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Conducting classroom design research with teachers

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Abstract

Design research is usually motivated by university members with experience and interest in building theory and instructional designs in collaboration with one teacher. Typically, the teacher is considered as a member of the research team, with the primary responsibility of implementing instruction. However, in this chapter, I describe a Classroom Design Research project that was conducted by a team comprised mostly of classroom teachers. Their goal was to create a stable instructional unit for integer addition and subtraction that they could use to help students learn the topic with meaning. In this paper, I outline the basic tenets of Classroom Design Research, including the instructional theory of Realistic Mathematics Education and how it guided them in designing instruction. I introduce the construct of a classroom learning trajectory and elaborate on it with the integer project. Finally, I argue that Design Research is mutually beneficial for researchers and teachers. The team of teachers that participated in Design Research embarked on a unique professional development experience, one in which they engaged in practices that supported a new way of preparing their instruction. Reciprocally, the teachers’ unique craft and pedagogical content knowledge shaped the integer instruction theory in unique ways that do not occur in typical Design Research.

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References

  • Battista, M. T. (1983). A complete model for operations on integers. Arithmetic Teacher, 30(9), 26–31.

    Google Scholar 

  • Bofferding, L. (2010). Addition and subtraction with negatives: acknowledging the multiple meanings of the minus sign. In P. Brosnan, D. B. Erchick, & L. Flevares (Eds.), Proceedings of the 32nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 703–710). Columbus: The Ohio State University.

    Google Scholar 

  • Burkhardt, H. & Swan, M. (2013). Task design for systemic improvement: principles and frameworks (pp. 431–440). Proceedings of the International Commission on Mathematical Instruction, Oxford.

  • Clements, D., & Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical Thinking and Learning, 6(2), 81–89.

    Article  Google Scholar 

  • Cobb, P. (2000). Conducting teaching experiments in collaboration with teachers. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 307–334). Mahwah: Erlbaum.

    Google Scholar 

  • Cobb, P. (2003). Investigating students’ reasoning about linear measurement as a paradigm case of design research. In N. Pateman (Series Ed.), M. Stephan, J. Bowers, & P. Cobb (with K. Gravemeijer) (Vol. Eds.), Journal for Research in Mathematics Education Monograph Series: Vol. 12. Supporting students’ development of measuring conceptions: analyzing students’ learning in social context (pp. 1–16). Reston: National Council of Teachers of Mathematics.

  • Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13. doi:10.3102/0013189X032001009.

    Article  Google Scholar 

  • Cobb, P., Gravemeijer, K., Yackel, E., McClain, K., & Whitenack, J. (1997). Mathematizing and symbolizing: the emergence of chains of signification in one first-grade classroom. In D. Kirshner & J. A. Whitson (Eds.), Situated cognition: social, semiotic, and psychological perspectives (pp. 151–233). Mahwah: Erlbaum.

    Google Scholar 

  • Cobb, P., & Jackson, K. (2011). Towards an empirically grounded theory of action for improving the quality of mathematics teaching at scale. Mathematics Teacher Education and Development, 13(1), 6–33.

    Google Scholar 

  • Cobb, P., & Jackson, K. (2015). Supporting teachers’ use of research-based instructional sequences. ZDM—The International Journal on Mathematics Education, 47(6) (this issue).

  • Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31, 175–190.

    Article  Google Scholar 

  • Confrey, J., & Lachance, A. (2000). Transformative reading experiments through conjecture-driven research design. In A. E. Kelly & A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 231–266). Mahwah: Erlbaum.

    Google Scholar 

  • Confrey, J., Maloney, A., Nguyen, K., Mojica, G., & Myers, M. (2009). Equipartitioning/splitting as a foundation of rational number reasoning. In M. Tzekaki, M. Kaldrimidou, & C. Sakonidis (Eds.), Proceedings of the 33rd conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 345–352). Thessaloniki: PME.

    Google Scholar 

  • Corcoran, T., Mosher, F., & Rogat, A. (2009). Learning progressions in science: an evidence-based approach to reform. Philadelphia: Consortium for Policy Research in Education.

    Google Scholar 

  • Daro, P., Mosher, F., & Cocoran, T. (2011). Learning trajectories in mathematics: A foundation for standards, curriculum, assessment, and instruction. Philadelphia: Consortium for Policy Research in Education.

    Google Scholar 

  • De Beer, H., Gravemeijer, K., & van Eijck, M. (2015). Discrete and continuous reasoning about change in primary school classrooms. ZDM—The International Journal on Mathematics Education, 47(6) (this issue).

  • Doorman, M., & Gravemeijer, K. (2008). Emergent modeling: discrete graphs to support the understanding of change and velocity. ZDM—The International Journal on Mathematics Education, 41, 199–211. doi:10.1007/s11858-008-0130-z.

    Article  Google Scholar 

  • Fosnot, C. T., & Dolk, M. (2005). “Mathematics” or “mathematizing”? In C. T. Fosnot (Ed.), Constructivism: theory, perspectives and practice (2nd ed., pp. 175–191). New York: Teachers College Press.

    Google Scholar 

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

  • Gallardo, A. (2002). The extension of the natural-number domain to the integers in the transition from arithmetic to algebra. Educational Studies in Mathematics, 49, 171–192. doi:10.1023/A:1016210906658.

    Article  Google Scholar 

  • Garcia, J. & Ruiz-Higueras, L (2013). Task design within the anthropological theory of the didactics: study and research courses for pre-school (pp. 421–430). In Proceedings of the International Commission on Mathematical Instruction, Oxford.

  • Glaeser, G. (1981). Epistémologie des nombres relatifs. Recherches en Didactique des Mathématiques, 2, 303–346.

    Google Scholar 

  • Glaser, B., & Strauss, A. (1967). The discovery of grounded research: strategies for qualitative research. New York: Aldine De Gruyter.

    Google Scholar 

  • Gravemeijer, K. (1994). Developing realistic mathematics education. Utrecht: CD Press.

  • Gravemeijer, K. (2004). Local instruction theories as a means of support for teachers in reform mathematics education. Mathematical Thinking and Learning, 6(2), 105–128.

    Article  Google Scholar 

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

    Chapter  Google Scholar 

  • Gravemeijer, K., & van Eerde, D. (2009). Design research as a means for building a knowledge vase for teachers and teaching in mathematics education. The Elementary School Journal, 109(5), 510–524.

    Article  Google Scholar 

  • Koichu, B., Zaslavsky, O., & Dolev, L. (2013). Effects of variations in task design using different representations of mathematical objects on learning: a case of a sorting task. In C. Margolinas (Ed.), Task design in mathematics education (pp. 461–470). Oxford: Proceedings of the International Commission on Mathematical Instruction.

    Google Scholar 

  • Lampert, M., Beasley, H., Ghousseini, H., Kazemi, E., & Franke, M. (2010). Using designed instructional activities to enable novices to manage ambitious mathematics teaching. In M.K. Stein, & L. Kucan (Eds.), Instructional explanations in the disciplines. doi:10.1007/978-1-4419-0594-9_9. New York: Springer, LLC.

  • Lampert, M., Franke, M., Kazemi, E., Ghousseini, H., Turrou, A., Beasley, H., et al. (2013). Keeping it complex: using rehearsals to support novice teacher learning of ambitious teaching. Journal of Teacher Education, 64(3), 226–243. doi:10.1177/0022487112473837.

    Article  Google Scholar 

  • Lappan, G., Fey, J., Fitzgerald, W., Friel, S., & Phillips, E. (2002). Connected mathematics. Upper Saddle River: Prentice Hall.

    Google Scholar 

  • Linchevski, L., & Williams, J. (1999). Using intuition from everyday life in “filling” the gap in children’s extension of their number concept to include the negative numbers. Educational Studies in Mathematics, 39, 131–147. doi:10.1023/A:1003726317920.

    Article  Google Scholar 

  • Lytle, P. A. (1994). Investigation of a model based on the neutralization of opposites to teach integer addition and subtraction. In J. P. da Ponte & J. F. Matos (Eds.), Proceedings of the 18th international conference for the psychology of mathematics education (Vol. III, pp. 192–199). Lisbon: University of Lisbon.

    Google Scholar 

  • Peled, I., Mukhopadhyay, S., & Resnick, L. B. (1989). Formal and informal sources of mental models for negative numbers. In G. Vergnaud, J. Rogalski, & M. Artigue (Eds.), Proceedings of the 13th international conference for the psychology of mathematics education (Vol. III, pp. 106–110). Paris: PME.

    Google Scholar 

  • Prediger, S. & Krägeloh, K. (2015). Low achievers learning to crack algebraic word problems—a design research project for aligning a strategic scaffolding tool to students’ mental processes. ZDM—The International Journal on Mathematics Education, 47(6) (this issue).

  • Rasmussen, C., Stephan, M., & Whitehead, K. (2004). Classroom mathematical practices and gesturing. Journal of Mathematical Behavior, 23, 301–323.

    Article  Google Scholar 

  • Schoenfeld, A. (2000). Models of the teaching process. Journal of Mathematical Behavior, 18(3), 243–261.

    Article  Google Scholar 

  • Schwarz, B. B., Kohn, A. S., & Resnick, L. B. (1993/1994). Positives about negatives: a case study of an intermediate model for signed numbers. The Journal of the Learning Sciences, 3, 37–92. doi:10.1207/s15327809jls0301_2.

  • Shulman, L. S. (1986). Those who understand: knowledge growth in teaching. Educational Researcher, 75(2), 4–14.

    Article  Google Scholar 

  • Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26, 114–145. doi:10.2307/749205.

    Article  Google Scholar 

  • Smith, J. P. (1995). The effects of a computer microworld on middle school students’ use and understanding of integers (unpublished doctoral dissertation). The Ohio State University, Columbus. http://rave.ohiolink.edu/etdc/view?acc_num=osu1248798217.

  • Steffe, L., & Olive, J. (2010). Children’s fractional knowledge. New York: Springer.

    Book  Google Scholar 

  • Steffe, L. P., von Glasersfeld, E., Richards, J., & Cobb, P. (1983). Children’s counting types: philosophy, theory, and application. New York: Praeger.

    Google Scholar 

  • Stephan, M., & Akyuz, D. (2012). A proposed instructional theory for integer addition and subtraction. Journal for Research in Mathematics Education, 43(4), 428–464.

    Article  Google Scholar 

  • Stephan, M., Akyuz, D., McManus, G., & Smith, J. (2012). Conditions that support the creation of a middle-school mathematics communities of learners. NCSM Journal of Mathematics Education Leadership, 14(1), 19–27.

    Google Scholar 

  • Stephan, M., Bowers, J., Cobb, P., & Gravemeijer K. (Eds.). (2003). Journal for Research in Mathematics Education Monograph Series: Vol. 12. Supporting students’ development of measuring conceptions: analyzing students’ learning in social context (N. Pateman, Series Ed.). Reston: National Council of Teachers of Mathematics.

  • Stephan, M. & Cobb, P. (2013). Teachers engaging in integer design research. In T. Plomp & N. Nieveen (Eds.), Educational design research: introduction and illustrative cases (pp. 277–298). Enschede: SLO (Netherlands institute for curriculum development).

  • Streefland, L. (1996). Negative numbers: reflections of a learning researcher. Journal of Mathematical Behavior, 15, 57–79. doi:10.1016/S0732-3123(96)90040-1.

    Article  Google Scholar 

  • Thompson, P. W., & Dreyfus, T. (1988). Integers as transformations. Journal for Research in Mathematics Education, 19, 115–133. doi:10.2307/749406.

    Article  Google Scholar 

  • Van den Heuvel-Panhuizen, M., & Drijvers, P. (in press). Realistic mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education. Dordrecht: Springer.

  • Vlassis, J. (2008). The role of mathematical symbols in the development of number conceptualization: the case of the minus sign. Philosophical Psychology, 21, 555–570. doi:10.1080/09515080802285552.

    Article  Google Scholar 

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Correspondence to Michelle. L. Stephan.

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Stephan, M.L. Conducting classroom design research with teachers. ZDM Mathematics Education 47, 905–917 (2015). https://doi.org/10.1007/s11858-014-0651-6

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