Skip to main content

Prospective Teachers’ Interactions with Interactive Diagrams: Semiotic Tools, Challenges and Well-Trodden Paths

Part of the ICME-13 Monographs book series (ICME13Mo)

Abstract

The goal of the study was to analyze prospective teachers’ interactions with interactive texts and to understand the affordance of the texts’ design, which was conducted within the semiotic framework, on the different stages of the interactions. The findings of the empirical study shed light on awareness of design functions of interactive text in the teachers’ interactions with the materials: they developed teaching plans and scenarios of student-textbook-teacher interaction that included similar tasks distinguished by the designed functions in different stages of the interaction and defined, for each task, different goals for teaching. However the teachers did not always take an advantage of the wide variety of options available with the interactive texts and preferred the familiar paths in teaching.

Keywords

  • Mathematics teachers’ resources
  • Interactive curriculum resources
  • Student-textbook-teacher interactions
  • Semiotics
  • Tasks design
  • Prospective teachers

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-73253-4_14
  • Chapter length: 18 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   169.00
Price excludes VAT (USA)
  • ISBN: 978-3-319-73253-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   219.99
Price excludes VAT (USA)
Hardcover Book
USD   219.99
Price excludes VAT (USA)
Fig. 14.1
Fig. 14.2
Fig. 14.3
Fig. 14.4
Fig. 14.5

References

  • Ball, D. L., & Cohen, D. K. (1996). Reform by the book: What is—or might be—the role of curriculum materials in teacher learning and instructional reform? Educational Researcher, 25(9), 6–14.

    Google Scholar 

  • Borwein, J. M. (2016). The life of Modern Homo Habilis Mathematicus: Experimental computation and visual theorems. In J. Monaghan & J. M. Borwein (Eds.), Tools and mathematics: Instruments for learning (pp. 23–90). Switzerland: Springer.

    CrossRef  Google Scholar 

  • Bremigan, E. G. (2005). An analysis of diagram modification and construction in students’ solutions to applied calculus problems. Journal for Research in Mathematics Education, 36(3), 248–277.

    Google Scholar 

  • Chazan, D., & Herbst, P. (2011). Challenges of particularity and generality in depicting and discussing teaching. For the Learning of Mathematics, 31(1), 9–13.

    Google Scholar 

  • Clark-Wilson, A., Sinclair, N., & Robutti, O. (2014). The mathematics teacher in the digital era. Dordrecht: Springer.

    Google Scholar 

  • Davis, P. H. (1995). The rise, fall and possible transfiguration of triangle geometry: A mini-history. The American Mathematical Monthly, 102(3), 204–214.

    CrossRef  Google Scholar 

  • Davydov, V. V. (1972/1990). 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 

  • Duval, R. (1995). Geometrical pictures: Kinds of representation and specific processings. In R. Sutherland & J. Mason (Eds.), Exploiting mental imagery with computers in mathematics education (pp. 142–157). Berlin: Springer.

    CrossRef  Google Scholar 

  • Fish, J., & Scrivener, S. (1990). Amplifying the mind’s eye: Sketching and visual cognition. Leonardo, 23(1), 117–126.

    CrossRef  Google Scholar 

  • Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht: Springer.

    Google Scholar 

  • Friesen, N. (2013). The past and likely future of an educational form: A textbook case. Educational Researcher, 42(9), 498–508.

    CrossRef  Google Scholar 

  • Goldenberg, P., & Mason, J. (2008). Shedding light on and with example spaces. Educational Studies in Mathematics, 69(2), 183–194.

    CrossRef  Google Scholar 

  • Herbst, P., Chazan, D., Chen, C., Chieu, V. M., & Weiss, M. (2011). Using comics-based representations of teaching, and technology, to bring practice to teacher education courses. ZDM Mathematics Education, 43(1), 91–103.

    CrossRef  Google Scholar 

  • Hoyles, C., & Lagrange, J. B. (2010). (Eds.), Mathematics education and technology—rethinking the terrain: The 17th ICMI Study (New ICMI Study Series, Vol. 13). Berlin: Springer.

    Google Scholar 

  • Lampert, M. (1990). When the problem is not the question and the solution is not the answer. American Educational Research Journal, 27(1), 29–63.

    CrossRef  Google Scholar 

  • Mason, J. (1995). Exploring the sketch metaphor for presenting mathematics using boxer. In A. A. diSessa, C. Hoyles, R. Noss, & L. D. Edwards (Eds.), Computers and exploratory learning (pp. 383–398). Berlin: Springer.

    CrossRef  Google Scholar 

  • Mason, J., & Pimm, D. (1984). Generic examples: Seeing the general in the particular. Educational Studies in Mathematics, 15(3), 227–289.

    CrossRef  Google Scholar 

  • Monaghan, J., & Trouche, L. (2016). Mathematics teachers and digital tools. In J. Monaghan, L. Trouche, & J. M. Borwein (Eds.), Tools and mathematics (pp. 357–384). Switzerland: Springer.

    CrossRef  Google Scholar 

  • Murata, A. (2008). Mathematics teaching and learning as a mediating process: The case of tape diagrams. Mathematical Thinking and Learning, 10(4), 374–406.

    CrossRef  Google Scholar 

  • Naftaliev, E. (2012). Interactive diagrams: Mathematical engagements with interactive text. Ph.D. thesis, University of Haifa, Faculty of Education, Haifa.

    Google Scholar 

  • Naftaliev, E., & Yerushalmy, M. (2011). Solving algebra problems with interactive diagrams: Demonstration and construction of examples. Journal of Mathematical Behavior, 30(1), 48–61.

    CrossRef  Google Scholar 

  • Naftaliev, E., & Yerushalmy, M. (2013). Guiding explorations: Design principles and functions of interactive diagrams. Computers in the Schools, 30(1–2), 61–75.

    CrossRef  Google Scholar 

  • Naftaliev, E., & Yerushalmy, M. (2017). Design digital tasks: Interactive diagrams as resource and constraint. In A. Leung & A. Baccaglini-Frank (Eds.), The role and potential of using digital technologies in designing mathematics education tasks (Vol. 8, pp. 153–173). Switzerland: Springer.

    CrossRef  Google Scholar 

  • Netz, R. (1999). The shaping of deduction in Greek mathematics. UK: Cambridge University Press.

    CrossRef  Google Scholar 

  • Nunokawa, K. (1994). Improving diagrams gradually: One approach to using diagrams in problem solving. For the Learning of Mathematics, 14(1), 34–38.

    Google Scholar 

  • Pepin, B., Gueudet, G., & Trouche, L. (2013). Re-sourcing teachers’ work and interactions: A collective perspective on resources, their use and transformation. ZDM Mathematics Education, 45(7), 929–943.

    CrossRef  Google Scholar 

  • Remillard, J. T. (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research, 75(2), 211–246.

    CrossRef  Google Scholar 

  • Remillard, J. T., & Bryans, M. (2004). Teachers’ orientations toward mathematics curriculum materials: Implications for teacher learning. Journal for Research in Mathematics Education, 35(5), 352–388.

    CrossRef  Google Scholar 

  • Rösken-Winter, B., Schüler, S., Stahnke, R., & Blömeke, S. (2015). Effective CPD on a large scale: Examining the development of multipliers. ZDM Mathematics Education, 47(1), 13–25.

    CrossRef  Google Scholar 

  • Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334–370). New York: MacMillan.

    Google Scholar 

  • Schwartz, J. L. (1999). Can technology help us make the mathematics curriculum intellectually stimulating and socially responsible? International Journal of Computers in the Mathematical Learning, 4(2/3), 99–119.

    CrossRef  Google Scholar 

  • Siegel, M. (1995). More than words: The generative power of transmediation for learning. Canadian Journal of Education, 20(4), 455–475.

    CrossRef  Google Scholar 

  • Stein, M. K., Remillard, J. T., & Smith, M. S. (2007). How curriculum influences student learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319–369). Greenwich, CT: Information Age Publishing.

    Google Scholar 

  • Stylianides, G. J., & Stylianides, A. J. (2014). The role of instructional engineering in reducing the uncertainties of ambitious teaching. Cognition and Instruction, 32(4), 374–415.

    CrossRef  Google Scholar 

  • Trouche, L., Drijvers, P., Gueudet, G., & Sacristan, A. (2012). Technology-driven developments and policy implications for mathematics education. In M. Clements, A. Bishop, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Third international handbook of mathematics education (pp. 753–789). New York: Springer.

    CrossRef  Google Scholar 

  • Yerushalmy, M. (2005). Functions of interactive visual representations in interactive mathematical textbooks. International Journal of Computers for Mathematical learning, 10(3), 217–249.

    CrossRef  Google Scholar 

Download references

Acknowledgements

I would like to thank Michal Yerushalmy, Daniel Chazan‏ and Osama Swidan for discussing of the ideas about the research.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Elena Naftaliev .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Verify currency and authenticity via CrossMark

Cite this chapter

Naftaliev, E. (2018). Prospective Teachers’ Interactions with Interactive Diagrams: Semiotic Tools, Challenges and Well-Trodden Paths. In: Fan, L., Trouche, L., Qi, C., Rezat, S., Visnovska, J. (eds) Research on Mathematics Textbooks and Teachers’ Resources. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-73253-4_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-73253-4_14

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-73252-7

  • Online ISBN: 978-3-319-73253-4

  • eBook Packages: EducationEducation (R0)