Theorizing in Design Research: Methodological reflections on developing and connecting theory elements for language-responsive mathematics classrooms

Referencias

Adler, J. (2001). Teaching mathematics in multilingual classrooms. Dordrecht, Netherlands: Kluwer. Bailey, A. L. (2007). The language demands of school: Putting academic English to the test. New Haven, CT: Yale. Bakker, A. (2018). Design Research in education. London, England: Routledge. Barab, S., & Squire, K. (Eds.) (2004). Design-Based Research: Clarifying the terms. Journal of the Learning Sciences, 13(1), Special Issue. Barwell, R., Clarkson, P., Halai, A., Kazima, M., Moschkovich, J., Planas, N. ...Villavicencio, M. (Eds.) (2016). Mathematics education and language diversity. The 21st ICMI Study. Dordrecht, Netherlands: Springer. Beck, K., & Krapp, A. (2006). Wissenschaftstheoretische Grundfragen der Pädagogischen Psychologie. In A. Krapp & B. Weidenmann (Eds.), Pädagogische Psychologie (4th ed., pp. 33-73). Weinheim, Germany: Beltz. Blum, W., Artigue, M., Mariotti, M. A., Sträßer, R. & van den Heuvel Panhuizen, M. (Eds.) (2019). European traditions in Didactics of Mathematics. Cham, Switzerland: Springer. Bruner, J. (1966). Toward a theory of instruction. Cambridge, MA: Harvard University Press. Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design Experiments in Educational Research. Educational Researcher, 32(1), 9-13. Cobb, P., Jackson, K., & Dunlap, C. (2016). Design Research: An analysis and critique. In L. D. English & D. Kirshner (Eds.), Handbook of international research in mathematics education (pp. 481-503). New York: Routledge. Confrey, J. (2006). The evolution of design studies as methodology. In K. R. Sawyer (Ed.), The Cambridge handbook of the learning sciences (pp. 135-152). Cambridge, MA: Cambridge University Press. Cramer, K., Behr, M., Post, T., & Lesh, R. (1997). Rational Number Project: Fraction lessons for the middle grades - Level 1. Dubuque, IA: Kendall/Hunt Publishing. Creswell, J.W. (2003). Research design: Qualitative, quantitative, and mixed methods approaches (2nd ed.). Thousand Oaks, CA: Sage. Cummins, J. (1986). Language proficiency and academic achievement. In J. Cummins & M. Swain (Eds.), Bilingualism in education: Aspects of theory, research and practice (pp. 138-161). London, England: Longman. DIME - Diversity in Mathematics Education Center for Learning and Teaching (2007). Culture, race, power in mathematics education. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 405-433). Charlotte, NC: Information Age. diSessa, A. A., & Cobb, P. (2004). Ontological innovation and the role of theory in design experiments. Journal of the Learning Sciences, 13(1), 77-103. Duit, R., Gropengießer, H., & Kattmann, U. (2005). Towards science education that is relevant for improving practice: The model of educational reconstruction. In H. E. Fischer (Ed.), Developing standards in research on science rducation (pp. 1-9). London, England: Taylor & Francis. Erath, K., Prediger, S., Quasthoff, U., & Heller, V. (2018). Discourse competence as important part of academic language proficiency in mathematics classrooms: The case of explaining to learn and learning to explain. Educational Studies in Mathematics, 99(2), 161-179. Gibbons, P. (2002). Scaffolding language, scaffolding learning. Teaching second language learners in the mainstream classroom. Portsmouth, England: Heinemann. Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics. Mathematical Thinking and Learning, 1(2), 155-177. Gravemeijer, K., & Cobb, P. (2006). Design Research from a learning design perspective. In J. van den Akker, K. Gravemeijer, S. McKenney, & N. Nieveen (Eds.), Educational Design Research: The design, development and evaluation of programs, processes and products (pp. 17-51). London, England: Routledge. Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65-97). New York: Macmillan. Hußmann, S., & Prediger, S. (2016). Specifying and structuring mathematical topics – a four- level approach for combining formal, semantic, concrete, and empirical levels exemplified for exponential growth. Journal für Mathematik-Didaktik, 37(Suppl. 1), 33-67. Hußmann, S., Thiele, J., Hinz, R., Prediger, S., & Ralle, B. (2013). Gegenstandsorientierte Unterrichtsdesigns entwickeln und erforschen - Fachdidaktische Entwicklungsforschung im Dortmunder Modell. In M. Komorek & S. Prediger (Eds.), Der lange Weg zum Unterrichtsdesign: Zur Begründung und Umsetzung genuin fachdidaktischer Forschungs- und Entwicklungsprogramme (pp. 19-36). Münster, Germany: Waxmann. ICMI (2009/2016). ICMI Study 21 Discussion Document: Mathematics Education and Language Diversity. Re-published in Barwell, R., Clarkson, P., Halai, A., Kazima, M., Moschkovich, J., Planas, N. ... Villavicencio, M. (Eds.). (2016). Mathematics education and language diversity: The 21st ICMI Study (pp. 297-308). Dordrecht, Netherlands: Springer. Lesh, R. (1979). Mathematical learning disabilities. In R. Lesh, D. Mierkiewicz, & M. Kantowski (Eds.), Applied mathematical problem solving (pp. 111-180). Columbus, OH: Ericismeac. Mason, J., & Waywood, A. (1996). The role of theory in mathematics education and research. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 1055-1089). Dordrecht, Netherlands: Kluwer. Mason, J., Graham, A., Pimm, D., & Gowar, N. (1985). Routes to/Roots of Algebra. Milton Keynes, England: University Press. McKenney, S., & Reeves, T. (2012). Conducting educational design research. London, England: Routledge. Moschkovich, J. (2013). Principles and guidelines for equitable mathematics teaching practices and materials for English Language Learners. Journal of Urban Mathematics Education, 6(1), 45-57. Niss, M. (2007). Reflections on the state of and trends in research in mathematics teaching and learning. From here to utopia. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 1293-1312). Reston, VA: NCTM. OECD (2007). PISA 2006. Science competencies for tomorrow's world (Vol. 2). Paris: OECD. Planas, N. (2018). Language as resource: A key notion for understanding the complexity of mathematics learning. Educational Studies in Mathematics, 98(3), 215-229. Plomp, T., & Nieveen, N. (2013). Educational Design Research: Illustrative cases. Enschede: SLO, Netherlands Institute for Curriculum Development. Pöhler, B., & Prediger, S. (2015). Intertwining lexical and conceptual learning trajectories. Eurasia Journal of Mathematics, Science, & Technology Education, 11(6), 1697-1722. Prediger, S. (2015). Theorien und Theoriebildung in didaktischer Forschung und Entwicklung. In R. Bruder, L. Hefendehl-Hebeker, B. Schmidt-Thieme & H.-G. Weigand (Eds.), Handbuch der Mathematikdidaktik (pp. 643-662). Heidelberg, Germany: Springer. Prediger, S. (2019, online first). Promoting and investigating teachers’ pathways towards expertise for language-responsive mathematics teaching. Mathematics Education Research Journal. doi: 10.1007/s13394-019-00258-1 Prediger, S., & Hein, K. (2017). Learning to meet language demands in multi-step mathematical argumentations: Design Research on a subject-specific genre. European Journal of Applied Linguistics, 5(2), 309-335. Prediger, S., & Krägeloh, N. (2015). The epistemic role of languages while constructing meaning for the variable as generalizers. In A. Halai & P. Clarkson (Eds.), Teaching and learning mathematics in multilingual classrooms (pp. 89-108). Rotterdam, Netherlands: Sense Publishers. Prediger, S., & Neugebauer, P. (2019, in preparation). Can monolingual and multilingual students equally profit from a language-responsive instructional approach for percentages? Differential effectiveness in a field trial study. Manuscript in preparation. Prediger, S., & Wessel, L. (2013). Fostering German language learners’ constructions of meanings for fractions – Design and effects of a language- and mathematics-integrated intervention. Mathematics Education Research Journal, 25(3), 435-456. Prediger, S., & Zindel, C. (2017). School academic language demands for understanding functional relationships: A design research project on the role of language in reading and learning. Eurasia Journal of Mathematics, Science and Technology Education, 13(7b), 4157-4188. Prediger, S., & Zwetzschler, L. (2013). Topic-specific Design Research with a focus on learning processes: The case of understanding algebraic equivalence in grade 8. In T. Plomp & N. Nieveen (Eds.), Educational Design Research: Illustrative cases (pp. 407- 424). Enschede: SLO, Netherlands Institute for Curriculum Development. Prediger, S., Clarkson, P., & Bose, A. (2016). Purposefully relating multilingual registers: Building theory and teaching strategies for bilingual learners based on an integration of three traditions. In R. Barwell, P. Clarkson, A. Halai, M. Kazima, J. Moschkovich, N. Planas ... M. Villavicencio (Eds.), Mathematics education and language diversity. The 21st ICMI Study (pp. 193-215). Dordrecht, Netherlands: Springer. Prediger, S., Wilhelm, N., Büchter, A., Gürsoy, E., & Benholz, C. (2018). Language proficiency and mathematics achievement – Empirical study of language-induced obstacles in a high stakes test, the central exam ZP10. Journal für Mathematik-Didaktik, 39(Supp. 1), 1-26. Presmeg, N. C. (1998). A semiotic analysis of students’ own cultural mathematics. Research forum report. In A. Olivier & K Newstead (Eds.), Proceedings of the 22nd Conference of PME (Vol. 1, pp. 136-151). Stellenbosch, SA: University. Quasthoff, U., Heller, V., & Morek, M. (2017). On the sequential organization and genre- orientation of discourse units in interaction. Discourse Studies, 19(1), 84-110. Radford, L., & Barwell, R. (2016). Language in mathematics education research. In A. Gutiérrez, G. Leder, & P. Boero (Eds.), The second handbook of research on the psychology of mathematics education. The journey continues (pp. 275-313). Rotterdam, Netherlands: Sense Publishers. Şahin-Gür, D., & Prediger, S. (2018). “Growth goes down, but of what?” A case study on language demands in qualitative calculus. In E. Bergqvist, M. Österholm, C. Granberg, & L. Sumpter (Eds.), Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 99-106). Umeå, Sweden: PME. Setati, M. (2005). Teaching mathematics in a primary multilingual classroom. Journal for Research in Mathematics Education, 36(5), 447-466. Solano-Flores, G. (2010). Function and form in research on language and mathematics Education. In J. Moschkovich (Ed.), Language and mathematics education: Multiple perspectives and directions for research (pp. 113-149). Charlotte, NC: IAP. Strauss, A., & Corbin, J. (1990). Basics of qualitative research. Grounded theory procedures and techniques. Newbury Park, CA: Sage. Thiel, C. (1996). Theorie. In J. Mittelstraß (Ed.), Enzyklopädie Philosophie und Wissenschaftstheorie (4th ed., pp. 260-270). Stuttgart, Germany: Springer. Toulmin, S. E. (1969). The uses of argument. Cambridge, MA: Cambridge University Press. US Congress (2001). No child left behind act. Washington D.C. van den Akker, J. (1999). Principles and methods of development research. In J. v. Akker, R. M. Branch, K. Gustafson, N. Nieveen, & T. Plomp (Eds.), Design approaches and tools in education and training (pp. 1-14). Boston, MA: Kluwer. van den Akker, J., Gravemeijer, K., McKenney, S., & Nieveen, N. (2006). Educational Design Research: The design, development and evaluation. London, England: Routledge. van den Heuvel-Panhuizen, M. (2003). The didactical use of models in Realistic Mathematics Education: An example from a longitudinal trajectory on percentage. Educational Studies in Mathematics, 54(1), 9-35. van den Heuvel-Panhuizen, M. (2005). Can scientific research answer the ‘what’ question of mathematics education? Cambridge Journal of Education, 35(1), 35-53. Wessel, L. (2015). Fach- und sprachintegrierte Förderung durch Darstellungsvernetzung und Scaffolding. Ein Entwicklungsforschungsprojekt zum Anteilbegriff. Heidelberg, Germany: Springer Spektrum. Yin, R. K. (1994). Case study research (2nd ed.). Thousand Oaks, CA: Sage.