Dealing with Function Word Problems: Identifying and Interpreting Verbal Representations

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


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.


Academic language demands Functions Word problems Verbal representations 


  1. Abedi, J., & Lord, C. (2001). The language factor in mathematics tests. Applied Measurement in Education, 14(3), 219–234. Scholar
  2. Aebli, H. (1981). Denken: Das Ordnen des Tuns. Band II: Denkprozesse. Stuttgart: Klett.Google Scholar
  3. 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
  4. 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
  5. 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
  6. Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1/2), 103–131. Scholar
  7. 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.CrossRefGoogle Scholar
  8. 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
  9. Heller, V., & Morek, M. (2015). Academic discourse as situated practice: An introduction. Linguistics & Education, 28(31), 174–186. Scholar
  10. 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
  11. Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, graphs, and graphing: Tasks, learning, and teaching. Review of Educational Research, 60(1), 1–64.CrossRefGoogle Scholar
  12. 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.CrossRefGoogle Scholar
  13. 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
  14. 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
  15. Niss, M. A. (2014). Functions learning and teaching. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 238–241). Dordrecht, Netherlands: Springer. Scholar
  16. 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. Scholar
  17. 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. Scholar
  18. 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
  19. 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
  20. 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
  21. Swan, M. (1985). The language of functions and graphs. An examination module for secondary schools. Nottingham, UK: Shell Centre.Google Scholar
  22. 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
  23. 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
  24. 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
  25. 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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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.TU Dortmund UniversityDortmundGermany

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