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ZDM

, Volume 50, Issue 1–2, pp 159–171 | Cite as

The impact of linguistic complexity on the solution of mathematical modelling tasks

  • Jennifer Plath
  • Dominik Leiss
Original Article

Abstract

Comprehending a mathematical modelling task is a central prerequisite for the following modelling process. In this study, we investigated the roles that the language proficiency of the students and the linguistic wording of the task play for the comprehension and the successful solving of mathematical modelling tasks. Five mathematical tasks with a constant modelling complexity and a varied linguistic complexity were developed. 634 students of comprehensive schools were tested and their socio-demographic factors as well as their language proficiency were measured. The results show a strong relationship between language proficiency and mathematical modelling achievement. Moreover, the findings suggest that increasing the linguistic complexity of mathematical modelling tasks results in lower solution frequencies.

Keywords

Mathematical modelling tasks Situation model Language proficiency Linguistic complexity 

References

  1. Abedi, J. (2006). Language issues in item development. In S. M. Downing & T. M. Haladyna (Eds.), Handbook of test development (pp. 377–398). Mahwah: L. Erlbaum.Google Scholar
  2. Abedi, J., & Leon, S. (1999). Impact of students’ language background variables on content-based performance: analyses and extent data. Los Angeles: University of California, National Center for Research on Evaluation, Standards and Student Testing (CRESST).Google Scholar
  3. Abedi, J., Leon, S., Wolf, M. K., & Farnsworth, T. (2008). Detecting test items differentially impacting the performance of ELL students. In M. K. Wolf, Herman Joan, J. Kim, J. Abedi, S. Leon & N. Griffin, et al. (Eds.), Providing validity evidence to improve the assessment of english language learners (pp. 55–80). Los Angeles: University of California, National Center for Research on Evaluation (CRESST).Google Scholar
  4. Abedi, J., & Lord, C. (2001). The language factor in mathematics tests. Applied Measurement in Education, 14(3), 219–234.CrossRefGoogle Scholar
  5. Artelt, C., Stanat, P., & Schiefele, U. (2001). Lesekompetenz: Testkonzeption und Ergebnisse. In J. Baumert, E. Klieme, M. Neubrand, M. Prenzel, U. Schiefele & W. Schneider, et al. (Eds.), PISA 2000. Basiskompetenzen von Schülerinnen und Schülern im internationalen Vergleich (pp. 69–137). Opladen: Leske + Budrich.Google Scholar
  6. Begeny, J. C., & Greene, D. J. (2014). Can readability formulas be used to successfully gauge difficulty od reading materials? Psychologie in the Schools, 51(2), 198–215.CrossRefGoogle Scholar
  7. Björnsson, C. H. (1968). Lesbarkeit durch Lix. Stockholm: Pedagogiskt Centrum.Google Scholar
  8. Blomhoj, M., & Jensen, T. H. (2007). Whats all the fuss about competencies? In W. Blum, P. Galbraith, H.-W. Henn & M. Niss (Eds.), New ICMI study series: vol. 10. Modelling and applications in mathematics education (pp. 45–56). New York: Springer.CrossRefGoogle Scholar
  9. Blum, W., Galbraith, P. L., Henn, H.-W., & Niss, M. (2007). Modelling and applications in mathematics education. The 14th ICMI study. New York: Springer.CrossRefGoogle Scholar
  10. Blum, W., & Leiss, D. (2007). How do students and teachers deal with modelling problems? In C. Haines, P. Gailbraith & W. Blum (Eds.) Mathematical modelling (ICTMA 12). Education, engineering and economics: proceedings from the twelfth international conference on the teaching of mathematical modelling and applications. (pp. 222–231). Chichester: Horwood.CrossRefGoogle Scholar
  11. Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM, 38(2), 86–95.CrossRefGoogle Scholar
  12. Borromeo Ferri, R. (2011). Wege zur Innenwelt des mathematischen Modellierens: Kognitive Analysen zu Modellierungsprozessen im Mathematikunterricht). Wiesbaden: Vieweg + Teubner.CrossRefGoogle Scholar
  13. Brandstätter, E. (1999). Confidence intervals as an alternative to significance tests. Methods of Psychological Research Online, 4(2), 33–46.Google Scholar
  14. Butler, F. A., Bailey, A. L., Stevens, R., Huang, B., & Lord, C. (2004). Academic English in fifth-grade mathematics, science, and social studies textbooks. Los Angeles: Center for Research on Evaluation Standards and Student Testing CRESST.Google Scholar
  15. Christmann, U. (2004). Verstehens- und Verständlichkeitsmessung: Methodische Ansätze in der Anwendungsforschung. In K. D. Lerch (Ed.), Recht verstehen: Verständlichkeit, Missverständlichkeit und Unverständlichkeit von Recht (pp. 33–62). Berlin: De Gruyter.Google Scholar
  16. Clarkson, P. C. (1991). Language comprehension errors: a further investigation. Mathematics Education Research Journal, 3(2), 24–33.CrossRefGoogle Scholar
  17. Cummins, J. (1979). Linguistic interdependence and the educational development of bilingual children. Review of Educational Research, 49(2), 222–251.CrossRefGoogle Scholar
  18. Cummins, J. (2000). Language, power and pedagogy: bilingual children in the crossfire. Clevedon: Multilingual Matters.Google Scholar
  19. Dabrowska, E. (2012). Different speakers, different grammars: individual differences in native language attainment. Linguistic Approaches to Bilingualism, 2, 219–253.CrossRefGoogle Scholar
  20. Duarte, J., Gogolin, I., & Kaiser, G. (2011). Sprachlich bedingte Schwierigkeiten von mehrsprachigen Schülerinnen und Schülern bei Textaufgaben. In E. Özdil & S. Prediger (Eds.), Mathematiklernen unter Bedingungen der Mehrsprachigkeit. Stand und Perspektive der Forschung und Entwicklung in Deutschland (pp. 35–54). Münster: Waxmann.Google Scholar
  21. Ellis, N. C. (2002). Frequency effects in language acquisition: A review with implications for theories of implicit and explicit language acquisition. Studies in Second Language Acquisition, 24(2), 143–188.Google Scholar
  22. Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. ZDM, 38(2), 143–162.CrossRefGoogle Scholar
  23. Gogolin, I., & Duarte, J. (2016). Bildungssprache. In J. Kilian, B. Brouȅr & D. Lüttenberg (Eds.), Handbuch Sprache in der Bildung. Handbücher Sprachwissenschaft (pp. 478–499). Berlin: De Gruyer.Google Scholar
  24. Gogolin, I., & Lange, I. (2011). Bildungssprache und durchgängige Sprachbildung. In S. Fürstenau & M. Gomolla (Eds.), Migration und schulischer Wandel. Mehrsprachigkeit (pp. 107–129). Wiesbaden: Verlag für Sozialwissenschaften.CrossRefGoogle Scholar
  25. Grotjahn, R. (2010). The C-Test: contributions from current research. Frankfurt am Main: Peter Lang GmbH Internationaler Verlag der Wissenschaften.Google Scholar
  26. Haag, N., Heppt, B., Roppelt, A., & Stanat, P. (2014). Linguistic simplification of mathematics items: effects for language minority students in Germany. European Journal of Psychology and Education, 30(2), 145–167.CrossRefGoogle Scholar
  27. 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, 24–34.CrossRefGoogle Scholar
  28. Heine, L., Domenech, M., Otto, L., Neumann, A., & Krelle, M. (under review). Modellierung sprachlicher Anforderungen in Testaufgaben verschiedener Unterrichtsfächer: Theoretische und empirische Grundlagen. Zeitschrift für angewandte Linguistik.Google Scholar
  29. Heinze, A., Herwartz-Emden, L., Braun, C., & Reiss, K. (2011). Die Rolle von Kenntnissen der Unterrichtssprache beim Mathematiklernen: Ergebnisse einer quantitativen Längsschnittstudie in der Grundschule. In S. Prediger & E. Özdil (Eds.), Mehrsprachigkeit: Bd. 32. Mathematiklernen unter Bedingungen der Mehrsprachigkeit. Stand und Perspektiven der Forschung und Entwicklung in Deutschland (pp. 11–33). Münster: Waxmann.Google Scholar
  30. Hofstetter, C. H. (2003). Contextual and mathematics accommodation test effects for English-language learners. Applied Measurement in Education, 16(2), 159–188.CrossRefGoogle Scholar
  31. Johnson, E., & Monroe, B. (2004). Simplified language as an accommodation on math tests. Assessment for Effective Intervention, 29(3), 35–45.CrossRefGoogle Scholar
  32. Kaiser, G., Blum, W., Borromeo Ferri R., Greefrath G. (2015). Modelling in mathematics education. In R. Bruder, L. Hefendehl-Hebecker, B. Schmidt-Thieme & H.-G. Weigand (Eds.), Handbuch der Mathematikdidaktik (pp. 355–382). Berlin: Springer.Google Scholar
  33. Kaiser, G., & Schwarz, I. (2003). Mathematische Literalität unter einer sprachlich-kulturellen Perspektive. Zeitschrift für Erziehungswissenschaften, 6(3), 357–377.CrossRefGoogle Scholar
  34. Kaiser, G., & Stender, P. (2013). Complex modelling problems in co-operative, self-directed learning environments. In G. Stillman, G. Kaiser, W. Blum & J. Brown (Eds.), Teaching mathematical modelling: connecting to research and practice (pp. 277–294). Dodrecht: Springer.CrossRefGoogle Scholar
  35. Köhne, J., Kronenwerth, S., Redder, A., Schuth, E., & Weinert, S. (2015). Bildungssprachlicher Wortschatz–linguistische und psychologische Fundierung und Itementwicklung. In A. Redder, J. Naumann & R. Tracy (Eds.), Forschungsinitiative Sprachdiagnostik und Sprachförderung–Ergebnisse, pp. 67–92.Google Scholar
  36. Leiss, D. (2007). “Hilf mir, es selbst zu tun”: Lehrerinterventionen beim mathematischen Modellieren. Hildesheim: Franzbecker.Google Scholar
  37. Leiss, D., Domenech, M., Ehmke, T., & Schwippert, K. (2017). Schwer-schwierig-diffizil: Zum Einfluss sprachlicher Komplexität von Aufgaben auf fachliche Leistungen in der Sekundarstufe 1. In D. Leiss, M. Hagena, A. Neumann & K. Schwippert (Eds.), Sprache im Fach Mathematik—Forschungsstand und Herausforderungen im Verlauf der Schulzeit (pp. 99–126). Münster: Waxmann (Reihe des Mercator Institus: Sprachliche Bildung.Google Scholar
  38. Leiss, D., Schukajlow, S., Blum, W., Messner, R., & Pekrun, R. (2010). The role of the situation model in mathematical modelling—task analyses, student competencies, and teacher interventions. Journal für Mathematik-Didaktik, 31(1), 119–141.CrossRefGoogle Scholar
  39. Martiniello, M. (2008). Language and the performance of English-language learners in math word problems. Harvard Educational Review, 78, 333–368.CrossRefGoogle Scholar
  40. Martiniello, M. (2009). Linguistic complexity, schematic representations, and differential item functioning for English language learners in math tests. Educational Assessment, 14(3–4), 160–179.CrossRefGoogle Scholar
  41. Matos, J. F., & Carreira, S. (1997). The quest for meaning in students’ mathematical modelling. In S. K. Houston, I. D. Huntley & N. T. Neill (Eds.), Teaching and learning mathematical modelling (ICTMA 7). Innovation, investigation and application (pp. 63–75). Chichester: Horwood Publishing.Google Scholar
  42. Mayer, R. E., & Hegarty, M. (1996). The process of understanding mathematical problems. In R. J. Sternberg & T. Ben-Zeev (Eds.), Studies in mathematical thinking and learning series. The nature of mathematical thinking (pp. 29–53). Mahwah: L. Erlbaum Associates.Google Scholar
  43. Mirdamadi, F. S., & DeJong, N. H. (2015). The effect of syntactic complexity on fluency: comparing actives and passives in L1 and L2 speech. Second Language Research, 31(1), 105–116.CrossRefGoogle Scholar
  44. Morek, M., & Heller, V. (2012). Bildungssprache: Kommunikative, epistemische, soziale und interaktive Aspekte ihres Gebrauchs. ZDM, 57(1), 67–101.Google Scholar
  45. Müller, K., & Ehmke, T. (2014). Soziale Herkunft als Bedingung der Kompetenzentwicklung. In M. Prenzel, C. Sälzer, E. Klieme & O. Köller (Eds.), PISA 2012. Fortschritte und Herausforderungen in Deutschland (pp. 245–274). Münster: Waxmann.Google Scholar
  46. Nippold, M. (2007). Later language development. School-age children, adolescents and young adults. Austin: Pro-Ed.Google Scholar
  47. OECD. (2014). PISA 2012 Results: what students know and can do: student performance in mathematics, reading and science. Paris: OECD.Google Scholar
  48. OECD. (2016). PISA 2015 results (volume 1): excellence and equity in education. Paris: OECD Publishing.Google Scholar
  49. Paetsch, J., & Felbrich, A. (2016). Longitudinale Zusammenhänge zwischen sprachlichen Kompetenzen und elementaren mathematischen Modellierungskompetenzen bei Kindern mit Deutsch als Zweitsprache. Psychologie in Erziehung und Unterricht, 63(1), 16–33.CrossRefGoogle Scholar
  50. Paetsch, J., Radmann, S., Felbrich, A., Lehrmann, R., & Stanat, P. (2015). Sprachkompetenz als Prädiktor mathematischer Kompetenzentwicklung von Kinder deutscher und nicht-deutscher Familiensprache. Zeitschrift für Entwicklungspsychologie und pädagogische Psychologie, 48(1), 27–41.Google Scholar
  51. Pennock-Roman, M., & Rivera, C. (2011). Mean effects of test accommodations for ELLs and Non-ELLs: a meta-analysis of experimental studies. Educational Measurement: Issues and Practice, 30(3), 10–28.CrossRefGoogle Scholar
  52. Prediger, S., Renk, N., Büchter, A., Gürsoy, E., & Benholz, C. (2013). Family background or language disadvantages? Factors for underachievement in high stakes tests. In A. Lindmeier & A. Heinze (Eds.) Proceedings of the 37th conference of the international group for the psychology of mathematics education (Vol. 4, pp. 4.49–4.56).Google Scholar
  53. Prediger, S., Wilhelm, N., Büchter, A., Gürsoy, E., & Benholz, C. (2015). Sprachkompetenz und Mathematikleistung—Empirische Untersuchung sprachlich bedingter Hürden in den Zentralen Prüfungen 10. Journal für Mathematik-Didaktik, 36(1), 77–104.CrossRefGoogle Scholar
  54. Renner, C. (2001). Recommendations to improve accessibility of text material on assessments for English language learners. Topeka: Kansas State Department of Education.Google Scholar
  55. Reusser, K. (1989). Vom Text zur Situation zur Gleichung. Kognitive Simulation von Sprachverständnis und Mathematisierung beim Lösen von Textaufgaben. Habilitationsschrift Universität Bern.Google Scholar
  56. Riebling, L. (2013). Heuristik der Bildungssprache. In I. Gogolin, I. Lange, U. Michel & H. H. Reich (Eds.), FörMig-Edition: Vol. 9. Herausforderung Bildungssprache. Und wie man sie meistert (pp. 106–153). Münster: Waxmann.Google Scholar
  57. Rost, J. (2004). Testtheorie und Testkonstruktion. Bern: Huber.Google Scholar
  58. Rumelhart, D. E. (1977). Toward an interactive model of reading. In S. Dornic (Ed.), Attention and performance VI (pp. 573–603). Hillsdale: Erlbaum.Google Scholar
  59. Runge, A. (2013). Die Nutzung von (bildungssprachlichen) Verben in naturwissenschaftlichen Aufgabenstellungen bei SchülerInnen der Jahrgangsstufe 4 und 5. In A. Redder & S. Weinert (Eds.), Sprachförderung und Sprachdiagnostik. Interdisziplinäre Perspektiven (pp. 152–173). Münster: Waxmann.Google Scholar
  60. Schmid-Barkow, I. (2010). Lesen—Lesen als Textverstehen. In H.-W. Huneke (Ed.), Taschenbuch des Deutschunterrichts: Vol. 1. Sprach- und Mediendidaktik (pp. 218–231). Baltmannsweiler: Schneider-Verl. Hohengehren.Google Scholar
  61. Scontras, G., Badecker, W., Shank, L., Lim, E., & Fedorenko, E. (2014). Syntactic complexity effects in sentence production. Cognitive Science, 38(1), 1–25.CrossRefGoogle Scholar
  62. Shaftel, J., Belton-Kocher, E., Glasnapp, D., & Poggio, J. (2006). The impact of language characteristics in mathematics test items on the performance of English language learners and students with disabilities. Educational Assessment, 11(2), 105–126.CrossRefGoogle Scholar
  63. Skehan, P. (2001). Tasks and language performance assessment. In M. Bygate, P. Skehan & M. Swain (Eds.), Researching pedagogic tasks: second language learning, teaching, and testing (pp. 167–185). London: Longman.Google Scholar
  64. Stillman, G. (2011). Applying metacognitive knowledge and strategies in applications and modelling tasks at secondary school. In G. Kaiser, W. Blum, R. Borromeo Ferro & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling. ICTMA 14 (pp. 165–180). Dodrecht: Springer.CrossRefGoogle Scholar
  65. Stillman, G., Brown, J., & Galbraith, P. (2010). Idetifying challanges within transition phases of mathematical modelling activities at year 9. In R. A. Lesh (Ed.), Modeling students’ mathematical modeling competencies. ICTMA 13 (pp. 385–398). London: Springer.CrossRefGoogle Scholar
  66. Ufer, S., Reiss, K., & Mehringer, V. (2013). Sprachstand, soziale Herkunkft und Bilingualität: Effekte auf Facetten mathematischer Kompetenz. In M. Becker-Mrotzek, K. Schramm, E. Thürmann & H. J. Vollmer (Eds.), Fachdidaktische Forschungen: Bd. 3. Sprache im Fach. Sprachlichkeit und fachliches Lernen (pp. 187–201). Münster: Waxmann.Google Scholar
  67. Verschaffel, L., van Dooren, W., Greer, B., & Mukhopadhyay, S. (2010). Reconceptualising word problems as exercises in mathematical modelling. Journal für Mathematik-Didaktik, 31(1), 9–29.CrossRefGoogle Scholar
  68. Vukovic, R. K., & Lesaux, N. K. (2013). The language of mathematics: investigating the ways language counts for children’s mathematical development. Journal of Experimental Child Psychology, 115(2), 227–244.CrossRefGoogle Scholar
  69. Wijaya, A., van den Heuvel-Panhuizen, Marja, & Doormann, M. (2015). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational Studies in Mathematics, 89(1), 41–65.CrossRefGoogle Scholar
  70. Wolf, M. K., & Leon, S. (2009). An investigation of the language demands in content assessments for English language learners. Educational Assessment, 14(3–4), 139–159.CrossRefGoogle Scholar

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© FIZ Karlsruhe 2017

Authors and Affiliations

  1. 1.Institut für Mathematik und ihre DidaktikLeuphana University of LueneburgLueneburgGermany

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