Curricular Implications of Concept Mapping in Secondary Mathematics Education

  • James J. Vagliardo

Recognition of deep-seated conceptual crosslinks in mathematics is often weak or nonexistent among students and faculty who view and study mathematics merely in procedural terms. Too often mathematical course content is presented as an approach to a currently considered problem with the mediation of deeper meaning and the connections to other mathematical ideas left unaddressed. The development of mathematical mindfulness requires that educators substantively address the topics they teach by locating the conceptual essence of fundamental ideas from a cultural-historical context. This important pedagogical work can be enhanced through the skilful use of concept mapping. This chapter provides an in-depth look at how concept mapping can be used in the development of a meaningful secondary mathematics’ curriculum that avoids rote learning and favors transcendent cognitive development.


Mathematics Educator Concept Mapping Mathematical Idea Mathematical Thought Substantive Knowledge 
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.


  1. Bronowsky, J. (1973). The ascent of man. Boston, MA: Little, Brown.Google Scholar
  2. Davydov, V. (1990). Types of generalization in instruction: Logical and psychological problems in the structuring of school curricula. Soviet studies in mathematics education (Vol. 2). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  3. Eves, H. (1969). An introduction to the history of mathematics (3rd ed.). New York: Holt, Rinehart and Winston.Google Scholar
  4. Lakoff, G., & Johnson, M. (1980). Metaphors we live by. Chicago, IL: University of Chicago Press.Google Scholar
  5. Langer, E. (1989). Mindfulness. Reading, MA: Addison-Wesley.Google Scholar
  6. Mandelbrot, B. (1977). The fractal geometry of nature. New York: W. H. Freeman.Google Scholar
  7. Novak, J. D., & Gowin, D. (1984). Learning how to learn. Cambridge, UK: Cambridge University Press.Google Scholar
  8. Schmittau, J. (1993). Vygotskian scientific concepts: Implications for mathematics education. Focus on Learning Problems in Mathematics, 15(2 and 3), 29–39.Google Scholar
  9. Schmittau, J. (2003). Cultural-historical theory and mathematics education. In A. Kozulin & others (Eds.), Vygotsky’s educational theory in cultural context (pp. 225–245). Cambridge, UK: Cambridge University Press.Google Scholar
  10. Turnbull, H. W. (1969). The great mathematicians. New York: New York University Press.Google Scholar
  11. Vygotsky, L. (1978). In M. Cole, V. John-Steiner, S. Scribner, & E. Souberman (Eds.), Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.State University of New YorkBinghamton, VestalUSA

Personalised recommendations