Text Comprehension as a Mediator in Solving Mathematical Reality-Based Tasks: The Impact of Linguistic Complexity, Cognitive Factors, and Social Background
Successfully solving reality-based tasks requires both mathematical and text comprehension skills. Previous research has shown that mathematical tasks.
- Pub. date: January 15, 2025
- Online Pub. date: October 22, 2024
- Pages: 23-39
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Successfully solving reality-based tasks requires both mathematical and text comprehension skills. Previous research has shown that mathematical tasks requiring language proficiency have lower solution rates than those that do not, indicating increased difficulty through textual input. Therefore, it is plausible to assume that a lack of text comprehension skills leads to performance problems. Given that different sociodemographic characteristics and cognitive factors can influence task performance, this study aims to determine whether text comprehension mediates the relationship between these factors and competence in solving reality-based tasks. Additionally, it examines the impact of systematic linguistic variation in texts. Using an experimental design, 428 students completed three reality-based tasks (word count: M = 212.4, SD = 19.7) with different linguistic complexities as part of a paper-pencil test. First, students answered questions about the situation-related text comprehension of each text, followed by a mathematical question to measure their competence in solving reality-based tasks. The results indicate that: a) Tasks with texts of lower linguistic complexity have a significantly higher solution rate for both text comprehension (d = 0.189) and mathematical tasks (d = 0.119). b) Cognitive factors are significant predictors of mathematical solutions. c) Text comprehension mediates the relationship between the impact of students’ cultural resources and cognitive factors and their competence to solve reality-based tasks. These findings highlight the importance of linguistic complexity for mathematical outcomes and underscore the need to reinforce text comprehension practice in mathematical education owing to its mediating role.
experimental design language in mathematics linguistic complexity mediation analysis reality based tasks
Keywords: Experimental design, language in mathematics, linguistic complexity, mediation analysis, reality-based tasks.
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References
Abedi, J., & Lord, C. (2001). The language factor in mathematics test. Applied Measurement in Education, 14(3), 219-234. https://doi.org/10.1207/S15324818AME1403_2
Björn, P. M., Aunola, K., & Nurmi, J.-E. (2016). Primary school text comprehension predicts mathematical word problem-solving skills in secondary school. Educational Psychology, 36(2), 362-377. https://doi.org/10.1080/01443410.2014.992392
Blomhøj, M., & Kjeldsen, T. H. (2006). Teaching mathematical modeling through project work. ZDM - Mathematics Education, 38, 163-177. https://doi.org/10.1007/BF02655887
Blum, W., Galbraith, P. L., Henn, H.-W., & Niss, M. (Eds.). (2007). Modelling and applications in mathematics education: The 14th ICMI study. Springer. https://doi.org/10.1007/978-0-387-29822-1
Blum, W., & Leiß, D. (2007). How do students and teachers deal with modelling problems? In C. Haines, P. Galbraith, W. Blum & S. Khan (Eds.), Mathematical modelling (ICTMA 12): Education, engineering and economics (pp. 222-231). Horwood Publishing. https://doi.org/10.1533/9780857099419.5.221
Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM - Mathematics Education, 38, 86-95. https://doi.org/10.1007/BF02655883
Borromeo Ferri, R. (2011). Wege zur Innenwelt des mathematischen Modellierens: Kognitive Analysen zu Modellierungsprozessen im Mathematikunterricht [Pathways to the inner world of mathematical modeling: Cognitive analyses of modeling processes in mathematics education]. Vieweg + Teubner.
Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. (1999). Children’s mathematics: Cognitively guided instruction (Vol. 1). Heinemann.
Carpenter, T. P., & Moser, J. M. (1984). The acquisition of addition and subtraction concepts in grades one through three. Journal for Research in Mathematics Education, 15(3), 179-202. https://doi.org/10.2307/748348
Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Routledge. https://doi.org/10.4324/9780203771587
Duarte, J., Gogolin, I., & Kaiser, G. (2011). Sprachlich bedingte Schwierigkeiten von mehrsprachigen Schülerinnen und Schülern bei Textaufgaben [Language-related difficulties of multilingual pupils with text tasks]. In S. Prediger & E. Özdil (Eds.), Mathematiklernen unter Bedingungen der Mehrsprachigkeit. Stand und Perspektive der Forschung und Entwicklung in Deutschland Mehrsprachigkeit (pp. 35-53). Waxmann.
Ehmke, T., Leiss, D., & Heine, L. (2024). The effects of linguistic demands of reality-based mathematical tasks: Discrepancy between teachers’ expectations and students’ performance [Manuscript submitted for publication].
Fuchs, L. S., Fuchs, D., Compton, D. L., Powell, S. R., Seethaler, P. M., Capizzi, A. M., Schatschneider, C., & Fletcher, J. M. (2006). The cognitive correlates of third-grade skill in arithmetic, algorithmic computation, and arithmetic word problems. Journal of Educational Psychology, 98(1), 29-43. https://doi.org/10.1037/0022-0663.98.1.29
Fuchs, L. S., Gilbert, J. K., Fuchs, D., Seethaler, P. M., & Martin, B. N. (2017). Text comprehension and oral language as predictors of word-problem solving: Insights into word-problem solving as a form of text comprehension. Scientific Studies of Reading, 22(2), 152-166. https://doi.org/10.1080/10888438.2017.1398259
Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. ZDM - Mathematics Education, 38, 143-162. https://doi.org/10.1007/BF02655886
Haag, N., Heppt, B., Roppelt, A., & Stanat, P. (2015). Linguistic simplification of mathematics items: Effect for language minority students in Germany. European Journal of Psychology of Education, 30, 145-167. https://doi.org/10.1007/s10212-014-0233-6
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. https://doi.org/10.1016/j.learninstruc.2013.04.001
Hattie, J. (2008). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. Routledge. https://doi.org/10.4324/9780203887332
Hegarty, M., Mayer, R. E., & Monk, C. A. (1995). Comprehension of arithmetic world problems: A comparison of successful and unsuccessful problem solvers. Journal of Educational Psychology, 87(1), 18-32. https://doi.org/10.1037/0022-0663.87.1.18
Heine, L., Domenech, M., Otto, L., Neumann, A., Krelle, M., Leiss, D., Höttecke, D., Ehmke, T., & Schwippert, K. (2018). Modellierung sprachlicher Anforderungen in Testaufgaben verschiedener Unterrichtsfächer: Theoretische und empirische Grundlagen [Modeling linguistic requirements in test items in different subjects: Theoretical and empirical foundations]. Zeitschrift Für Angewandte Linguistik, 2018(69), 69-96. https://doi.org/10.1515/zfal-2018-0017
Heine, L., Leiss, D., & Ehmke, T. (2024). Academic language features in mathematical modelling tasks raise difficulty in reading comprehension for secondary students [Manuscript submitted for publication].
Heinle, A., Schiepe-Tiska, A., Reinhold, F., Heine, J.-H., & Holzberger, D. (2022). Supporting student motivation in class: The motivational potential of tasks. Zeitschrift Für Erziehungswissenschaft, 25, 453-470. https://doi.org/10.1007/s11618-022-01090-3
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 [The role of knowledge of the language of instruction in mathematics learning: Results of a quantitative longitudinal study in elementary school]. In S. Prediger & E. Özdil (Eds.), Mathematiklernen unter Bedingungen der Mehrsprachigkeit. Stand und Perspektiven der Forschung und Entwicklung in Deutschland. Mehrsprachigkeit (pp. 11-33). Waxmann.
Johnson, E., & Monroe, B. (2004). Simplified language as an accommodation on math tests. Assessment for Effective Intervention, 29(3), 35-45. https://doi.org/10.1177/073724770402900303
Jones, I., Swan, M., & Pollitt, A. (2015). Assessing mathematical problem solving using comparative judgement. International Journal of Science and Mathematics Education, 13, 151-177. https://doi.org/10.1007/s10763-013-9497-6
Kaiser, G. (2017). The teaching and learning of mathematical modelling. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 267-291). National Council of Teachers of Mathematics.
Kaiser, G., & Schwartz, B. (2006). Mathematical modeling as a bridge between school and university. ZDM - Mathematics Education, 38, 196-208. https://doi.org/10.1007/BF02655889
Kintsch, W., & Greeno, J. G. (1985). Understanding and solving word arithmetic problems. Psychological Review, 92(1), 109-129. https://doi.org/10.1037/0033-295X.92.1.109
Kirsch, I., de Jong, J., Lafontaine, D., McQueen, J., Mendelovits, J., & Monseur, C. (2002). Reading for change: Performance and engagement across countries: Results from PISA 2000. OECD. https://doi.org/10.1787/9789264099289-en
Knabbe, A., Leiss, D., & Ehmke, T. (2024). Reality-based tasks with complex-situations: Identifying sociodemographic and cognitive factors for solution. International Journal of Science and Mathematics Education. Advance online publication. https://doi.org/10.1007/s10763-024-10463-5
Leiss, D., Domenech, M., Ehmke, T., & Schwippert, K. (2017). Schwer-schwieriger-diffizil: Zum Einfluss sprachlicher Komplexität von Aufgaben auf fachliche Leistungen in der Sekundarstufe 1. [Difficult-more difficult-most difficult: The influence of linguistic complexity of tasks on subject performance in secondary level 1]. In D. Leiss, M. Hagena, A. Neumann & K. Schwippert (Eds.), Mathematik und Sprache. Empirischer Forschungsstand und unterrichtliche Herausforderungen (pp. 99-125). Waxmann.
Leiss, D., Ehmke, T., & Heine, L. (2024). Reality-based tasks for competency-based education: The need for an integrated analysis of subject-specific, linguistic, and contextual task features. Learning and Individual Differences, 114, Article 102518. https://doi.org/10.1016/j.lindif.2024.102518
Leiss, D., Plath, J., & Schwippert, K. (2019). Language and mathematics - Key factors influencing the comprehension process in reality-based tasks. Mathematical Thinking and Learning, 21(2), 131-153. https://doi.org/10.1080/10986065.2019.1570835
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, 119-141. https://doi.org/10.1007/s13138-010-0006-y
Lindberg, S. M., Hyde, J. S., Petersen, J. L., & Linn, M. C. (2010). New trends in gender and mathematics performance: A meta-analysis. Psychological Bulletin, 136(6), 1123-1135. https://doi.org/10.1037/a0021276
Maaß, K. (2010). Classification scheme for modelling tasks. Journal für Mathematik-Didaktik, 31, 285-311. https://doi.org/10.1007/s13138-010-0010-2
Matos, J. F., & Carreira, S. (1995). Cognitive processes and representations involved in applied problem solving. In C. Sloyer, W. Blum, & I. Huntley (Eds.), Advances and perspectives in teaching of mathematical modelling and applications (ICTMA-6) (pp. 71-80). Ellis Horwood.
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). L. Erlbaum Associates.
McNeish, D. (2023). A practical guide to selecting and blending approaches for clustered data: Clustered errors, multilevel models, and fixed-effect models. Psychological Methods. Advance online publication. https://doi.org/10.1037/met0000620
Muthén, L. K., & Muthén, B. O. (1998-2017). Mplus user guide (8th ed.). Muthén & Muthén. https://bit.ly/4djsjSy
Newman, K. (1977). An analysis of sixth-grade pupils’ errors on written mathematical tasks. In M. A. Clements & J. Foyster (Eds.), Research in mathematics education in Australia (pp. 239-258). Swinburne Press.
Nimely, D. R., Jr., Nyamu, F. K., & Waititu, M. M. (2023). Relationship between learners’ reading comprehension, arithmetic skills and ability to solve word-problems: A case of secondary school in Nakuru County, Kenya. East African Journal of Education and Social Science, 4(4), 40-48. https://doi.org/10.46606/eajess2023v04i04.0301
Niss, M. (2015). Mathematical competencies and PISA. In K. Stacey, & R. Turner (Eds.), Assessing mathematical literacy. The PISA experience (pp. 5-34). Springer.
Niss, M., Blum, W., & Galbraith, P. L. (2007). Introduction. In W. Blum, P. L. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 3-32). Springer. https://doi.org/10.1007/978-0-387-29822-1_1
Organization for Economic Co-operation and Development. (1999). Measuring student knowledge and skills: A new framework for assessment. https://bit.ly/3XIpbvh
Organization for Economic Co-operation and Development. (2013). PISA 2012 results: Excellence trough equity. https://doi.org/10.1787/9789264201132-en
Organization for Economic Co-operation and Development. (2014). PISA 2012 technical report. https://doi.org/10.1787/6341a959-en
Organization for Economic Co-operation and Development. (2019). PISA 2018 results (Volume II): Where all students can succeed. https://doi.org/10.1787/b5fd1b8f-en
Palm, T. (2002). The realism of mathematical school tasks. Features and consequences. [Unpublished doctoral dissertation]. University of Umea.
Plath, J. (2020). Verstehensprozesse bei der Bearbeitung realitätsbezogener Mathematikaufgaben: Klassische Textaufgaben vs. Zeitungstexte [Comprehension processes during solving reality-based mathematical problems: Word problems vs. newspaper texts]. Journal für Mathematik-Didaktik, 41, 237-266. https://doi.org/10.1007/s13138-019-00148-w
Plath, J., & Leiss, D. (2018). The impact of linguistic complexity on the solution of mathematical modelling tasks. ZDM Mathematics Education, 50, 159-171. https://doi.org/10.1007/s11858-017-0897-x
Pongsakdi, N., Kajamies, A., Veermans, K., Lertola, K., Vauras, M., & Lehtinen, E. (2020). What makes mathematical word problem solving challenging? Exploring the roles of word problem characteristics, text comprehension, and arithmetic skills. ZDM - Mathematics Education, 52, 33-44. https://doi.org/10.1007/s11858-019-01118-9
Preacher, K. J., & Hayes, A. F. (2008). Contemporary approaches to assessing mediation in communication research. In A. F. Hayes., M. D. Slater & L. B., Snyder (Eds.), Sourcebook of advanced data analysis methods for communication research (pp. 13-54). Sage Publications, Inc. https://doi.org/10.4135/9781452272054.n2
Prediger, S., & Wessel, L. (2018). Brauchen mehrsprachige Jugendliche eine andere fach- und sprachintegrierte Förderung als einsprachige? [Do multilingual young people need different subject and language-integrated support than monolinguals?]. Zeitschrift für Erziehungswissenschaft, 21, 361-382. https://doi.org/10.1007/s11618-017-0785-8
Prediger, S., Wilhelm, N., Büchter, A., Gürsoy, E., & Benholz, C. (2015). Sprachkompetenz und Mathematikleistung – Empirische Untersuchungen sprachlich bedingter Hürden in den Zentralen Prüfungen 10 [Language competence and mathematics performance - Empirical studies of language-related hurdles in the central examinations 10]. Journal für Mathematik-Didaktik, 36, 77-104. https://doi.org/10.1007/s13138-015-0074-0
Reinhold, F., Hofer, S., Berkowitz, M., Strohmaier, A., Scheuerer, S., Loch, F., Vogel-Heuser, B., & Reiss, K. (2020). The role of spatial, verbal, numerical, and general reasoning abilities in complex word problem solving for young female and male adults. Mathematics Education Research Journal, 32, 189-211. https://doi.org/10.1007/s13394-020-00331-0
Reinhold, F., Strohmaier, A., Hoch, S., Reiss, K., Böheim, R., & Seidel, T. (2020). Process data from electronic textbooks indicate students’ classroom engagement. Learning and Individual Differences, 83–84, Article 101934. https://doi.org/10.1016/j.lindif.2020.101934
Reusser, K. (1989). Vom Text zur Situation zur Gleichung–Kognitive Simulation von Sprachverständnis und Mathematisierung beim Lösen von Textaufgabe [From text to situation to equation - Cognitive simulation of language comprehension and mathematization when solving text problems]. (Habilitationsschrift). Universität Bern. https://doi.org/10.5167/uzh-261776
Schmidt, S., Ennemoser, M., & Krajewski, K. (2012). DEMAT 9. Deutscher Mathematiktest für neunte Klassen [DEMAT 9. German mathematics test for ninth grade]. Hogrefe.
Sim, M., Kim, S.-Y., & Suh, Y. (2022). Sample size requirements for simple and complex mediation models. Educational and Psychological Measurement, 82(1), 76-106. https://doi.org/10.1177/00131644211003261
Stephany, S. (2017). Textkohärenz als Einflussfaktor beim Lösen mathematischer Textaufgaben [Text coherence as an influencing factor when solving mathematical text problems]. In D. Leiss, M. Hagena, A. Neumann & K. Schwippert (Eds.), Mathematik und Sprache. Empirischer Forschungsstand und unterrichtliche Herausforderungen (pp. 43-61). Waxmann.
Strohmaier, A. R., Ehmke, T., Härtig, H., & Leiss, D. (2023). On the role of linguistic features for comprehension and learning from STEM texts. A meta-analysis. Educational Research Review, 39, Article 100533. https://doi.org/10.1016/j.edurev.2023.100533
Thevenot, C. (2010). Arithmetic word problem solving: Evidence for the construction of a mental model. Acta Psychologica, 133(1), 90-95. https://doi.org/10.1016/j.actpsy.2009.10.004
Ufer, S., Leiss, D., Stanat, P., & Gasteiger, H. (2020). Sprache und Mathematik – theoretische Analysen und empirische Ergebnisse zum Einfluss sprachlicher Fähigkeiten in mathematischen Lern- und Leistungssituationen [Language and mathematics - theoretical analyses and empirical results on the influence of language skills in mathematical learning and performance situations]. Journal für Mathematik-Didaktik, 41, 1-9. https://doi.org/10.1007/s13138-020-00164-1
van Dijk, T. A., & Kintsch, W. (1983). Strategies of discourse comprehension. Academic Press.
Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of world problems. Swets & Zeitlinger.
Verschaffel, L., Schukajlow, S., Star, J., & Van Dooren, W. (2020). Word problems in mathematics education: A survey. ZDM Mathematics Education, 52, 1-16. https://doi.org/10.1007/s11858-020-01130-4
Vilenius-Tuohimaa, P. M., Aunola, K., & Nurmi, J.-E. (2008). The association between mathematical word problems and reading comprehension. Educational Psychology, 28(4), 409-426. https://doi.org/10.1080/01443410701708228
Walkington, C., Clinton, V., & Shivraj, P. (2018). How readability factors are differentially associated with performance for students of different backgrounds when solving mathematics word problems. American Educational Research Journal, 55(2), 362-414. https://doi.org/10.3102/0002831217737028
Wienecke, L.-M., Leiss, D., & Ehmke, T. (2023). Taking notes as a strategy for solving reality-based tasks in mathematics. International Electronic Journal of Mathematics Education, 18(3), Article em0744. https://doi.org/10.29333/iejme/13312
Wijaya, A., van den Heuvel-Panhuizen, M., & Doormann, M. (2015). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational Studies in Mathematics, 89, 41-65. https://doi.org/10.1007/s10649-015-9595-1
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. https://doi.org/10.1080/10627190903425883