International Electronic Journal of Mathematics Education

Are Word Problems Really More Difficult for Students with Low Language Proficiency? Investigating Percent Items in Different Formats and Types
  • Article Type: Research Article
  • International Electronic Journal of Mathematics Education, 2017 - Volume 12 Issue 3, pp. 667-687
  • Published Online: 31 Oct 2017
  • Article Views: 327 | Article Download: 266
  • Open Access Full Text (PDF)
AMA 10th edition
In-text citation: (1), (2), (3), etc.
Reference: Pöhler B, George AC, Prediger S, Weinert H. Are Word Problems Really More Difficult for Students with Low Language Proficiency? Investigating Percent Items in Different Formats and Types. Int Elect J Math Ed. 2017;12(3), 667-687.
APA 6th edition
In-text citation: (Pöhler et al., 2017)
Reference: Pöhler, B., George, A. C., Prediger, S., & Weinert, H. (2017). Are Word Problems Really More Difficult for Students with Low Language Proficiency? Investigating Percent Items in Different Formats and Types. International Electronic Journal of Mathematics Education, 12(3), 667-687.
Chicago
In-text citation: (Pöhler et al., 2017)
Reference: Pöhler, Birte, Ann Cathrice George, Susanne Prediger, and Henrike Weinert. "Are Word Problems Really More Difficult for Students with Low Language Proficiency? Investigating Percent Items in Different Formats and Types". International Electronic Journal of Mathematics Education 2017 12 no. 3 (2017): 667-687.
Harvard
In-text citation: (Pöhler et al., 2017)
Reference: Pöhler, B., George, A. C., Prediger, S., and Weinert, H. (2017). Are Word Problems Really More Difficult for Students with Low Language Proficiency? Investigating Percent Items in Different Formats and Types. International Electronic Journal of Mathematics Education, 12(3), pp. 667-687.
MLA
In-text citation: (Pöhler et al., 2017)
Reference: Pöhler, Birte et al. "Are Word Problems Really More Difficult for Students with Low Language Proficiency? Investigating Percent Items in Different Formats and Types". International Electronic Journal of Mathematics Education, vol. 12, no. 3, 2017, pp. 667-687.
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Pöhler B, George AC, Prediger S, Weinert H. Are Word Problems Really More Difficult for Students with Low Language Proficiency? Investigating Percent Items in Different Formats and Types. Int Elect J Math Ed. 2017;12(3):667-87.

Abstract

Achievement gaps between students with low and high language proficiency appear for word problems, but is this due to their text format or their conceptual challenges? A test with percent problems of different types and in pure, text and visual format was conducted with N=308 seventh graders. Students’ scores were analyzed statistically by a cognitive diagnosis model. Unlike expected, the probability for students with low language proficiency to solve items in text format is not lower than in pure format. These results are interpreted as indication that conceptual challenges might impact stronger than reading challenges.

References

  • Abedi, J. (2004). Will You Explain the Question?. Principal Leadership, 4(7), 27-31.
  • 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.
  • Abedi, J., & Lord, C. (2001). The language factor in mathematics tests. Applied Measurement in Education, 14(3), 219-234.
  • Behr, M. J., Harel, G., Post, T. R., & Lesh, R. (1992). Rational number, ratio, and proportion. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 296–332). New York: Macmilian.
  • Carpenter, T. P., Corbitt, M. K., Kepner, H. S., Lindquist, M. M., & Reys, R. E. (1980). NAEP note: Problem solving. The Mathematics Teacher, 73(6), 427-433.
  • de la Torre, J. (2009). DINA model parameter estimation: A didactic. Journal of Educational and Behavioral Statistics, 34(1), 115–130.
  • de La Torre, J. & Minchen, N. (2014). Cognitively Diagnostic Assessments and the Cognitive Diagnosis Model Framework. Psicología Educativa, 20(2), 89–97.
  • de la Torre, J., & Lee, Y.-S. (2010). A note on the invariance of the DINA model parameters. Journal of Educational Measurement, 47(1), 115–127.
  • DiBello, L., Roussos, L., & Stout, W. (2007). Review of cognitively diagnostic assessment and a summary of psychometric models. In C. R. Rao & S. Sinharay (Eds.), Handbook of Statistics, Volume 26, Psychometics (pp. 979–1030). Amsterdam: Elsevier.
  • Dole, S., Cooper, T.J., Baturo, A.R., & Conoplia, Z. (1997). Year 8, 9 and 10 students’ understanding and access of percent knowledge. In A. Begg (Ed.), People in mathematics education. Proceedings of 20th MERGA (pp. 7-11). Rotorua: Merga.
  • Duarte, J., Gogolin, I. & Kaiser, G. (2011). Sprachlich bedingte Schwierigkeiten von mehrsprachigen Schülerinnen und Schülern bei Textaufgaben. In S. Prediger & E. Özdil (Eds.), Mathematiklernen unter Bedingungen der Mehrsprachigkeit (pp. 35-53). Münster: Waxmann.
  • Fischer, G.H. & Molenaar, I.W. (1995). Rasch models: foundations, recent developments and applications. New York: Springer.
  • George, A. C. & Robitzsch, A. (2014). Multiple group cognitive diagnosis models, with an emphasis on differential item functioning. Psychological Test and Assessment Modeling, 56(4), 405–432.
  • George, A. C. & Robitzsch, A. (2015). Cognitive diagnosis models in R: A didactic. The Quantitative Methods for Psychology, 11(3), 189–205.
  • George, A. C., Robitzsch, A., Kiefer, T., Groß, J., & Ünlü, A. (2016). The R Package CDM for cognitive diagnosis modeling. Journal of Statistical Software, 74(2), 1–24.
  • 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.
  • 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, 22(28), 24–34.
  • Haertel, E. H. (1989). Using restricted latent class models to map the skill structure of achievement items. Journal of Educational Measurement, 26, 301–323.
  • Hafner, T. (2012). Proportionalität und Prozentrechnung. Wiesbaden: Vieweg + Teubner.
  • 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.
  • Jitendra, A. K., & Star, J. R. (2012). An exploratory study contrasting high- and low-achieving students' percent word problem solving. Learning and Individual Differences, 22(1), 151-158.
  • Johnson, M., Lee, Y.-S., Sachdeva, R. J., Zhang, J., Waldman, M., & Park, J. Y. (2013, March). Examination of gender differences using the multiple groups DINA model. Paper presented at the 2013 Annual Meeting of the National Council on Measurement in Education, San Francisco CA.
  • Koedinger, K.R. & Nathan, M. J. (2004). The real story behind the story problems. Effects of representations on quantitative reasoning. The Journal of the Learning Sciences, 13(2), 129-164.
  • Kouba, V., Brown, C., Carpenter, T., Lindquist, M., Silver, E., & Swafford, J. (1988). Results of 4th NAEP Assessment of Mathematics. Arithmetic Teacher, 35(8), 14-19.
  • Martiniello, M. (2008). Language and the performance of English-language learners in math word problems. Harvard Educational Review, 78(2), 333–368.
  • Maydeu-Olivares. (2013). Goodness-of-fit assessment of item response theory models. Measurement: Interdisciplinary Research and Perspectives, 11, 71–137.
  • 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.
  • OECD (2007). PISA 2006. Vol. 2: Data. Paris: OECD.
  • Parker, M. & Leinhardt, G. (1995). Percent: A Privileged Proportion. Review of Educational Research, 65(4), 421-481.
  • Paulus (2009). Die Bücheraufgabe zur Bestimmung des kulturellen Kapitals bei Grundschülern. URL: http://psydok.sulb.uni-saarland.de/volltexte/2009/2368/.
  • Pöhler, B., & Prediger, S. (2015). Intertwining lexical and conceptual learning trajectories - A design research study on dual macro-scaffolding towards percentages. Eurasia Journal of Mathematics, Science & Technology Education, 11(6), 1697-1722.
  • Pöhler, B., Prediger, S., & Neugebauer, P. (2017, in press). Content- and language integrated learning: A field experiment for percentages. To appear in Proceedings of the 41st Annual Meeting of the International Group for the Psychology of Mathematics Education (PME 41). Singapore: PME.
  • Pöhler, B., Prediger, S., & Weinert, H. (2016). Cracking percent problems in different formats - The role of texts and visual models for students with low and high language proficiency. In K. Krainer & N. Voundrová (Eds.), CERME 9. Proceedings  of the Ninth Congress of the European Society for Research in Mathematics Education (pp. 331-338). Prague: Charles University / ERME.
  • 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 37th PME (4, 49-59). Kiel: PME.
  • 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.
  • R Core Team (2015). R: A language and environment for statistical computing. R Foundation for Statistical Computing. Vienna, Austria. Retrieved from http://www.R-project.org
  • Redder, A. & Wagner, J. (2015): Bispra-Test. Project internal test development, adapted from Uesseler et al. 2015.
  • Robitzsch, A., Kiefer, T., George, A. C. & Ünlü, A. (2016). CDM: Cognitive Diagnosis Modeling. R Package version 3.1-14. Retrieved from http://CRAN.R-project.org/package=CDM.
  • 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.
  • Tatsuoka, K. K. (Ed). (1984). Analysis of errors in fraction addition and subtraction problems. Final Report for Grant No. NIE-G-81-0002. Urbana, IL: University of Illinois.
  • Uesseler, S., Runge, A., & Redder, A. (2013). „Bildungssprache“ diagnostizieren. Entwicklung eines Instruments zur Erfassung von bildungssprachlichen Fähigkeiten bei Viert- und Fünftklässlern. In A. Redder & S. Weinert (Eds.), Sprachförderung und Sprachdiagnostik. Interdisziplinäre Perspektiven (pp. 42-67). Münster: Waxmann.
  • Van den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic mathematics education. Educational Studies in Mathematics, 54(1), 9-35.
  • Van den Heuvel-Panhuizen, M. (2005). The role of contexts in assessment problems in mathematics. For the Learning of Mathematics, 25 (2), 2-9.
  • Walkington, C., Cooper, J., & Howell, E. (2013). Effects of visual representations and interest-based personalization on solving percent problems. In Martinez, M. & Castro Superfine, A. (Eds.), Proceedings of 35th PME-NA (pp. 533-536). Chicago: University of Illinois.
  • Walzebug, A. (2014). Is there a language-based social disadvantage in solving mathematical items? Learning, Culture and Social Interaction 3 (2), 159-169.
  • 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.
  • Xu, X. & von Davier, M. (2008). Comparing multiple-group multinomial log-linear models for multidimensional skill distributions in the general diagnostic model (rr-08-35). Educational Testing Service.

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