Impacting Mathematical and Technological Creativity with Dynamic Technology Scaffolding

  • Sandra R. MaddenEmail author
Part of the Mathematics Education in the Digital Era book series (MEDE, volume 10)


This chapter reports on studies conducted during the past decade that investigated mathematical learning for teaching with technology (MLTT) and its relationship to creativity. Though related to mathematical knowledge for teaching (MKT) (Ball et al. in J Teach Educ 59, 389–407, 2008) and technological pedagogical content knowledge (TPCK) (Mishra and Koehler in Teachers Coll Rec 180(6):1017–1054, 2006; Niess in Teach Teach Educ 21(5):509–523, 2005), mathematical learning for teaching with technology has a strong dispositional component coupled with curiosity, creativity, and meaning making (Thompson in Third handbook of international research in mathematics education. Taylor and Francis, London, pp. 435–461, 2015). Using design-based research methods (Cobb et al. in Educ Researcher 32(1):9–13, 2003) a framework for dynamic technological scaffolding (DTS) has emerged in support of teacher learning. DTS has provided fertile ground for the design and further study of learning trajectories in which learners are exploring and eventually creating cognitively challenging mathematical task sequences in the presence of new (to them) physical and technological tools. By harnessing teachers’ motivation to inculcate curiosity, engagement, and learning for their students, these design studies have created conditions where teachers have become curious, creative, and technologically savvy to the point where many have gone on to pursue similar kinds of experiences with their mathematics students. This chapter will explore and present DTS as created and implemented with secondary mathematics teachers and DTS as creative work pursued by teachers.


Curiosity Creativity Dynamic technology scaffolding Provocative tasks Design research 


  1. Bakker, A. (2002). Route-type and landscape-type software for learning statistical data analysis. Paper presented at the International Conference on Teaching Statistics, Cape Town, South Africa.Google Scholar
  2. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 389–407.CrossRefGoogle Scholar
  3. Beghetto, R. A., & Kaufman, J. C. (2009). Do we all have multicreative potential? ZDM Mathematics Education, 41, 39–44.CrossRefGoogle Scholar
  4. Boaler, J., & Greeno, J. (2000). Identity, agency, and knowing in mathematical worlds. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning: International perspectives on mathematics education (pp. 171–200). Westport, CT: Ablex Publishing.Google Scholar
  5. Cobb, P., Confrey, J., DiSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.CrossRefGoogle Scholar
  6. Cohen, E. G. (1994). Designing groupwork: Strategies for the heterogeneous classroom. New York, NY: Teachers College Press.Google Scholar
  7. Csikszentmihalyi, M. (2000). Implications of a systems perspective for the study of creativity. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 313–338). Cambridge, UK: Cambridge University Press.Google Scholar
  8. Cuoco, A., Goldenberg, E. P., & Mark, J. (1996). Habits of mind: An organizing principle for mathematics curricula. Journal of Mathematical Behavior, 15, 375–402.CrossRefGoogle Scholar
  9. de Freitas, E., & Sinclair, N. (2014). Mathematics and the body: Material entanglements in the classroom. New York, NY: Cambridge University Press.CrossRefGoogle Scholar
  10. Doerr, H. M., & Pratt, D. (2008). The learning of mathematics and mathematical modeling. In M. K. Heid & G. W. Blume (Eds.), Research on technology and the teaching and learning of mathematics: Volume 1. Research syntheses (Vol. 1, pp. 259–286). Charlotte, NC: Information Age Publishing Inc.Google Scholar
  11. Dorst, K., & Cross, N. (2001). Creativity in the design process: Co-evolution of problem-solution. Design Studies, 22(5), 425–437.CrossRefGoogle Scholar
  12. Edwards, M. T., & Phelps, S. (2008). Can you fathom this? Connecting data analysis algebra, and probability simulation. Mathematics Teacher, 102(3), 210–217.Google Scholar
  13. Ekmekci, A., Corkin, D., & Papakonstantinou, A. (2015). Technology use of mathematics teachers at urban schools. Paper presented at the 2015 Annual Meeting of American Educational Research Association, Chicago, IL.Google Scholar
  14. Ervynck, G. (1991). Mathematical creativity. In D. Tall (Ed.), Advanced mathematical thinking (pp. 42–53). Dordrecht, The Netherlands: Kluwer Academic Publishers.Google Scholar
  15. Frykholm, J. (2004). Teachers’ tolerance for discomfort: Implications for curricular reform in mathematics. Journal of Curriculum and Supervision, 19(2), 125–149.Google Scholar
  16. Goldin, G. A. (2003). Representation in school mathematics: A unifying research perspective. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 275–285). Reston, VA: NCTM.Google Scholar
  17. Guin, D., & Trouche, L. (1998). The complex process of converting tools into mathematical instruments: The case of calculators. International Journal of Computers for Mathematical Learning, 3(3), 195–227.CrossRefGoogle Scholar
  18. Hirsch, C. R., Fey, J. T., Hart, E. W., Schoen, H. L., & Watkins, A. E. (2015). Core-plus mathematics: Contemporary mathematics in context, Course 1. Columbus, OH: McGraw-Hill Education.Google Scholar
  19. Holyoak, K. J., & Thagard, P. (1995). Mental leaps: Analogy in creative thought. Cambridge, MA: MIT Press.Google Scholar
  20. Johnson, D. W., & Johnson, R. T. (2009). Energizing learning: The instructional power of conflict. Educational Researcher, 38(1), 37–51.CrossRefGoogle Scholar
  21. Jonassen, D. H. (1994). Technology as cognitive tools: Learners as designers. ITForum Paper, 1, 67–80.Google Scholar
  22. Jonassen, D. H., & Reeves, T. C. (1996). Learning with technology: Using computers as cognitive tools. In D. H. Jonassen (Ed.), Handbook of research for educational communications and technology (1st ed., pp. 693–719). New York, NY: Macmillan.Google Scholar
  23. Kadijevich, D. M., & Madden, S. R. (2015). Comparing approaches for developing TPCK. In New directions in technological and pedagogical content knowledge research: Multiple perspectives (pp. 125–146). Charlotte, NC: Information Age Publishing.Google Scholar
  24. Kashdan, T. B., & Fincham, F. D. (2002). ‘Facilitating creativity by regulating curiosity’: Comment. American Psychologist, 57(5), 373–374.CrossRefGoogle Scholar
  25. Loewenstein, G. (1994). The psychology of curiosity: A review and reinterpretation. Psychological Bulletin, 116(1), 75–98.CrossRefGoogle Scholar
  26. Madden, S. R. (2008). Dynamic technology scaffolding: A design principle with potential to support statistical conceptual understanding. Paper presented at the 11th International Congress on Mathematics Education, Monterrey, Mexico.Google Scholar
  27. Madden, S. R. (2010). Designing mathematical learning environments for teachers. Mathematics Teacher, 104(4), 274–282.Google Scholar
  28. Madden, S. R. (2011). Statistically, technologically, and contextually provocative tasks: Supporting teachers’ informal inferential reasoning. Mathematical Thinking and Learning, 13(1–2), 109–131.CrossRefGoogle Scholar
  29. Madden, S. R. (2013). Supporting teachers’ instrumental genesis with dynamic mathematical software. In D. Polly (Ed.), Common core mathematics standards and implementing digital technologies (pp. 295–318). Hershey, PA: IGI Global.CrossRefGoogle Scholar
  30. Madden, S. R., & Gonzales, A. (2017). Nurturing persistent problem solvers: Heart work. Mathematics Teacher, 111(3).Google Scholar
  31. Martinovic, D., & Zhang, Z. (2012). Situating ICT in the teacher education program: Overcoming challenges, fulfilling expectations. Teaching and Teacher Education, 28(3), 461–469.Google Scholar
  32. Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 180(6), 1017–1054.CrossRefGoogle Scholar
  33. National Governors Association Center for Best Practices, and Council of Chief State School Officers. (2010). Common core state standards (Mathematics). Washington, D.C.: National Governors Association Center for Best Practices, Council of Chief State School Officers. Retrieved from
  34. NCTM. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: The National Council of Teachers of Mathematics.Google Scholar
  35. NCTM. (2000). Principles and standards for school mathematics. Reston, VA: The National Council of Teachers of Mathematics.Google Scholar
  36. NCTM. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  37. Niess, M. L. (2005). Preparing teachers to teach science and mathematics with technology: Developing a technology pedagogical content knowledge. Teaching and Teacher Education, 21(5), 509–523.CrossRefGoogle Scholar
  38. Niess, M. L. (2006). Guest editorial: Preparing teachers to teach mathematics with technology. Contemporary Issues in Technology and Teacher Education, 6(2), 195–203.Google Scholar
  39. Pea, R. (1985). Beyond amplification: Using the computer to reorganize mental functioning. Educational Psychologist, 20(4), 167–182.CrossRefGoogle Scholar
  40. Polya, G. (1945). How to solve it: A new aspect of mathematical method. Princeton, NJ: Princeton University Press.Google Scholar
  41. Presmeg, N. (2007). The role of culture in teaching and learning mathematics. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 1, pp. 435–460). Charlotte, NC: Information Age Publishing.Google Scholar
  42. Ryan, R. M., & Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. American Psychologist, 55(1), 68–78.CrossRefGoogle Scholar
  43. Santos-Trigo, M., & Machin, M. C. (2013). Framing the use of computational technology in problem solving approaches. Mathematics Enthusiast, 10(1), 279–302.Google Scholar
  44. Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. Zentralblatt für Didaktik der Mathematik, 29(3), 75–80. Scholar
  45. Simon, M. A., & Tzur, R. (2004). Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory. Mathematical Thinking and Learning, 6(2), 91–104.CrossRefGoogle Scholar
  46. Sowder, J. (2007). The mathematical education and development of teachers. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 157–224). Charlotte, NC: Information Age Publishing.Google Scholar
  47. Sriraman, B. (2004). The characteristics of mathematical creativity. The Mathematics Educator, 14(1), 19–34.Google Scholar
  48. Sriraman, B. (2009). The characteristics of mathematical creativity. ZDM Mathematics Education, 41, 13–27. Scholar
  49. Steen, L. (Ed.). (1990). On the shoulders of giants: New approaches to numeracy. Washington, D. C.: National Academy Press.Google Scholar
  50. Stein, M. K., Smith, M. S., Henningsen, M., & Silver, E. A. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. New York: Teachers College Press.Google Scholar
  51. Sternberg, R. J. (Ed.) (1988). The nature of creativity: Contemporary psychological perspectives. New York, NY: Cambridge University Press.Google Scholar
  52. Sullivan, F. R. (2017). Creativity, technology, and learning. New York, NY: Routledge.CrossRefGoogle Scholar
  53. Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12, 257–285.CrossRefGoogle Scholar
  54. Thompson, P. W. (2015). Researching mathematical meanings for teaching. In L. D. English & D. Kirshner (Eds.), Third handbook of international research in mathematics education (pp. 435–461). London, UK: Taylor and Francis.Google Scholar
  55. Thompson, P. W., Carlson, M. P., Byerley, C., & Hatfield, N. (2014). Schemes for thinking with magnitudes: A hypothesis about foundational reasoning abilities in algebra. In K. C. Moore, L. P. Steffe, & L. L. Hatfield (Eds.), Epistemic algebra students: Emerging models of students' algebraic knowing. WISDOMe Monographs (Vol. 4, pp. 1–24). Laramie, WY: University of Wyoming.Google Scholar
  56. Vygotsky, L. S. (2004). Imagination and creativity in childhood. Journal of Russian and East European Psychology, 42(1), 7–97.CrossRefGoogle Scholar
  57. Wilson, M., & Lloyd, G. M. (2000). Sharing mathematical authority with students: The challenge for high school teachers. Journal for Research in Mathematics Education, 15(2), 146–169.Google Scholar
  58. Wing, J. (2006). Computational thinking. Communications of the ACM, 49(3), 33–35.Google Scholar
  59. Zbiek, R. M., Heid, M. K., Blume, G. W., & Dick, T. P. (2007). Research on technology in mathematics education: A perspective of constructs. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 2, pp. 1169–1208). Charlotte, NC: Information Age Publishing.Google Scholar
  60. Zbiek, R. M., & Hollebrands, K. (2008). A research-informed view of the process of incorporating mathematics technology into classroom practice by in-service and prospective teachers. In M. K. Heid & G. W. Blume (Eds.), Research on technology and the teaching and learning of mathematics: Volume I. Research Syntheses. Charlotte, NC: Information Age Publishing Inc.Google Scholar

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of MassachusettsAmherstUSA

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