Analysing Mathematical Word Problem Solving with Secondary Education CLIL Students: A Pilot Study
Keywords:CLIL, mathematics, secondary education, word problem solving, contextual factors, reading comprehension, student evaluation.
Análisis de la resolución de problemas con estudiantes AICLE de educación secundaria: un estudio piloto
Análise da resolução de problemas com alunos CLIL do ensino médio: um estudo piloto
The purpose of this study is to investigate to what extent the use of L2 in math tests influences bilingual education learners’ process of word problem solving in a mandatory secondary education school with Content and Language Integrated Learning (CLIL). The reading comprehension level of the students was analysed using a standards-based assessment and the questions used in Programme for International Student Assessment (PISA) tests. The word problems were selected according to the students’ level of reading-comprehension and mathematical competence. Leaners also had to answer a questionnaire, which was used to analyse if contextual factors were affecting mathematical performance in L2. To this end, the questionnaire included some questions related to the bilingual history of the students and their perception about solving word problems in English. Data were analysed through one-way or two-way ANOVA tests to find out which factors were relevant. Results show that solving word problems is not only affected by the use of L2, but that it also depends on the mathematical difficulty, irrespective of the students’ level of language proficiency. The findings, hence, imply that interaction between linguistic difficulty and mathematical complexity is at the centre of the issues affecting word problem solving.
To reference this article (APA) / Para citar este artículo (APA) / Para citar este artigo (APA)
Cabezuelo, R. & Pavón, V. (2019). Analysing mathematical word problem solving with secondary education CLIL students: A pilot study. LACLIL, 12(1), 18-45. DOI: https://doi.org/10.5294/laclil.2019.12.1.2
* New version of PDF 22/01/2020: Change in order of authors. This changes can be seen in "To reference this article", in the first page and the cornices. No other change was made.
Abedi, J. (2002). Standardized achievement tests and English language learners: Psychometrics issues. Educational Assessment, 8(3), 231–257. DOI: https://doi.org/10.1207/S15326977EA0803_02
Abedi, J., & Lord, C. (2001). The language factor in mathematics tests. Applied Measurement in Education, 14(3), 219–234. DOI: https://doi.org/10.1207/S15324818AME1403_2
Adanur, Y., Yagiz, O., & IŞik, A. (2004). Mathematics and language. Journal of the Korea Society of Mathematical Education Series D: Research in Mathematical Education, 8(1), 31–37. Retrieved from https://www.semanticscholar.org/paper/Mathematics-and-Language-Adanur-Ya%C4%9F%C4%B1z/358c34c870078bd4a42568fdec29838d442e37c5
AGAEVE. (2017). Evaluación ESCALA: cuestionario de contexto. Familia. Retrieved from http://www.juntadeandalucia.es/educacion/agaeve/profesorado-primaria-escala-contexto.html
Bernardo, A. B. (1999). Overcoming obstacles to understanding and solving word problems in mathematics. Educational Psychology, 19(2), 149–163. DOI: https://doi.org/10.1080/0144341990190203
Bernardo, A. B. (2002). Language and mathematical problem solving among bilinguals. Journal of Psychology: Interdisciplinary and Applied, 136(3), 283–297. DOI: https://doi.org/10.1080/00223980209604156
Bialystok, E. (2001). Bilingualism in development: Language, literacy, and cognition. Cambridge, UK: Cambridge University Press.
Cambridge. (2017a). Cambridge English: Preliminary (PET) exam format. Retrieved from http://www.cambridgeenglish.org/exams-and-tests/preliminary/exam-format
Cambridge. (2017b). The Cambridge English scale. Retrieved from http://www.cambridgeenglish.org/exams-and-tests/cambridge-english-scale
Caro, D. H., & Cortés, D. (2012). Measuring family socioeconomic status: An illustration using data from PIRLS 2006. IERI Monograph Series. Issues and Methodologies in Large-Scale Assessments, 5, 9–33. Retrieved from http://www.ierinstitute.org/fileadmin/Documents/IERI_Monograph/IERI_Monograph_Volume_05_Chapter_1.pdf
Council of Europe. (2001). Common European framework of reference for languages. Cambridge, UK: Cambridge University Press.
Coyle, D., Hood, P., & Marsh, D. (2010). CLIL: Content and language integrated learning. Cambridge, UK: Cambridge University Press.
Cummins, J. (2000). Bilingual education and bilingualism: Language, power and pedagogy: Bilingual children in the crossfire (1). Bristol, UK: Multilingual Matters.
Cummins, D. D., Kintsch, W., Reusser, K., & Weimer, R. (1988). The role of understanding in solving word problems. Cognitive psychology, 20(4), 405–438. DOI: https://doi.org/10.1016/0010-0285(88)90011-4
Dalrymple-Smith, A., Karagiannakis, V., & Papadopoulos, K. (2012). Does international education risk the development of students’ mother tongues? An investigation into language use in mathematics classrooms (Unpublished project-based research). Utrecht University, Utrecht, The Netherlands.
Ensminger, M. E., Forrest, C. B., Riley, A. W., Kang, M., Green, B. F., Starfield, B., & Ryan, S. A. (2000). The validity of measures of socioeconomic status of adolescents. Journal of Adolescent Research, 15(3), 392–419. DOI: https://doi.org/10.1177/0743558400153005
Grabner, R. H., Saalbach, H., & Eckstein, D. (2012). Language-switching costs in bilingual mathematical learning. Mind, Brain, and Education, 6(3), 147–155. DOI: https://doi.org/10.1111/j.1751-228X.2012.01150.x
Halliday, M. A. K. (1978). Sociolinguistic aspects of mathematical education. In M. A. K. Halliday (Ed.), Language as social semiotic: The social interpretation of language and meaning (pp. 194–204). London, UK: Edward Arnold.
Hansen-Thomas, H., Langman, J., & Farias, T. (2018). The role of language objectives: Strengthening math and science teachers’ language awareness with emergent bilinguals in secondary classrooms. LACLIL, 11(2), 193–214. DOI: https://doi.org/10.5294/laclil.2018.11.2.2
Hattie, J. A. (2009). Visible learning: A synthesis of 800 + meta-analyses on achievement. Abingdon, UK: Routledge.
Hiebert, J., & LeFever, P. (1987). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge in mathematics (pp. 1–27). Hillsdale, NJ: Erlbaum.
INEE. (2013). Estímulos PISA de Matemáticas liberados: aplicación como recurso didáctico en la ESO. Retrieved from http://recursostic.educacion.es/inee/pisa/matematicas/_private/pisamatematicas2013.pdf
Jäppinen, A-K. (2005). Thinking and content learning of Mathematics and Science as cognitional development in content and language integrated learning (CLIL): Teaching through a foreign language in Finland. Language and Education, 19(2), 148–169. Retrieved from https://www.unifg.it/sites/default/files/allegatiparagrafo/20-01-2014/jappinen_thinking_and_content_learning_in_mathematics_and_science.pdf
Jiménez-Jiménez, A. F. (2015). Private speech during problem-solving activities in bilingual speakers. International Journal of Bilingualism, 19(3), 259–281. DOI: https://doi.org/10.1177/1367006913509902
Junta de Andalucía. (2016). Plan estratégico de desarrollo de las lenguas en Andalucía. Horizonte 2020. Retrieved from https://www.juntadeandalucia.es/export/drupaljda/plan_estrategico.pdf
Kempert, S., Saalbach, H., & Hardy, I. (2011). Cognitive benefits and costs of bilingualism in elementary school students: The case of mathematical word problems. Journal of Educational Psychology, 103(3), 547–561. DOI: http://dx.doi.org/10.1037/a0023619
Lancaster, N. (2018). Extramural exposure and language attainment: The examination of input-related variables in CLIL programmes. Porta Linguarum, 29, 91–114. Retrieved from http://digibug.ugr.es/handle/10481/54024
Lorenzo, F. (2008). Instructional discourse in bilingual settings. An empirical study of linguistic adjustments in content and language-integrated learning. Language Learning Journal, 36(1), 21–33. DOI: https://doi.org/10.1080/09571730801988470
Lyster, R. (2007). Learning and teaching languages through content: A counterbalanced approach. Amsterdam, The Netherlands: John Benjamins.
May, T., & Ong, S. (2011). Teaching Mathematics and Science in English in Malaysian classrooms: The impact of teacher beliefs on classroom practices and student learning. Journal of English for Academic Purposes, 10, 2–18. DOI: https://doi.org/10.1016/j.jeap.2010.11.001
Morgan, C. (2007). Who is not multilingual now? Educational Studies in Mathematics, 64, 239–242. DOI: http://doi.org/10.1007/s10649-006-9064-y
Moschkovich, J. N. (2005). Using two languages when learning mathematics. Educational Studies in Mathematics, 64, 121–144. DOI: https://doi.org/10.1007/s10649-005-9005-1
Moschkovich, J. N. (2007). Beyond words to mathematical content: Assessing English learners in the mathematics classroom. Assessing Mathematical Proficiency, 53, 345–352. Retrieved from https://www.researchgate.net/publication/237281918_Beyond_Words_to_Mathematical_Content_Assessing_English_Learners_in_the_Mathematics_Classroom
Moschkovich, J. N. (2015). Academic literacy in mathematics for English learners. The Journal of Mathematical Behavior, 40, 43–62. DOI: https://doi.org/10.1016/j.jmathb.2015.01.005
Novotná, J., Hadj-Moussová, Z., & Hofmannová, M. (2005). Teacher training for CLIL – Competences of a CLIL teacher. Retrieved from: http://people.fjfi.cvut.cz/novotant/jarmila.novotna/Novotna-et-alsemt01.pdf
OECD. (2006). Education at a Glance. Paris, France: OECD Publishing.
OECD. (2013). Education at a Glance, Paris, France: OECD Publishing.
OECD. (2014). PISA 2012 technical report. Paris, France: OECD Publishing.
OECD. (2016). PISA 2015 assessment and analytical framework: Science, reading, mathematic and financial literacy. Paris, France: OECD publishing.
Orden de 28 de junio de 2011, by which state bilingual schools in the Autonomous Region of Andalusia are regulated.
Ouazizi, K. (2016). The effects of CLIL education on the subject matter (Mathematics) and the target language (English), LACLIL, 9(1), 110–137. DOI: https://doi.org/10.5294/laclil.2016.9.1.5
Rutkowski, D., & Rutkowski, L. (2013). Measuring socioeconomic background in PISA: One size might not fit all. Research in Comparative and International Education, 8(3), 259–278. DOI: https://doi.org/10.2304/rcie.2013.8.3.259
Schleicher, A., Zimmer, K., Evans, J., & Clements, N. (2009). PISA 2009 assessment framework: Key competencies in reading, mathematics and science. Paris, France: OECD Publishing (NJ1).
Sigley, R., & Wilkinson, L. C. (2015). Ariel’s cycles of problem solving: An adolescent acquires the mathematics register. Journal of Mathematical Behavior, 40, 75–87. DOI: https://doi.org/10.1016/j.jmathb.2015.03.001
Sirin, S. R. (2005). Socioeconomic status and academic achievement: A meta-analytic review of research. Review of Educational Research, 75(3), 417–453. DOI: https://doi.org/10.3102/00346543075003417
Smit, J., & Van Eerde, A. A. (2011). A teacher’s learning process in dual design research: Learning to scaffold language in a multilingual mathematics classroom. Mathematics Education, 43, 889–900. DOI: https://doi.org/10.1007/s11858-011-0350-5
Spelke, E. S., & Tsivkin, S. (2001). Language and number: A bilingual training study. Cognition, 78, 45–88. DOI: https://doi.org/10.1016/S0010-0277(00)00108-6
Surmont, J., Struys, E., Ven Den Noort, M., & Van Der Craen, P. (2016). The effects of CLIL in mathematical content learning: A longitudinal study. Studies in Second Language Learning and Teaching, 6(2), 319–337. DOI: http://doi.org/10.14746/ssllt.2016.6.2.7
Swetz, F. J. (2012). Mathematical expeditions: Exploring word problems across the ages. Baltimore, MD: John Hopkins University Press.
Tavares, N. J. (2015). How strategic use of L1 in an L2-medium mathematics classroom facilitates L2 interaction and comprehension, International Journal of Bilingual Education and Bilingualism, 18(3), 319–335. DOI: https://doi.org/10.1080/13670050.2014.988115
Van Rinsveld, A., Brunner, M., Landerl, K., Schiltz, C., & Ugen, S. (2015). The relation between language and arithmetic in bilinguals: Insights from different stages of language acquisition. Frontiers in Psychology, 6(265), 1–15. DOI: https://doi.org/10.3389/fpsyg.2015.00265
Van Rinsveld, A., Schiltz, C., Brunner, M., Landerl, K., & Ugen, S. (2016). Solving arithmetic problems in first and second language: Does the language context matter? Learning and Instruction, 42, 72–82. DOI: https://doi.org/10.1016/j.learninstruc.2016.01.003
White, K. R. (1982). The relation between socioeconomic status and academic achievement. Psychological Bulletin, 91(3), 461–481. DOI: http://dx.doi.org/10.1037/0033-2909.91.3.461
Willms, J. D., & Tramonte, L. (2015). Towards the development of contextual questionnaires for the PISA for development study. Retrieved from https://www.oecd-ilibrary.org/docserver/5js1kv8crsjf-en.pdf?expires=1563951052&id=id&accname=guest&checksum=404F909C23AD91A5DF544DB9E2783E7C
How to Cite
Authors who publish with this journal agree to the following terms:
This journal and its papers are published with the Creative Commons License Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0). You are free to share copy and redistribute the material in any medium or format if you: give appropriate credit, provide a link to the license, and indicate if changes were made; don’t use our material for commercial purposes; don’t remix, transform, or build upon the material.
Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).