Intertwining Lexical and Conceptual Learning Trajectories - A Design Research Study on Dual Macro-Scaffolding towards Percentages

Birte Pöhler; Susanne Prediger

doi:10.12973/eurasia.2015.1497a

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Birte Pöhler ¹, Susanne Prediger ¹ ^*

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¹ TU Dortmund^* Corresponding Author

Abstract

Background:
Monolingual or multilingual students with low academic language proficiency need to acquire conceptual understanding for percentages and the language to communicate about them.

Materials and methods:
The design research study explores how these two learning goals can be fostered by a macro-scaffolding approach for seventh grade students.

Results:
The dual hypothetical learning trajectory starts from students’ prior experiences and guides them, via several levels, towards the mathematical models and meanings (conceptual learning trajectory) as well as towards the necessary vocabulary for thinking and communicating about them (lexical learning trajectory), linked by the percent bar. For lexical scaffolding, the processes of offering, building and reflecting lexical means on different levels are focused. The qualitative empirical investigations of the design experiments show in depth how students’ conceptual understanding evolved together with the lexical means.

Conclusions:
For this purpose, the interpretative reconstruction of semiotic chains is instrumental.

Keywords

percentages
design research
macro scaffolding
language learners
conceptual scaffolding

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 11, Issue 6, 2015, 1697-1722

https://doi.org/10.12973/eurasia.2015.1497a

Publication date: 29 Sep 2015

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References

Barwell, R., Clarkson, P., Halai, A., Kazima, M., Moschkovich, J., Planas, N., Setati-Phakeng, M., Valero, P., & Villavicencio, M. (Eds.) (2015). Mathematics education and language diversity: The 21st ICMI Study. Dordrecht: Springer.
Confrey, J. (2006). The evolution of design studies as methodology. In K. Sawyer (ed.), Cambridge Handbook of the Learning Sciences (pp. 135-152). Cambridge: Cambridge University Press.
Cummins, J. (2000). Language, power and pedagogy. Clevedon: Multilingual Matters.
Ellerton, N. & Clarkson, P. (1996). Language Factors in Mathematics Teaching and Learning. In A.J. Bishop et al. (Eds.), International Handbook of Mathematics Education. Dordrecht: Kluwer, 987-1033.
Freudenthal, H. (1983). Didactical Phenomenology of Mathematical Structures. Dordrecht: Reidel.
Gibbons, P. (2002). Scaffolding Language, Scaffolding learning. Teaching second language learners in the mainstream classroom. Portsmouth: Heinemann.
Gravemeijer, K. (1998). Developmental Research as a Research Method. In J. Kilpatrick & A. Sierpinska (Eds.), What is research in mathematics education and what are its results? (pp. 277-295). Dordrecht: Kluwer.
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. v. d. Akker, K. Gravemeijer, S. McKenney, & N. Nieveen (Eds.), Educational design research (pp. 17-51). London: Routledge.
Hafner, T. (2012). Proportionalität und Prozentrechnung in der Sekundarstufe I. Wiesbaden: Vieweg + Teubner.
Hammond, J. & Gibbons, P. (2005). Putting Scaffolding to Work: The contribution of scaffolding in articulating ESL education. Prospect. An Australian Journal of TESOL, 20(1), 6-30.
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.
Kouba, V., Brown, C., Carpenter, T., Lindquist, M., Silver, E., & Swafford, J. (1988). Results of 4th NAEP Assessment of Mathematics. Arithmetic Teacher, 35(8), 14-19.
Lamon, S. J. (2007). Rational Numbers and Proportional Reasoning. In Lester, F K. (Eds.), Second Handbook of Research on Mathematic Teaching and Learning. New York: Macmillan, 629-667.
Morgan, C., Craig, T., Schuette, M., & Wagner, D. (2014). Language and communication in mathematics education: an overview of research in the field. ZDM, 46(6), 843-853.
Moschkovich, J. N. (2010). Recommendations for Research on Language and Mathematics Education. In J. Moschkovich (ed.), Language and Mathematics education (pp. 1-28). Charlotte: Information Age.
Niederhaus, C., Pöhler, B., & Prediger, S. (2015, in press). Relevante Sprachmittel für mathematische Textaufgaben – Korpuslinguistische Annäherung am Beispiel Prozentrechnung. To appear in E. Tschirner, O. Bärenfänger, & J. Möhring (Eds.), Kompetenzprofile Deutsch als fremde Bildungssprache. Stauffenberg: Tübingen.
Parker, M. & Leinhardt, G. (1995). Percent: A Privileged Proportion. Review of Educational Research, 65(4), 421-481.
Pimm, D. (1987). Speaking mathematically. London: Routledge.
Pöhler, B., Prediger, S., & Weinert, H. (2015, in press). Cracking percent problems in different formats – The role of texts and visual models for students with low and high language proficiency. To appear in Proceedings of CERME 8, Prague. Charles University / ERME.
Prediger, S. (2013). Focussing structural relations in the bar board – a design research study for fostering all students’ conceptual understanding of fractions. In B. Ubuz, C. Haser, & M.A. Mariotti (Eds.), Proceedings of the 8th Congress of the European Society for Research in Mathematics Education (pp. 343-352). Ankara: METU / ERME.
Prediger, S. (2016, in press). „Kapital multiplizirt durch Faktor halt, kann ich nicht besser erklären“ – Sprachschatzarbeit für einen verstehensorientierten Mathematikunterricht. To appear in B. Lütke et al. (Eds.), Fachintegrierte Sprachbildung. Berlin: de Gruyter.
Prediger, S. & Krägeloh, N. (2015, in press). “x-arbitrary means any number, but you do not know which one” The epistemic role of languages while constructing meaning for the variable as generalizers. To appear in A. Halai, & P. Clarkson (Eds.), Teaching & Learning Mathematics in Multilingual Classrooms. Issues for policy, practice and teacher education. Rotterdam: Sense.
Prediger, S. & Pöhler, B. (2016, in press). The interplay of micro- and macro-scaffolding: An empirical reconstruction for the case of an intervention on percentages. Submitted for ZDM – Mathematics Education, 48(1).
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. & 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. (2015, in press). Building theory and teaching strategies for bilingual learners based on an integration of three traditions. To appear in R. Barwell, P. Clarkson, A. Halai, M. Kazima, J. Moschkovich, N. Planas, M. Setati-Phakeng, P. Valero, P., & M. Villavicencio (Eds.), Mathematics education and language diversity: The 21st ICMI Study. Dordrecht: Springer.
Prediger, S., Link, M., Hinz, R., Hußmann, S., Thiele, J., & Ralle, B. (2012). Lehr-Lernprozesse initiieren und erforschen – Fachdidaktische Entwicklungsforschung im Dortmunder Modell. Mathematischer und Naturwissenschaftlicher Unterricht, 65(8), 452-457.
Prediger, S., Selter, C., Hußmann, S., & Nührenbörger, M. (2014). Mathe sicher können – Brüche, Prozente, Dezimalzahlen. Förderbausteine und Handreichungen für ein Diagnose- und Förderkonzept zur Sicherung mathematischer Basiskompetenzen. Berlin: Cornelsen.
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: University.
Schleppegrell, M. J. (2004). The language of schooling: A functional linguistics perspective. Mahwah: Lawrence Erlbaum.
Smit, J., Bakker, A., & Wegerif, R. (Eds.) (2016, in prep.). Scaffolding and Dialogic Teaching in Mathematics Education. Thematic issue of ZDM – Mathematics Education, 48(1).
Smit, J., van Eerde, H. A. A., & Bakker, A. (2013). A conceptualisation of whole-class scaffolding. British Educational Research Journal, 39(5), 817-834.
Thürmann, E., Vollmer, H., & Pieper, I. (2010). Language(s) of schooling: Focusing on vulnerable learners. In Council of Europe (Ed.), The linguistic and educational integration of children and adolescents from migrant backgrounds studies and resources. Straßbourg: Council of Europe.
Van den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic mathematics education. Educational Studies in Mathematics, 54(1), 9-35.
Wood, D. J., Bruner, J. S., & Ross, G. (1976). The role of tutoring in problem solving. Journal of Child Psychiatry and Psychology, 17(2), 89-100.

How to cite this article

APA

Pöhler, B., & Prediger, S. (2015). Intertwining Lexical and Conceptual Learning Trajectories - A Design Research Study on Dual Macro-Scaffolding towards Percentages. Eurasia Journal of Mathematics, Science and Technology Education, 11(6), 1697-1722. https://doi.org/10.12973/eurasia.2015.1497a

Vancouver

Pöhler B, Prediger S. Intertwining Lexical and Conceptual Learning Trajectories - A Design Research Study on Dual Macro-Scaffolding towards Percentages. EURASIA J Math Sci Tech Ed. 2015;11(6):1697-722. https://doi.org/10.12973/eurasia.2015.1497a

AMA

Pöhler B, Prediger S. Intertwining Lexical and Conceptual Learning Trajectories - A Design Research Study on Dual Macro-Scaffolding towards Percentages. EURASIA J Math Sci Tech Ed. 2015;11(6), 1697-1722. https://doi.org/10.12973/eurasia.2015.1497a

Chicago

Pöhler, Birte, and Susanne Prediger. "Intertwining Lexical and Conceptual Learning Trajectories - A Design Research Study on Dual Macro-Scaffolding towards Percentages". Eurasia Journal of Mathematics, Science and Technology Education 2015 11 no. 6 (2015): 1697-1722. https://doi.org/10.12973/eurasia.2015.1497a

Harvard

Pöhler, B., and Prediger, S. (2015). Intertwining Lexical and Conceptual Learning Trajectories - A Design Research Study on Dual Macro-Scaffolding towards Percentages. Eurasia Journal of Mathematics, Science and Technology Education, 11(6), pp. 1697-1722. https://doi.org/10.12973/eurasia.2015.1497a

MLA

Pöhler, Birte et al. "Intertwining Lexical and Conceptual Learning Trajectories - A Design Research Study on Dual Macro-Scaffolding towards Percentages". Eurasia Journal of Mathematics, Science and Technology Education, vol. 11, no. 6, 2015, pp. 1697-1722. https://doi.org/10.12973/eurasia.2015.1497a