Advertisement

Concept Mapping a Teaching Sequence and Lesson Plan for “Derivatives”

  • Karoline Afamasaga-Fuata’i
Chapter

The chapter presents a student teacher’s work from a study, which investigated secondary preservice teachers’ use of concept maps and vee diagrams as pedagogical tools to (i) guide the critical analysis of the content of a mathematics syllabus, and (ii) develop their skills in designing activities that promote working mathematically. Through in-class presentations and critiques of concept maps, student teachers engaged in the processes of reasoning, justifying, verifying, and validating to ensure that visually displayed interconnections effectively reflected their intended meanings. Bobby’s concept maps presented here, illustrate the conceptual structure underpinning a teaching sequence, a lesson and an assessment plan as part of a required course assignment, to communicate his perceptions of what it means to developmentally and conceptually teach “Derivatives” in contrast to simply compiling a sequential list of sub-topics. Main insights from the findings suggested that constructing concept maps (a) prompted Bobby to reflect more deeply about his own mathematics knowledge beyond the assignment topic and (b) challenged him to strategically organize his conceptual analysis results into hierarchical displays of concept networks to parsimoniously and meaningfully illustrate the interconnectedness between key and subsidiary concepts as his pedagogical planning progresses from a 2-year curriculum and topic syllabus notes to a teaching sequence, lessons and an assessment plan.

Keywords

Student Teacher Lesson Plan Teaching Sequence Concept Hierarchy Middle Branch 
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.

Notes

Acknowledgments

This research study was made possible by a research grant from the University of New England. My thanks to Bobby for permission to use his concept maps in the case study reported in this chapter.

References

  1. Afamasaga-Fuata’i, K. (2004a). Concept maps and vee diagrams as tools for learning new mathematics topics. In A. J. Canãs, J. D. Novak, & Gonázales (Eds.), Concept maps: Theory, methodology, technology. Proceedings of the First International Conference on Concept Mapping September 14–17, 2004 (pp. 13–20). Spain: Dirección de Publicaciones de la Universidad Pública de Navarra.Google Scholar
  2. Afamasaga-Fuata’i, K. (2004b). An undergraduate’s understanding of differential equations through concept maps and vee diagrams. In A. J. Canãs, J. D. Novak & Gonázales (Eds.), Concept maps: Theory, methodology, technology. Proceedings of the First International Conference on Concept Mapping September 14–17, 2004 (pp. 21–29). Dirección de Publicaciones de la Universidad Pública de Navarra, Spain.Google Scholar
  3. Afamasaga-Fuata’i, K. (2005). Students’ conceptual understanding and critical thinking? A case for concept maps and vee diagrams in mathematics problem solving. In M. Coupland, J., Anderson, & T. Spencer (Eds.), Making Mathematics Vital. Proceedings of the Twentieth Biennial Conference of the Australian Association of Mathematics Teachers (AAMT) (pp. 43–52). January 17–21, 2005. University of Technology, Sydney, Australia: AAMT.Google Scholar
  4. Afamasaga-Fuata’i, K. (2006). Developing a more conceptual understanding of matrices and systems of linear equations through concept mapping and vee diagrams. FOCUS on Learning Problems in Mathematics, 28(3 and 4), 58–89.Google Scholar
  5. Afamasaga-Fuata’i, K. (2007). Communicating students’ understanding of undergraduate mathematics using concept maps. In J. Watson & K. Beswick, (Eds.), Mathematics: Essential Research, Essential Practice. Proceedings of the 30th Annual Conference of the Mathematics Education Research Group of Australasia (Vol. 1, pp. 73–82). University of Tasmania, Australia: MERGA.Google Scholar
  6. Ausubel, D. P. (2000). The acquisition and retention of knowledge: A cognitive view. Dordrecht; Boston: Kluwer Academic Publishers.Google Scholar
  7. Bobis, J., Mulligan, J., & Lowrie, T. (2004). Mathematics for children. Challenging children to think mathematically. Australia: Pearson Prentice Hill.Google Scholar
  8. Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.CrossRefGoogle Scholar
  9. New South Wales Board of Studies (NSW BOS) (2002). Mathematics K-6 Syllabus 2002.Google Scholar
  10. Novak, J. D. (2004). A science education research program that led to the development of the concept mapping tool and new model for education. In A. J. Canãs, J. D. Novak, & Gonázales (Eds.), Concept maps: Theory, methodology, technology. Proceedings of the First International Conference on Concept Mapping September 14–17, 2004 (pp. 457–467). Spain: Dirección de Publicaciones de la Universidad Pública de Navarra.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.University of New EnglandAustralia

Personalised recommendations