Advertisement

Progressive Visualization Tasks and Semiotic Chaining for Mathematics Teacher Preparation: Towards a Conceptual Framework

  • Barbara M. KinachEmail author
Chapter
Part of the ICME-13 Monographs book series (ICME13Mo)

Abstract

Visualization plays an important role in mathematics learning, but in the United States where many prospective teachers (PTs) have few if any experiences learning mathematics through visualization, mathematics teacher educators are challenged to design tasks that generate within PTs’ thinking an appreciation for the role visualization plays in mathematics learning. This chapter examines the affordances of progressive visualization tasks and semiotic chaining for use in mathematics teacher preparation. To the literature on dyadic and nested forms of semiotic chaining, data analysis in this chapter contributes a new type of semiotic chaining based on Peirce’s three principles of diagrammatic reasoning.

Keywords

Teacher education-preservice Learning trajectories (Progressions) Technology 

References

  1. Adeyemi, C. M. (2004). Semiotic chaining: Preservice teacher belief and instructional practices (Doctoral dissertation). Retrieved from ProQuest Dissertations and Theses. (Accession Order No. AAT 3172873).Google Scholar
  2. Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52, 215–241.CrossRefGoogle Scholar
  3. Bishop, A. (1980). Spatial abilities and mathematics education—A review. Educational Studies in Mathematics, 11, 257–269.CrossRefGoogle Scholar
  4. Bruner, J. S. (1961). The process of education. Cambridge, MA: Harvard University Press.Google Scholar
  5. Cramer, K. (2003). Using a translation model for curriculum development and classroom instruction. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 35–58). Mahwah, NJ: Lawrence Erlbaum.Google Scholar
  6. Dienes, Z. P. (1973). A theory of mathematics learning. In F. J. Crosswhite, J. L. Highins, A. R. Osborne, & R. J. Shunway (Eds.), Teaching mathematics: Psychological foundations (pp. 137–148). Ohio, OH: Charles A. Jones Publishing.Google Scholar
  7. Hall, M. A. (2000). Bridging the gap between everyday and classroom mathematics: An investigation of two teachers’ intentional use of semiotic chains. Retreived from ProQuest Dissertations and Theses. (Accession Order No. AAT 9971753).Google Scholar
  8. Joswick, H. (1996). The object of semeiotic. In V. M. Colapietro & T. M. Olshewsky (Eds.), Peirce’s doctrine of signs: Theory, applications, and connections (pp. 93–102). Berlin, Germany: Walter de Gruyter & Co.Google Scholar
  9. Kadunz, G. (2016). Geometry, a means of argumentation. In A. Saenz-Ludlow & G. Kadunz (Eds.), Semiotics as a tool for learning mathematics: How to describe the construction, visualization, and communication of mathematical concepts. Rotterdam, The Netherlands: Sense Publishers. Google Scholar
  10. Kinach, B. M. (2002). A cognitive strategy for developing pedagogical content knowledge in the secondary mathematics methods course: Toward a model of effective practice. Teaching and Teacher Education, 18, 51–71.CrossRefGoogle Scholar
  11. Krutetskii, V. A. (1976). The psychology of mathematical abilities in school children. Chicago, IL: University of Chicago.Google Scholar
  12. MIND Research Institute. (2014). Spatial-temporal (ST) math. Irvine, CA: The MIND Research Institute.Google Scholar
  13. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.Google Scholar
  14. National Governors Association Center for Best Practices, Council of Chief State School Officers. (2010). Common core state standards (Mathematics). Washington, DC: Author.Google Scholar
  15. Peirce, C. S. (1992). The essential Peirce (Vol. 1, 1867–1893). In N. Houser & C. Kloesel (Eds.). Bloomington, IN: Indiana University Press.Google Scholar
  16. Peirce, C. S. (1998). The essential Peirce (Vol. 2, 1893–1903). In Peirce Edition Project (Eds.). Bloomington, IN: Indiana University Press.Google Scholar
  17. Presmeg, N. (2006a). Research on visualization in learning and teaching mathematics. In A. Gutierrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 205–235). Rotterdam, The Netherlands: Sense Publishers.Google Scholar
  18. Presmeg, N. (2006b). Semiotics and the “connections” standard: Significance of semiotics for teachers of mathematics. Educational Studies in Mathematics, 61, 163–182.CrossRefGoogle Scholar
  19. Presmeg, N. (2013). Contemplating visualization as an epistemological learning tool in mathematics. ZDMThe International Journal on Mathematics Education, 46, 151–157.Google Scholar
  20. Rivera, F. D., Steinbring, H., & Arcavi, A. (2013). Visualization as an epistemological learning tool. ZDMThe International Journal on Mathematics Education, 46, 1–2.Google Scholar
  21. Sáenz-Ludlow, A., & Kadunz, G. (2016). Constructing knowledge seen as a semiotic activity. In A. Sáenz-Ludlow & G. Kadunz (Eds.), Semiotics as a tool for learning mathematics: How to describe the construction, visualization, and communication of mathematical concepts (pp. 1–21). Rotterdam, The Netherlands: Sense Publishers.CrossRefGoogle Scholar
  22. Stjernfelt, F. (2007). Diagrammatology: An investigation on the borderlines of phenomenology, ontology, and semiotics. Dordrecht, The Netherlands: Springer.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Mary Lou Fulton Teachers CollegeArizona State UniversityMesaUSA

Personalised recommendations