Analysing Mathematical Word Problem Solving with Secondary Education CLIL Students: A Pilot Study

Rafael Cabezuelo; Víctor Pavón

doi:10.5294/laclil.2019.12.1.2

Autores/as

Rafael Cabezuelo Autor/a Instituto de Educacion Secundaria López Neyra, Córdoba, Spain http://orcid.org/0000-0003-4518-7617
Víctor Pavón Autor/a University of Córdoba (Spain) http://orcid.org/0000-0003-3063-1746

DOI:

https://doi.org/10.5294/laclil.2019.12.1.2

Palabras clave:

CLIL, AICLE, matemáticas, ensañanza secundaria, resolución de problemas, factores de contexto, comprensión lectora, evaluación del estudiante.

Resumen

Analysing Mathematical Word Problem Solving with Secondary Education CLIL Students: A Pilot Study

Análise da resolução de problemas com alunos CLIL do ensino médio: um estudo piloto

El objetivo de este estudio es investigar hasta qué punto el uso de la L2 en las pruebas de matemáticas influye en el proceso de resolución de problemas por el alumnado. Esta investigación ha tenido lugar en un instituto de educación secundaria obligatoria que sigue la metodología del Aprendizaje Integrado de Contenidos y Lenguas Extranjeras (AICLE). Se analizó el nivel de comprensión lectora del alumnado por medio de una evaluación basada en estándares, utilizando las preguntas de los cuestionarios de PISA. Los problemas se seleccionaron de acuerdo con el nivel real de comprensión lectora y de competencia matemática de los estudiantes. Además, se administró un cuestionario para analizar si algunos factores contextuales estaban afectando al desempeño matemático en la L2, en el cual se incluyeron algunas cuestiones relacionadas con la historia bilingüe del alumnado y de su percepción con relación a la resolución de problemas en inglés. Los datos se analizaron mediante pruebas ANOVA (uno o dos factores) para analizar qué factores eran relevantes. Los resultados muestran que la resolución de problemas no solo se ve afectada por el uso de la L2 sino que también depende de la dificultad matemática, independientemente del nivel de dominio del idioma de los alumnos. Los hallazgos sugieren, por tanto, que la interacción entre la dificultad lingüística y la complejidad matemática es uno de los principales aspectos que afectan a la resolución de problemas.

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

Received: 05/02/2019

Approved: 23/04/2019

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Biografía del autor/a

Víctor Pavón, University of Córdoba (Spain)

Víctor Pavón-Vázquez is Assistant Professor at the University of Córdoba (Spain), where he teaches in the areas of EFL methodology and bilingual education. He is a member of the Committee for Language Accreditation within the CRUE (the national association of Rectors of Spanish universities), Head of the Dept. of English and German Philology, and President of the Language Policy Commission at the University of Córdoba. He has published in international journals such as the International Journal of Bilingual Education and Bilingualism, Language Policy, Theory Into Practice, Language Learning Journal or the European Journal of Applied Linguistics. As an author, researcher and lecturer, he is active in education development programmes in Europe and beyond, participating in educational projects in Europe, USA, Japan, Mexico, Russia, Cape Verde, Guatemala, Kirgizstan and Turkmenistan. His current interests focus on research and development for capacity building, and subsequent competence building of staff, to support the implementation of bilingual education programmes, and on the delineation of language policies in an international context.

Citas

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