Skip to main content
SpringerLink
Log in

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

  • Chapter
  • First Online:
Research on Mathematics Textbooks and Teachers’ Resources

Part of the book series: ICME-13 Monographs ((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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

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.

    Chapter  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.

    Article  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.

    Chapter  Google Scholar 

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

    Article  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.

    Article  Google Scholar 

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

    Article  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.

    Article  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.

    Article  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.

    Chapter  Google Scholar 

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

    Article  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.

    Chapter  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.

    Article  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.

    Article  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.

    Article  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.

    Chapter  Google Scholar 

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

    Book  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.

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  Google Scholar 

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

    Article  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.

    Article  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.

    Chapter  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.

    Article  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

  1. Achva Academic College, Arugot, Israel

    Elena Naftaliev

Authors
  1. Elena Naftaliev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Elena Naftaliev .

Editor information

Editors and Affiliations

  1. Southampton Education School, University of Southampton, Southampton, United Kingdom

    Lianghuo Fan

  2. Institut Français de l’Education, École Normale Supérieure de Lyon, Lyon, France

    Luc Trouche

  3. Faculty of Education, Beijing Normal University, Beijing, China

    Chunxia Qi

  4. EIM—Institut für Mathematik, Universität Paderborn, Paderborn, Germany

    Sebastian Rezat

  5. School of Education, The University of Queensland, Brisbane, Queensland, Australia

    Jana Visnovska

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Check for updates. 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)

Publish with us

Policies and ethics

Search

Navigation