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Dealing with Function Word Problems: Identifying and Interpreting Verbal Representations

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Language and Communication in Mathematics Education

Part of the book series: ICME-13 Monographs ((ICME13Mo))

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.

    Article  Google Scholar 

  • Aebli, H. (1981). Denken: Das Ordnen des Tuns. Band II: Denkprozesse. Stuttgart: Klett.

    Google Scholar 

  • 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.

    Google Scholar 

  • Drollinger-Vetter, B. (2011). Verstehenselemente und strukturelle Klarheit. Fachdidaktische Qualität der Anleitung von mathematischen Verstehensprozessen im Unterricht. Münster, New York, NY, München, Berlin: Waxmann.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, graphs, and graphing: Tasks, learning, and teaching. Review of Educational Research, 60(1), 1–64.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Romberg, T. A., Fennema, E., & Carpenter, T. P. (Eds.). (1993). Integrating research on the graphical representation of functions. Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Swan, M. (1985). The language of functions and graphs. An examination module for secondary schools. Nottingham, UK: Shell Centre.

    Google Scholar 

  • 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.

    Google Scholar 

  • Thürmann, E., Vollmer, H., & Pieper, I. (2010). Language(s) of schooling: Focusing on vulnerable learners. In Studies and resources. Straßbourg, France: Council of Europe.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

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Authors and Affiliations

  1. TU Dortmund University, Vogelpothsweg 87, 44227, Dortmund, Germany

    Carina Zindel

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  1. Carina Zindel
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Correspondence to Carina Zindel .

Editor information

Editors and Affiliations

  1. Education Department, University of California, Santa Cruz, Santa Cruz, California, USA

    Judit N. Moschkovich

  2. Faculty of Education, University of New Brunswick, Fredericton, New Brunswick, Canada

    David Wagner

  3. Centre for Education Innovation and Action, Tata Institute of Social Sciences, Bombay, India

    Arindam Bose

  4. Faculty of Education, State University of Campinas, Campinas, São Paulo, Brazil

    Jackeline Rodrigues Mendes

  5. Institut für Erziehungswissenschaft, Technische Universität Dresden, Dresden, Germany

    Marcus Schütte

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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., Schütte, 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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  • DOI: https://doi.org/10.1007/978-3-319-75055-2_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-75054-5

  • Online ISBN: 978-3-319-75055-2

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