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Seeking research-grounded solutions to problems of practice: classroom-based interventions in mathematics education

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Abstract

Research on classroom-based interventions in mathematics education has two core aims: (a) to improve classroom practice by engineering ways to act upon problems of practice; and (b) to deepen theoretical understanding of classroom phenomena that relate to these problems. Although there are notable examples of classroom-based intervention studies in mathematics education research since at least the 1930s, the number of such studies is small and acutely disproportionate to the number of studies that have documented problems of classroom practice for which solutions are sorely needed. In this paper we first make a case for the importance of research on classroom-based interventions and identify three important features of this research, which we then use to review the papers in this special issue. We also consider the issue of ‘scaling up’ promising classroom-based interventions in mathematics education, and we discuss a major obstacle that most such interventions find on the way to scaling up. This obstacle relates to their long duration, which means that possible adoption of these interventions would require practitioners to do major reorganizations of the mathematics curricula they follow in order to accommodate the time demands of the interventions. We argue that it is important, and conjecture that it is possible, to design interventions of short duration in mathematics education to alleviate major problems of classroom practice. Such interventions would be more amenable to scaling up, for they would allow more control over confounding variables and would make more practicable their incorporation into existing curriculum structures.

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References

  • Alibali, M. W., Nathan, M. J., Church, R. B., Wolfgram, M. S., Kim, S., & Knuth, E. J. (2013). Teachers’ gestures and speech in mathematics lessons: Forging common ground by resolving trouble spots. ZDM—The International Journal on Mathematics Education, 45(3), this issue. doi:10.1007/s11858-012-0476-0.

  • Balacheff, N. (1988). Aspects of proof in pupils’ practice of school mathematics. In D. Pimm (Ed.), Mathematics, teachers and children (pp. 216–235). London: Hodder & Stoughton.

    Google Scholar 

  • Ball, D. L. (1990). Prospective elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education, 21(2), 132–144.

    Article  Google Scholar 

  • Bishop, A. J. (1998). Research, effectiveness, and the practitioners’ world. In A. Sierpinska & J. Kilpatrick (Eds.), Mathematics education as a research domain: A research for identity (an ICMI study) (pp. 33–45). London: Kluwer.

    Chapter  Google Scholar 

  • Cai, J., & Silver, E. A. (1995). Solution processes and interpretations of solutions in solving a division-with-remainder story problem: Do Chinese and U.S. students have similar difficulties? Journal for Research in Mathematics Education, 26(5), 491–497.

    Article  Google Scholar 

  • Chazan, D. (1993). High school geometry students’ justifications for their views of empirical evidence and mathematical proof. Educational Studies in Mathematics, 24(4), 359–387.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Cohen, D. K., & Hill, H. (2001). Learning policy: When state education reform works. New Haven, CT: Yale University Press.

    Google Scholar 

  • Cohen, G. L., Garcia, J., Apfel, N., & Master, A. (2006). Reducing the racial achievement gap: A social–psychological intervention. Science, 313, 1307–1310.

    Article  Google Scholar 

  • De Corte, E. (2007). Design experiments: A tool for bridging the theory–practice gap relating to education. Paper presented in a Symposium on ‘Design-based research: promises, potential and pitfalls’ at the 12th Biennial Conference for Research on Learning and Instruction, Budapest, Hungary.

  • Fawcett, H. P. (1938). The nature of proof (1938 Yearbook of the National Council of Teachers of Mathematics). New York, NY: Bureau of Publications, Teachers College, Columbia University.

    Google Scholar 

  • Harel, G., & Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. In A. H. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research in collegiate mathematics education III (pp. 234–283). Providence, RI: American Mathematical Society.

    Google Scholar 

  • Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31, 396–428.

    Article  Google Scholar 

  • Heid, K. M. (2010a). The task of research manuscripts—advancing the field of mathematics education. Journal for Research in Mathematics Education, 41, 434–437.

    Google Scholar 

  • Heid, K. M. (2010b). Where’s the math (in mathematics education research)? Journal for Research in Mathematics Education, 41, 102–103.

    Google Scholar 

  • Jahnke, H. N., & Wambach, R. (2013). Understanding what a proof is: A classroom-based approach. ZDM—The International Journal on Mathematics Education, 45(3), this issue. doi:10.1007/s11858-013-0502-x.

  • Kaasila, R., Pehkonen, E., & Hellinen, A. (2010). Finnish pre-service teachers’ and upper secondary students’ understanding of division and reasoning strategies used. Educational Studies in Mathematics, 73(3), 247–261.

    Article  Google Scholar 

  • Knuth, E. J., Choppin, J., Slaughter, M., & Sutherland, J. (2002). Mapping the conceptual terrain of middle school students’ competencies in justifying and proving. In D. S. Mewborn, P. Sztajn, D. Y. White, H. G. Weigel, R. L. Bryant, & K. Nooney (Eds.), Proceedings of the 24th annual meeting of the North American chapter of the international group for the psychology of mathematics education (Vol. 4, pp. 1693–1670). Athens, GA: Clearinghouse for Science, Mathematics, and Environmental Education.

  • Kulesza, M., Apperson, M., Larimer, M. E., & Copeland, A. L. (2010). Brief alcohol intervention for college drinkers: How brief is it? Addictive Behaviors, 35, 730–733.

    Article  Google Scholar 

  • Lehrer, R., Kobiela, M., & Weinberg, P. J. (2013). Cultivating inquiry about space in a middle school mathematics classroom. ZDM—The International Journal on Mathematics Education, 45(3), this issue. doi:10.1007/s11858-012-0479-x.

  • Li, Y., & Kulm, G. (2008). Knowledge and confidence of pre-service mathematics teachers: The case of fraction division. ZDM—The International Journal on Mathematics Education, 40, 833–843.

    Article  Google Scholar 

  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Malara, N. A., & Zan, R. (2008). The complex interplay between theory in mathematics education and teachers’ practice: Reflections and examples. In L. D. English (Ed.), Handbook of international research in mathematics education (2nd ed., pp. 535–560). New York, NY: Routledge.

    Google Scholar 

  • Mariotti, M. A. (2013). Introducing students to geometric theorems: How the teacher can exploit the semiotic potential of a DGS. ZDM—The International Journal on Mathematics Education, 45(3), this issue. doi:10.1007/s11858-013-0495-5.

  • Martin, W. G., & Harel, G. (1989). Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education, 20, 41–51.

    Article  Google Scholar 

  • Perrenet, J., & Taconis, R. (2009). Mathematical enculturation from the students’ perspective: Shifts in problem-solving behaviour during the bachelor programme. Educational Studies in Mathematics, 71, 181–198.

    Article  Google Scholar 

  • Philippou, G. N., & Christou, C. (1998). The effects of a preparatory mathematics program in changing prospective teachers’ attitudes towards mathematics. Educational Studies in Mathematics, 35, 189–206.

    Article  Google Scholar 

  • Roberts, N., & Stylianides, A. J. (2013). Telling and illustrating stories of parity: A classroom-based design experiment on young children’s use of narrative in mathematics. ZDM—The International Journal on Mathematics Education, 45(3), this issue. doi:10.1007/s11858-012-0474-2.

  • Ruthven, K., & Goodchild, S. (2008). Linking researching and teaching: Towards synergy of scholarly and craft knowledge. In L. D. English (Ed.), Handbook of international research in mathematics education (2nd ed., pp. 561–588). New York, NY: Routledge.

    Google Scholar 

  • Ruthven, K., & Hofmann, R. (2013). Chance by design: Devising an introductory probability module for implementation at scale in English early-secondary education. ZDM—The International Journal on Mathematics Education, 45(3), this issue. doi:10.1007/s11858-012-0470-6.

  • Saxe, G. B., Diakow, R., & Gearhart, M. (2013). Towards curricular coherence in integers and fractions: A study of the efficacy of a lesson sequence that uses the number line as the principal representational context. ZDM—The International Journal on Mathematics Education, 45(3), this issue. doi:10.1007/s11858-012-0466-2.

  • Schoenfeld, A. H. (2006). Design experiments. In J. L. Green, G. Camilli, & P. B. Elmore (with A. Skukauskaite, & E. Grace) (Eds.), Handbook of complementary methods in education research (pp. 193–205). Washington, DC: American Educational Research Association.

  • Schram, P., Wilcox, S. K., Lappan, G., & Lanier, P. (1988). Changing preservice teachers’ beliefs about mathematics education. In C. A. Mahers, G. A. Goldin, & R. B. Davis (Eds.), Proceedings of the 11th conference of the North American group for the psychology of mathematics education (Vol. 1, pp. 296–302). New Brunswick, NY: Rutgers University.

  • Shilling-Traina, L. N., & Stylianides, G. J. (2013). Impacting prospective teachers’ beliefs about mathematics. ZDM—The International Journal on Mathematics Education, 45(3), this issue. doi:10.1007/s11858-012-0461-7.

  • Sierpinska, A., & Kilpatrick, J. (Eds.). (1998). Mathematics education as a research domain: A research for identity (an ICMI study). London: Kluwer.

    Google Scholar 

  • Simon, M. A. (1993). Prospective elementary teachers’ knowledge of division. Journal for Research in Mathematics Education, 24(3), 233–254.

    Article  Google Scholar 

  • Simon, M. A., & Blume, G. W. (1996). Justification in the mathematics classroom: A study of prospective elementary teachers. Journal of Mathematical Behavior, 15, 3–31.

    Article  Google Scholar 

  • Stevenson, A., & Lindberg, C. A. (Eds.) (2012). New Oxford American Dictionary (3rd ed.). Oxford: Oxford University Press. http://www.oxfordreference.com/view/10.1093/acref/9780195392883.001.0001/acref-9780195392883. Accessed 25 Mar 2013.

  • Stylianides, A. J. (2009). Breaking the equation “empirical argument = proof”. Mathematics Teaching, 213, 9–14.

    Google Scholar 

  • Stylianides, A. J., & Stylianides, G. J. (2009a). Proof constructions and evaluations. Educational Studies in Mathematics, 72(2), 237–253.

    Article  Google Scholar 

  • Stylianides, G. J., & Stylianides, A. J. (2009b). Facilitating the transition from empirical arguments to proof. Journal for Research in Mathematics Education, 40, 314–352.

    Google Scholar 

  • Stylianides, A. J., & Stylianides, G. J. (forthcoming). Impacting positively on students’ mathematical problem solving beliefs: An instructional intervention of short duration. Journal of Mathematical Behavior.

  • Swars, S. L., Smith, S. Z., Smith, M. E., & Hart, L. C. (2009). A longitudinal study of effects of a developmental teacher preparation program on elementary prospective teachers’ mathematics beliefs. Journal of Mathematics Teacher Education, 12, 47–66.

    Article  Google Scholar 

  • Tabach, M., Hershkowitz, R., & Dreyfus, T. (2013). Learning beginning algebra in a computer-intensive environment. ZDM—The International Journal on Mathematics Education, 45(3), this issue. doi:10.1007/s11858-012-0458-2.

  • Tabak, I. (2004). Reconstructing context: Negotiating the tension between exogenous and endogenous educational design. Educational Psychologist, 39(4), 225–233.

    Article  Google Scholar 

  • Tirosh, D., & Graeber, A. O. (1990). Evoking cognitive conflict to explore preservice teachers’ thinking about division. Journal for Research in Mathematics Education, 21(2), 98–108.

    Article  Google Scholar 

  • Valero, P., & Vithal, R. (1998). Research methods of the ‘north’ revisited from the ‘south’. In A. Olivier, & K. Newstead (Eds.), Proceedings of the 22nd conference of the international group for the psychology of mathematics education (Vol. 4, pp. 153–160). Stellenbosch, South Africa.

  • Walton, G. M., & Cohen, G. L. (2007). A question of belonging: Race, social fit, and achievement. Journal of Personality and Social Psychology, 92, 82–96.

    Article  Google Scholar 

  • Walton, G. M., & Cohen, G. L. (2011). A brief social-belonging intervention improves academic and health outcomes among minority students. Science, 331, 1447–1451.

    Article  Google Scholar 

  • Wiliam, D., & Lester, F. K. (2008). On the purpose of mathematics education research: Making productive contributions to policy and practice. In L. D. English (Ed.), Handbook of international research in mathematics education (2nd ed., pp. 32–48). New York, NY: Routledge.

    Google Scholar 

  • Wittmann, E. C. (2001). Developing mathematics education in a systemic process. Educational Studies in Mathematics, 48(1), 1–20.

    Article  Google Scholar 

  • Yeager, D. S., & Walton, G. M. (2011). Social–psychological interventions in education: They’re not magic. Review of Educational Research, 81, 267–301.

    Article  Google Scholar 

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Authors and Affiliations

  1. Faculty of Education, University of Cambridge, 184 Hills Road, Cambridge, CB2 8PQ, UK

    Andreas J. Stylianides

  2. Department of Education, University of Oxford, 15 Norham Gardens, Oxford, OX2 6PY, UK

    Gabriel J. Stylianides

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  1. Andreas J. Stylianides
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  2. Gabriel J. Stylianides
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Correspondence to Andreas J. Stylianides.

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We contributed equally both to the preparation of this paper and to the preparation of this special issue as Guest Editors. The order of our names is alphabetical.

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Stylianides, A.J., Stylianides, G.J. Seeking research-grounded solutions to problems of practice: classroom-based interventions in mathematics education. ZDM Mathematics Education 45, 333–341 (2013). https://doi.org/10.1007/s11858-013-0501-y

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