Abstract
The intertwined conceptual and language demands of word problems for functional relationships can be challenging. A design research study containing 16 design experiments in a laboratory setting with ninth and tenth graders explored one typical challenge, recognizing the core of functional relationships in different representations. Adequately connecting verbal and symbolic representations requires identifying and interpreting the verbal representation by addressing the relevant facets. A qualitative analysis of students’ solution processes shows different approaches to this task.
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References
Abedi, J., & Lord, C. (2001). The language factor in mathematics tests. Applied Measurement in Education, 14(3), 219–234. https://doi.org/10.1207/s15324818ame1403_2.
Aebli, H. (1981). Denken: Das Ordnen des Tuns. Band II: Denkprozesse. Stuttgart: Klett.
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, CT: Yale.
Drollinger-Vetter, B. (2011). Verstehenselemente und strukturelle Klarheit. Fachdidaktische Qualität der Anleitung von mathematischen Verstehensprozessen im Unterricht. Münster, New York, NY, München, Berlin: Waxmann.
Duval, R. (2000). Basic issues for research in mathematics education. In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th conference of PME (pp. 55–69). Hiroshima, Japan: Nishiki Print Co., Ltd.
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1/2), 103–131. https://doi.org/10.1007/s10649-006-0400-z.
Glade, M., & Prediger, S. (2017). Students’ individual schematization pathways—Empirical reconstructions for the case of part-of-part determination for fractions. Educational Studies in Mathematics, 94(2), 185–203.
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 conference of PME (pp. 145–152). Thessaloniki, Greece: PME.
Heller, V., & Morek, M. (2015). Academic discourse as situated practice: An introduction. Linguistics & Education, 28(31), 174–186. https://doi.org/10.1016/j.linged.2014.01.008.
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.
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. N. (1998). Resources for refining mathematical conceptions: Case studies in learning about linear functions. The Journal of the Learning Sciences, 7(2), 209–237.
Moschkovich, J. N. (2010). Recommendations for research on language and mathematics education. In J. Moschkovich (Ed.), Language and mathematics education (pp. 1–28). Charlotte, NC: Information Age.
Moschkovich, J. N., 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, NJ: Lawrence Erlbaum Associates.
Niss, M. A. (2014). Functions learning and teaching. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 238–241). Dordrecht, Netherlands: Springer. https://doi.org/10.1007/978-94-007-4978-8_96.
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, Netherlands: Springer. https://doi.org/10.1007/978-3-319-14511-2_11.
Prediger, S., Wilhelm, N., Büchter, A., Gürsoy, E., & Benholz, C. (2015). Sprachkompetenz und Mathematikleistung—Empirische Untersuchung sprachlich bedingter Hürden in den Zentralen. Journal für Mathematik-Didaktik, 36(1), 77–104. https://doi.org/10.1007/s13138-015-0074-0.
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 & 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 (pp. 407–424). Enschede: SLO Institute for Curriculum Development.
Romberg, T. A., Fennema, E., & Carpenter, T. P. (Eds.). (1993). Integrating research on the graphical representation of functions. Hillsdale, NJ: Lawrence Erlbaum Associates.
Swan, M. (1985). The language of functions and graphs. An examination module for secondary schools. Nottingham, UK: Shell Centre.
Thompson, P.-W. (2011). Quantitative reasoning and mathematical modeling. In L. L. Hatfield, S. Chamberlain, & S. Belbase (Eds.), New perspectives and directions for collaborative research in mathematics education (pp. 33–57). Laramie, WY: University of Wyoming.
ThĂĽrmann, E., Vollmer, H., & Pieper, I. (2010). Language(s) of schooling: Focusing on vulnerable learners. In Studies and resources. StraĂźbourg, France: 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.
Zindel, C. (in preparation, to appear in 2018). Den Funktionsbegriff im Kern verstehen—Entwicklungsforschungsstudie zu Bearbeitungs- und Lernwegen in einem fach- und sprachintegrierten Lehr-Lern-Arrangement (Doctoral dissertation in preparation). TU Dortmund University, Germany.
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Zindel, C. (2018). Dealing with Function Word Problems: Identifying and Interpreting Verbal Representations. In: Moschkovich, J., Wagner, D., Bose, A., Rodrigues Mendes, J., SchĂĽtte, M. (eds) Language and Communication in Mathematics Education. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-75055-2_7
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