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Guiding Mathematical Inquiry in Mobile Settings

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Constructing Knowledge for Teaching Secondary Mathematics

Part of the book series: Mathematics Teacher Education ((MTEN,volume 6))

Abstract

Engaging mathematics students in active exploration of real-life scenarios and supporting inquiry processes are major challenges for teachers. It requires a shift in the teacher’s role from lecturing and telling to listening, observing, facilitating, and guiding. In our exploratory work we found that mobile devices can offer a challenging setting for educators to deepen their thinking about sensing mathematics and about socially constructing and mediating mathematical knowledge. The unique qualities of this setting follow from the mobility that enables learners to share knowledge. To demonstrate the possibilities of such a setting, we present innovative function graphing applications for mobile phones and a sequence of tasks designed to support the qualitative and quantitative inquiry of functions. We suggest that by engaging in such tasks, mathematics teachers can rethink their pedagogical, curricular, and subject matter knowledge, connect mathematical knowledge with real-life contexts, and interact socially in ways that support the creation of a community of proficient mathematics teachers.

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References

  • Botzer, G., & Yerushalmy, M. (2007). Mobile applications for mobile learning. In Kinshuk, D. G. Sampson, M. Spector, & P. Isaias (Eds.), Proceedings of the cognition & exploratory learning in digital age (CELDA) conference (pp. 313–316). Algrave: IADIS Press.

    Google Scholar 

  • Carrejo, D. J., & Marshall, J. (2007). What is mathematical modelling? Exploring prospective teachers’ use of experiments to connect mathematics to the study of motion. Mathematics Education Research Journal, 19(1), 45–76.

    Article  Google Scholar 

  • Chazan, D., & Schnepp, M. (2002). Methods, goals beliefs, commitments, and manner in teaching: dialogue against a calculus backdrop. In J. Brophy (Ed.), Social constructivist teaching (Vol. 9, pp. 171–195). Greenwich: JAI Press.

    Google Scholar 

  • Cobb, P. (2002). Reasoning with tools and inscriptions. The Journal of the Learning Sciences, 11(2–3), 187–215.

    Google Scholar 

  • Daher, W. (2009). Students’ perceptions of learning mathematics with cellular phones and applets. International Journal of Emerging Technologies in Learning, 4(1), 23–28.

    Google Scholar 

  • Genossar, S., Botzer, G., & Yerushalmy, M. (2008, February 6). Learning with mobile technology: A case study with students in mathematics education. Proceedings of the CHAIS Conference on Instructional Technologies Research. (in Hebrew).

    Google Scholar 

  • Gravemeijer, K., & Stephan, M. (2002). Emergent models as an instructional design heuristic. In K. R. Gravemeijer, R. Lehrer, B. van Oers, & L. Verschaffel (Eds.), Symbolizing, modelling and tool use in mathematics education (pp. 145–169). Dordrecht: Kluwer Academic.

    Chapter  Google Scholar 

  • Hegedus, S., & Kaput, J. (2003). Exciting new opportunities to make mathematics an expressive classroom activity using newly emerging connectivity technology. In N. A. Pateman, B. J. Dougherty & J. Zilliox (Eds.), Proceedings of the 27th conference of the PME-NA (Vol. 1, p. 293). Honolulu: College of Education, University of Hawaii.

    Google Scholar 

  • Hoppe, H. U., Joiner, R., Milrad, M., & Sharples, M. (2003). Wireless and mobile technologies in education. Journal of Computer Assisted Learning, 19(3), 255–261.

    Article  Google Scholar 

  • Johnson, L., Levine, A., & Smith, R. (2009). The 2009 horizon report. Austin: The New Media Consortium.

    Google Scholar 

  • Kaput, J. J., & Roschelle, J. (1997). Deepening the impact of technology beyond assistance with traditional formalisms in order to democratize access to ideas underlying calculus. In E. Pehkonen (Ed.), Proceedings of the 21st conference of the international group for the psychology of mathematics education (Vol. 1, pp. 105–112). Lahti: PME.

    Google Scholar 

  • Kieran, C., & Yerushalmy, M. (2004). Research on the role of technological environments in algebra learning and teaching. In K. Stacey, H. Shick, & M. Kendal (Eds.), The future of the teaching and learning of algebra. The 12th ICMI study. New ICMI (International Commission on Mathematical Instruction) study series (Vol. 8, pp. 99–152). Dordrecht: Kluwer Academic.

    Google Scholar 

  • Lehrer, R., & Schauble, L. (2000). Modelling in mathematics and science. In R. Glaser (Ed.), Advances in instructional psychology: Educational design and cognitive science (Vol. 5, pp. 101–159). Mahwah: Lawrence Erlbaum.

    Google Scholar 

  • Leikin, R. (2004). Towards high quality geometrical tasks: Reformulation of a proof problem. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th international conference for the psychology of mathematics education (Vol. 3, pp. 209–216). Bergen: Bergen University College.

    Google Scholar 

  • Liu, C. C., & Kao, L. C. (2007). Do handheld devices facilitate face-to-face collaboration? Handheld devices with large shared display groupware to facilitate group interactions. Journal of Computer Assisted Learning, 23, 285–299.

    Article  Google Scholar 

  • Low, L., & O’Connell, M. (2006). Learner-centric design of digital mobile learning. Paper presented at Learning on the Move, Brisbane, Australia.

    Google Scholar 

  • Mazur, E. (1997). Peer instruction: A user’s manual. Englewood Cliffs: Prentice Hall.

    Google Scholar 

  • Naismith, L., Lonsdale, P., Vavoula, G., & Sharples, M. (2004). Literature review in mobile technologies and learning, Report 11, Future lab Series. http://www.futurelab.org.uk/research/reviews/reviews_11_and12/11_01.htm.

  • Nemirovsky, R., & Borba, M. (2003). Perceptuo-motor activity and imagination in mathematics learning. In N. A. Pateman, B. J. Dougherty, & J. Zilliox (Eds.), Proceedings of the 27th conference of the PME-NA (Vol. 1, pp. 103–104). Honolulu: College of Education, University of Hawaii.

    Google Scholar 

  • Pachler, N., Bachmair, B., & Cook, J. (2010). Mobile Learning: Structures, Agency, Practices. New York: Springer.

    Book  Google Scholar 

  • Roschelle, J., Vahey, P., Tatar, D., Kaput, J., & Hegedus, S. J. (2003). Five key considerations for networking in a handheld-based mathematics classroom. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 2003 joint meeting of PME and PMENA (Vol. 4, pp. 71–78). Honolulu: University of Hawaii.

    Google Scholar 

  • Roschelle, J., Patton, C., & Tatar, D. (2007). Designing networked handheld devices to enhance school learning. In M. Zelkowitz (Ed.), Advances in computers (Vol. 70, pp. 1–60). London: Elsevier.

    Google Scholar 

  • Scardamalia, M., & Bereiter, C. (2002). Knowledge building. Encyclopedia of education (2nd ed.). New York: Macmillan Reference.

    Google Scholar 

  • Schwartz, J., & Yerushalmy, M. (1995). On the need for a bridging language for mathematical modeling. For the Learning of Mathematics, 15(2), 29–35.

    Google Scholar 

  • Sever, G., & Yerushalmy, M. (2007). To sense and to visualize functions: The case of graphs’ stretching. In P. P. Demetra & P. George (Eds.), The Fifth Conference of the European Society for Research in Mathematics Education (CERME5) (pp. 1509–1518). Larnaca: Department of Education, University of Cyprus.

    Google Scholar 

  • Sharples, M. (2000). The design of personal mobile technologies for lifelong learning. Computers & Education, 34(3–4), 177–193.

    Article  Google Scholar 

  • Sharples, M. (2009). Methods for evaluating mobile learning. In G. N. Vavoula, N. Pachler, & A. Kukulska-Hulme (Eds.), Researching mobile learning: Frameworks, tools and research design. Oxford: Peter Lang, pp. 17–39.

    Google Scholar 

  • Shternberg, B., & Yerushalmy, M. (2003). Models of functions and models of situations: On design of a modeling based learning environment. In H. M. Doerr & R. Lesh (Eds.). Beyond constructivism: A model and modeling perspective on teaching, learning, and problem solving in mathematics education (pp. 479–500). Mahwah: Lawrence Erlbaum.

    Google Scholar 

  • Shuler, C. (2009). Pockets of potential. The Joan Ganz Cooney Center at Sesame Workshop. http://joanganzcooneycenter.org/pdf/pockets_of_potential.pdf. Accessed 10 June.

    Google Scholar 

  • Tinker, R. (2001). E-learning quality: The Concord model for learning from a distance. Bulletin of the National Association of Secondary School Principals, 85(628), 36–46.

    Google Scholar 

  • Vahey, P., Tatar, D., & Roschelle, J. (2004). Leveraging handhelds to increase student learning: Engaging middle school students with the mathematics of change. In Y. B. Kafai, W. A. Sandoval, N. Enyedy, A. S. Nixon, & F. Herrera (Eds.), Proceedings of the 6th international conference on learning sciences (pp. 553–560). Mahwah: Lawrence Erlbaum.

    Google Scholar 

  • Wagner, E. D. (2005). Enabling mobile learning. EDUCASE Review, 40(3), 40–53.

    Google Scholar 

  • Wei, F., Chen, G., Wang, C., & Yi-Li, L. (2007). Ubiquitous discussion forum: Introducing mobile phones and voice discussion into a web discussion forum, Journal of Educational Multimedia and Hypermedia, 16(2), 125–140

    Google Scholar 

  • Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477.

    Article  Google Scholar 

  • Yerushalmy, M., & Shternberg, B. (2001). Charting visual course to the concept of function. In A. A. Cuoco & F. R. Curcio (Eds.), The roles of representation in school mathematics (Yearbook of the national council of teachers of mathematics) (pp. 90–102). Reston: NCTM.

    Google Scholar 

  • Yerushalmy, M., Weizman, A., & Shavit, Z. (2006). Math4Mobile. http://www.Math4Mobile.com/

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Correspondence to Michal Yerushalmy .

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Yerushalmy, M., Botzer, G. (2011). Guiding Mathematical Inquiry in Mobile Settings. In: Zaslavsky, O., Sullivan, P. (eds) Constructing Knowledge for Teaching Secondary Mathematics. Mathematics Teacher Education, vol 6. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-09812-8_12

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