.Google Scholar - Karpinski, L. C. (1915).
*Robert of Chester’s Latin translation of the algebra of Al-Khowarizmi*. New York: Macmillan.Google Scholar - Morrow, L. J. (1998). Whither algorithms? Mathematics educators express their views. In L. J. Morrow & M. J. Kenney (Eds.),
*The teaching and learning of algorithms in school mathematics*(pp. 1–6). Reston, VA: National Council of Teachers of Mathematics.Google Scholar - Morrow, L. J., & Kenney, M. J. (Eds.) (1998).
*The teaching and learning of algorithms in school mathematics*. Reston, VA: National Council of Teachers of Mathematics.Google Scholar - National Council of Teachers of Mathematics. (1989).
*Curriculum and evaluation standards for school mathematics*. Reston, VA: Author.Google Scholar - National Council of Teachers of Mathematics. (2000).
*Principles and standards for school mathematics*. Reston, VA: Author.Google Scholar - Novak, J. D., & Gowin, D. B. (1984).
*Learning how to learn*. New York: Cambridge University Press.Google Scholar - Schmidt, W., Houang, R., & Cogan, L. (2002). A coherent curriculum: The case of mathematics.
*The American Educator, 26*(2), 10–26.Google Scholar - Schmittau, J. (2003). Cultural-historical theory and mathematics education. In A. Kozulin, B. Gindis, S. Miller, & V. Ageyev (Eds.),
*Vygotsky’s educational theory in cultural context*(pp. 225–245). New York: Cambridge University Press.Google Scholar - Schmittau, J. (2004). Vygotskian theory and mathematics education: Resolving the conceptual-procedural dichotomy.
*European Journal of Psychology of Education**XIX*(1), 19–43.CrossRefGoogle Scholar - Vygotsky, L. S. (1986).
*Thought and language*. Cambridge, MA: MIT Press.Google Scholar - Wu, H. (1999). Basic skills versus conceptual understanding: A bogus dichotomy in mathematics education.
*American Educator,*Fall Issue, 1–7.Google Scholar