School Academic Language Demands for Understanding Functional Relationships: A Design Research Project on the Role of Language in Reading and Learning

Susanne Prediger; Carina Zindel

doi:10.12973/eurasia.2017.00804a

Full Text (PDF)

Susanne Prediger ¹ ^* , Carina Zindel ¹

More Detail

¹ TU Dortmund University, Germany^* Corresponding Author

Abstract

Acquiring conceptual understanding of functions is far from being trivial for most students, especially language learners. The article reports on a design research project with students in Grades 8-11 (n = 94) that fostered academic language learners’ development of conceptual understanding in the interplay of different semiotic representations. Theoretical and qualitative analyses of students’ learning pathways and obstacles allowed the specification of school academic language demands based on concept demands for dealing with functional relationships. The strong interplay between concept and language demands can be described by the correspondence of conceptual compaction of conceptual facets and the language-related condensation of their verbalizations.

Keywords

communicative and epistemic role of language
conceptual understanding
design research
functions
topic-specific academic language demands

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 13, Issue 7b, July 2017, 4157-4188

https://doi.org/10.12973/eurasia.2017.00804a

Publication date: 21 Jun 2017

Article Views: 4417

Article Downloads: 2095

Open Access References How to cite this article

References

Abedi, J. (2006). Language issues in item-development. In S. M. Downing & T. M. Haldyna (Eds.), Handbook of test development (pp. 377–398). Mahwah: Erlbaum. doi:10.4324/9780203874776.ch17.
Abedi, J., & Lord, C. (2001). The language factor in mathematics tests. Applied Measurement in Education, 14(3), 219–234. doi:10.1207/s15324818ame1403_2.
Aebli, H. (1981). Denken: das Ordnen des Tuns. Band II: Denkprozesse. Stuttgart: Klett.
Bailey, A. L. (Ed.). (2007). The language demands of school: Putting academic English to the test. New Haven: Yale.
Bailey, A. L., Butler, F., Stevens, R., & Lord, C. (2007): Further specifying the language demands of school. In A.L. Bailey (Ed.): The language demands of school. Putting academic English to the test (pp. 103–156). New Haven: Yale.
Barwell, R. (2012). Discursive Demands and Equity in Second Language Mathematics Classrooms. In B. Herbel-Eisenmann, J. Choppin, D. Wagner, & D. Pimm (Eds.), Equity in Discourse for Mathematics Education (pp. 147–163). Dordrecht: Springer. doi:10.1007/978-94-007-2813-4_9.
Bruner, J. S. (1967). Toward a theory of instruction. Cambridge: Harvard University Press.
Carlson, M. & Oehrtman, M. (2005). Research sampler: 9. Key aspects of knowing and learning the concept of function. Mathematical Association of America. http://www.maa.org/programs/faculty-and-departments/curriculum-department-guidelines-recommendations/teaching-and-learning/9-key-aspects-of-knowing-and-learning-the-concept-of-function [March, 28, 2016].
Chamot, A. U. & O'Malley, J. M. (1994). The CALLA handbook: Implementing the cognitive academic language learning approach. Reading: Addison-Wesley.
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.
Confrey, J., & Smith, E. (1994). Exponential Functions, Rates of Change, and the Multiplicative Unit. Educational Studies in Mathematics, 26(2/3), 135–164. doi:10.1007/bf01273661.
Cummins, J. (2000). Language, Power and Pedagogy: Bilingual Children in the Crossfire. Clevedon: Multilingual Matters.
Drollinger-Vetter, B. (2011). Verstehenselemente und strukturelle Klarheit. Fachdidaktische Qualität der Anleitung von mathematischen Verstehensprozessen im Unterricht. Münster, New York, NY, München, Berlin: Waxmann.
Dubinsky, E., & Harel, G. (1992). The nature of the process conception of function. In G. Harel & E. Dubinsky (Eds.), The concept of function—Aspects of epistemology and pedagogy. MAA Notes 25 (pp. 85–105). Washington, DC: Mathematical Association of America.
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1/2), 103–131. doi:10.1007/s10649-006-0400-z.
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: The design, development and evaluation of programs, processes and products (pp. 17–51). London: Routledge.
Haag, N., Heppt, B., Roppelt, A., & Stanat, P. (2015). Linguistic simplification of mathematics items: effects for language minority students in Germany. European Journal of Psychology of Education, 30(2), 145–167. doi:10.1007/s10212-014-0233-6.
Haag, N., Heppt, B., Stanat, P., Kuhl, P., & Pant, H. A. (2013). Second language learners' performance in mathematics: Disentangling the effects of academic language features. Learning and Instruction, 28(0), 24–34. doi:10.1016/j.learninstruc.2013.04.001.
Halliday, M. A. K. (1978). Language as social semiotic: The social interpretation of language and meaning. Maryland: University Park Press.
Heinze, A., Reiss, K., Rudolph-Albert, F., Herwartz-Emden, L., & Braun, C. (2009). The development of mathematical competence of migrant children in German primary schools. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33rd PME (pp. 145-152). Thessaloniki: PME.
Heller, V. & Morek, M. (2015). Academic discourse as situated practice: An introduction. Linguistics & Education, 28(31), 174–186. doi:10.1016/j.linged.2014.01.008.
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.
Hirsch, E. D. (2003). Reading Comprehension Requires Knowledge - of Words and the World. Scientific Insights into the Fourth-Grade Slump and the Nation’s Stagnant Comprehension Scores. American Educator, 4(1), 10–44.
Jorgensen, R. (2011). Language, Culture and Learning Mathematics: A Bourdieuian Analysis of Indigenous Learning. In C. Wyatt-Smith, J. Elkins, & S. Gunn (Eds.), Multiple Perspectives on Difficulties in Learning Literacy and Numeracy (pp. 315–329). Dordrecht: Springer Netherlands. doi:10.1007/978-1-4020-8864-3_15.
Lampert, M. & Cobb, P. (2003). Communication and learning in the mathematics classroom. In J. Kilpatrick & D. Shifter (Eds.), Research Companion to the NCTM Standards (pp. 237–249). Reston: National Council of Teachers of Mathematics.
Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, Graphs, and Graphing: Tasks, Learning, and Teaching. Review of Educational Research, 60(1), 1–64.
Moschkovich, J. (2002). A situated and sociocultural perspective on bilingual mathematics learners. Mathematical Thinking and Learning, 4(2/3), 189–212. doi:10.1207/s15327833mtl04023_5.
Moschkovich, J. (2010). Recommendations for Research on Language and Mathematics Education. In J. Moschkovich (Ed.), Language and Mathematics education (pp. 1–28). Charlotte: Information Age.
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.
Moschkovich, J. (2015). Academic literacy in mathematics for English Learners. The Journal of Mathematical Behavior, 40(A), 43–62. doi:10.1016/j.jmathb.2015.01.005.
Moschkovich, J., Schoenfeld, A., & Arcavi, A. (1993). Aspects of Understanding: On multiple perspectives and representations of linear relations and connections among them. In T. A. Romberg, E. Fennema & T. P. Carpenter (Eds.), Integrating research on the graphical representation of functions (pp. 69–100). Hillsdale, N.J.: Lawrence Erlbaum Associates.
MSW NRW - Ministerium für Schule und Weiterbildung des Landes Nordrhein-Westfalen (2012): Zentrale Prüfungen 2012 für den Mittleren Schulabschluss. Mathematik. Düsseldorf: Ministry of School and Continuous Professional Development.
Mullis, I. V. S., Martin, M. O., Foy, P., & Arora, A. (2012). TIMSS 2011 international results in mathematics. Chestnut Hill: TIMSS & PIRLS International Study Center, Boston College.
Niss, M. A. (2014). Functions Learning and Teaching. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 238–241). Dordrecht: Springer Netherlands. doi:10.1007/978-94-007-4978-8_96.
OECD (2007). Science Competencies for Tomorrow's World (PISA 2006) (Vol. 2). Paris: OECD.
OECD (2016). Low-performing students: Why they fall behind and how to help them succeed. Paris: OECD, doi:10.1787/9789264250246-en.
Pimm, D. (1987). Speaking mathematically - Communication in mathematics classrooms. London: Routledge.
Prediger, S. & Krägeloh, N. (2016). “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. In A. Halai & P. Clarkson (Eds.), Teaching and Learning Mathematics in Multilingual Classrooms: Issues for policy, practice and teacher education (pp. 89–108). Rotterdam: Sense. doi:10.1007/978-94-6300-229-5_7.
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. doi:10.1007/s13394-013-0079-2.
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. Setati-Phakeng, P. Valero, & M. Villavicencio Ubillús (Eds.), Mathematics Education and Language Diversity (pp. 193–215). Dordrecht: Springer. doi:10.1007/978-3-319-14511-2_11.
Prediger, S., Gravemeijer, K., Confrey, J. (2015b). Design research with a focus on learning processes: an overview on achievements and challenges. ZDM Mathematics Education 47(6), 877–891. doi:10.1007/s11858-015-0722-3.
Prediger, S., Link, M., Hinz, R., Hußmann, S., Thiele, J., & Ralle, B. (2012). Lehr-Lernprozesse initiieren und erforschen—Fachdidaktische Entwicklungsforschung im Dortmunder Modell. Der Mathematische und Naturwissenschaftliche Unterricht, 65(8), 452–457.
Prediger, S., Wilhelm, N., Büchter, A., Benholz, C., & Gürsoy, E. (2015a). Sprachkompetenz und Mathematikleistung—Empirische Untersuchung sprachlich bedingter Hürden in den Zentralen Prüfungen 10. Journal für Mathematik-Didaktik, 36(1), 77–104. doi:10.1007/s13138-015-0074-0.
Romberg, T. A., Fennema, E., & Carpenter, T. P. (Eds.) (1993). Integrating research on the graphical representation of functions. Hillsdale: Lawrence Erlbaum Associates.
Schleppegrell, M. J. (2004). The language of schooling: A functional linguistics perspective. Mahwah, NJ: Lawrence Erlbaum. doi:10.4324/9781410610317.
Secada, W. G. (1992). Race, ethnicity, social class, language and achievement in mathematics. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 623–660). New York: MacMillan.
Sfard, A. (2008). Thinking as communicating. Human development, the growth of discourses, and mathematizing. Cambridge: Cambridge University Press.
Snow, C. E., & Uccelli, P. (2009). The Challenge of Academic Language. In D. R. Olson & N. Torrance (Eds.), The Cambridge handbook of literacy (pp. 112–133). Cambridge: Cambridge University Press. doi:10.1017/cbo9780511609664.008.
Swan, M. (1985). The language of functions and graphs. An examination module for secondary schools. Nottingham, Manchester, Shell Centre for Mathematical Education; Joint Matriculation Board (Testing strategic skills).
Thompson, P. W. (2011). Quantitative Reasoning and Mathematical Modeling. In L. L. Hatfield, S. Chamberlain und S. Belbase (Eds.), New perspectives and directions for collaborative research in mathematics education: papers from a planning conference for WISDOM (pp. 33–57). Laramie WY: University of Wyoming.
Thürmann, E., Vollmer, H., & Pieper, I. (2010). Language(s) of Schooling: Focusing on vulnerable learners. Studies and resources. Straßbourg: Council of Europe.
Ufer, S., Reiss, K., & Mehringer, V. (2013). Sprachstand, soziale Herkunft und Bilingualität: Effekte auf Facetten mathematischer Kompetenz. In M. Becker-Mrotzek, K. Schramm, E. Thürmann, & H. J. Vollmer (Eds.), Sprache im Fach - Sprachlichkeit und fachliches Lernen (pp. 167–184). Münster: Waxmann.
Vergnaud, G. (1996). The Theory of Conceptual Fields. In L. P. Steffe, P. Nesher, P. Cobb, B. Sriraman, & B. Greer (Eds.), Theories of mathematical learning (pp. 219–239). Mahwah, NJ: Lawrence Erlbaum Associates.
Vollrath, H. J. (1989). Funktionales Denken. Journal für Mathematik-Didaktik 10(1), 3–37.
Vygotsky, L.S. (1978). Mind in society. The development of higher psychological processes. Cambridge: Harvard University Press.
Zindel, C. (2013). Funktionale Abhängigkeiten in Textaufgaben erkennen und nutzen. Diagnose und Förderung. Unpublished Master Thesis, supervised by S. Prediger. TU Dortmund University.

How to cite this article

APA

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. https://doi.org/10.12973/eurasia.2017.00804a

Vancouver

Prediger S, Zindel C. School Academic Language Demands for Understanding Functional Relationships: A Design Research Project on the Role of Language in Reading and Learning. EURASIA J Math Sci Tech Ed. 2017;13(7b):4157-88. https://doi.org/10.12973/eurasia.2017.00804a

AMA

Prediger S, Zindel C. School Academic Language Demands for Understanding Functional Relationships: A Design Research Project on the Role of Language in Reading and Learning. EURASIA J Math Sci Tech Ed. 2017;13(7b), 4157-4188. https://doi.org/10.12973/eurasia.2017.00804a

Chicago

Prediger, Susanne, and Carina Zindel. "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 2017 13 no. 7b (2017): 4157-4188. https://doi.org/10.12973/eurasia.2017.00804a

Harvard

Prediger, S., and 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), pp. 4157-4188. https://doi.org/10.12973/eurasia.2017.00804a

MLA

Prediger, Susanne et al. "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, vol. 13, no. 7b, 2017, pp. 4157-4188. https://doi.org/10.12973/eurasia.2017.00804a