Advertisement

Zeitschrift für Erziehungswissenschaft

, Volume 21, Issue 1, pp 71–96 | Cite as

Language switching costs in bilingual mathematics learning: Transfer effects and individual differences

  • Esther Volmer
  • Roland H. Grabner
  • Henrik Saalbach
Schwerpunkt
  • 444 Downloads

Abstract

There is an implicit assumption in Content- and Language Integrated Learning that the acquired knowledge is represented independently of the language of instruction. However, it could be shown in several experimental intervention studies that cognitive costs (i. e. longer reaction times and lower accuracy) arise when the languages of study and retrieval do not match. In the present study, we focused on arithmetic fact learning and investigated whether these cognitive costs generalize to more complex contexts. In addition, we explored the relationship between the cognitive costs and individual differences in executive functions, intelligence, mathematical competence and second language (L2) proficiency. Participants were 58 German-French bilingual university students (L2 proficiency B2 or above). They studied multiplication facts for 3 consecutive days in either their L1 or L2, followed by a test in both languages on the 4th day. Cognitive costs caused by language switching between training and test were found for both problems requiring simple fact retrieval and problems requiring knowledge application in novel, more complex text problems. The costs were negatively related with L2 proficiency and positively with inhibition. This study shows for the first time that language switching costs can be found in situations when knowledge needs to be applied in a new context, as it is often necessary in classroom learning. Implications of this study will be discussed with regards to bilingual arithmetic learning.

Keywords

Arithmetic text problems Bilingual education Cognitive costs Content- and language integrated learning (CLIL) Executive functions Language Switching Costs Transfer 

Sprachwechselkosten beim zweisprachigen Mathematiklernen: Transfereffekte und individuelle Unterschiede

Zusammenfassung

Bei fremdsprachlichem Fachunterricht wird implizit davon ausgegangen, dass das erworbene Wissen unabhängig von der Instruktionssprache repräsentiert ist. In mehreren experimentellen Interventionsstudien konnte allerdings gezeigt werden, dass kognitive Kosten in Form von längeren Reaktionszeiten und höheren Fehlerzahlen entstehen, wenn die Sprache beim Wissensabruf nicht mit der Instruktionssprache übereinstimmt. In der vorliegenden Studie wurde für arithmetisches Faktenlernen untersucht, ob sich diese Kosten auf komplexere Aufgaben übertragen. Weiterhin wurde deren Zusammenhang mit exekutiven Funktionen, Intelligenz, Rechen- und Sprachkompetenzen in der Zweitsprache (L2) geprüft. Die Studienteilnehmer waren 58 zweisprachige (deutsch-französisch) Studierende (L2-Sprachfähigkeiten B2 oder höher). Sie lernten die Ergebnisse von Multiplikationsaufgaben über 3 aufeinanderfolgende Tage in der L1 oder L2, mit einem anschließenden Test auf beiden Sprachen am 4. Tag. Kognitive Kosten durch Sprachwechsel zwischen Training und Testung wurden für die Reaktionszeiten bei Aufgaben, die einen einfachen Faktenabruf erforderten, sowie bei Transferaufgaben, die Anwendung des Wissens in einem neuen, komplexeren Kontext erfordern, gefunden. Das Ausmaß der Kosten zeigte negative Zusammenhänge mit den Sprachfähigkeiten in L2 und positive Zusammenhänge mit Inhibition. Mit dieser Studie konnte erstmalig gezeigt werden, dass kognitive Kosten auch in Situationen entstehen, in denen Gelerntes in einen neuen Kontext gestellt wird, wie es im Rahmen schulischen Lernens erforderlich ist. Implikationen der Studie werden im Hinblick auf zweisprachiges Mathematiklernen diskutiert.

Schlüsselwörter

Mathematische Textaufgaben Bilingualer Unterricht Kognitive Kosten Fremdsprachlicher Fachunterricht Exekutive Funktionen Sprachwechselkosten Transfer 

References

  1. Abedi, J., & Lord, C. (2001). The language factor in mathematics tests. Applied Measurement in Education, 14(3), 219–234.CrossRefGoogle Scholar
  2. de Abreu, E. P. M. J., Cruz-Santos, A., Tourinho, C. J., Martin, R., & Bialystok, E. (2012). Bilingualism enriches the poor: enhanced cognitive control in low-income minority children. Psychological Science, 23(11), 1364–1371.CrossRefGoogle Scholar
  3. Bergström, K., Klatte, M., Steinbrink, C., & Lachmann, T. (2016). First and second language acquisition in German children attending a kindergarten immersion program: a combined longitudinal and cross-sectional study. Language Learning, 66(2), 386–418.CrossRefGoogle Scholar
  4. Bialystok, E. (2006). Effect of bilingualism and computer video game experience on the Simon task. Canadian Journal of Experimental Psychology, 60(1), 68–79.CrossRefGoogle Scholar
  5. Bialystok, E. (2009). Bilingualism: the good, the bad, and the indifferent. Bilingualism: Language and Cognition, 12(01), 3.CrossRefGoogle Scholar
  6. Bialystok, E. (2015). Bilingualism and the development of executive function: the role of attention. Child Development Perspectives, 9(2), 117–121.CrossRefGoogle Scholar
  7. Bialystok, E., & Martin, M. M. (2004). Attention and inhibition in bilingual children: evidence from the dimensional change card sort task. Developmental Science, 7(3), 325–339.CrossRefGoogle Scholar
  8. Bialystok, E., Craik, F. I. M., Klein, R., & Viswanathan, M. (2004). Bilingualism, aging, and cognitive control: evidence from the Simon task. Psychology and aging, 19(2), 290–303.CrossRefGoogle Scholar
  9. Bialystok, E., Craik, F. I., Grady, C., Chau, W., Ishii, R., Gunji, A., & Pantev, C. (2005). Effect of bilingualism on cognitive control in the Simon task: evidence from MEG. NeuroImage, 24(1), 40–49.CrossRefGoogle Scholar
  10. Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects ?: State, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37–68.CrossRefGoogle Scholar
  11. Brysbaert, M. (2013). LexTALE_FR: A fast, free, and efficient test to measure language proficiency in French. Psychologica Belgica, 53(1), 23–37.CrossRefGoogle Scholar
  12. Carlson, S. M., & Meltzoff, A. N. (2008). Bilingual experience and executive functioning in young children. Developmental Science, 11(2), 282–298.CrossRefGoogle Scholar
  13. Cheng, L., Li, M., Kirby, J. R., Qiang, H., & Wade-Woolley, L. (2010). English language immersion and students’ academic achievement in English, Chinese and mathematics. Evaluation & Research in Education, 23(3), 151–169.CrossRefGoogle Scholar
  14. Council for Cultural Co-operation (2009). Common European Framework of Reference for Languages: learning, teaching, assessment (10th edn.). Cambridge: Cambridge University Press.Google Scholar
  15. Council of Europe (2002). Common European framework of reference for languages: learning, teaching, assessment; case studies. Language policies. Strasbourg: Council of Europe Publishing.Google Scholar
  16. Crystal, D. (2008). Two thousand million? English Today, 24(01), 3–6.CrossRefGoogle Scholar
  17. Dallinger, S., Jonkmann, K., Hollm, J., & Fiege, C. (2016). The effect of content and language integrated learning on students’ English and history competences—Killing two birds with one stone? Learning and Instruction, 41, 23–31.CrossRefGoogle Scholar
  18. Dowker, A. (2005). Individual differences in arithmetic: Implications for psychology, neuroscience and education. Hove: Psychology Press.CrossRefGoogle Scholar
  19. EACEA, Eurydice, & Eurostat (2012). Key data on teaching languages at school in Europe. Brussels: Eurydice.Google Scholar
  20. Ekstrom, R. B., French, J. W., Harman, H. H., & Dermen, D. (1976). Kit of factor-referenced cognitive tests Google Scholar
  21. Eurydice (2006). Content and Language Integrated Learning (CLIL) at School in Europe. Brussels: Eurydice.Google Scholar
  22. Geary, D. C. (2013). Early foundations for mathematics learning and their relations to disabilities. Current directions in psychological science, 22(1), 23–27.CrossRefGoogle Scholar
  23. Gentner, D., & Goldin-Meadow, S. (2003). Language in mind: advances in the study of language and thought. Cambridge: MIT Press.Google Scholar
  24. Grabner, R. H., & De Smedt, B. (2012). Oscillatory EEG correlates of arithmetic strategies: a training study. Frontiers in Psychology, 3(428), 1–11.Google Scholar
  25. Grabner, R. H., Ischebeck, A., Reishofer, G., Koschutnig, K., Delazer, M., Ebner, F., & Neuper, C. (2009). Fact learning in complex arithmetic and figural-spatial tasks: the role of the angular gyrus and its relation to mathematical competence. Human Brain Mapping, 30(9), 2936–2952.CrossRefGoogle Scholar
  26. Grabner, R. H., Saalbach, H., & Eckstein, D. (2012). Language-switching costs in bilingual mathematics learning. Mind, Brain, and Education, 6(3), 147–155.CrossRefGoogle Scholar
  27. Green, D. W. (1998). Mental control of the bilingual lexico-semantic system. Bilingualism: Language and Cognition, 1(02), 67.CrossRefGoogle Scholar
  28. Gumperz, J. J., & Levinson, S. C. (1996). Rethinking linguistic relativity Google Scholar
  29. Hilchey, M. D., & Klein, R. M. (2011). Are there bilingual advantages on nonlinguistic interference tasks? Implications for the plasticity of executive control processes. Psychonomic bulletin & review, 18(4), 625–658.CrossRefGoogle Scholar
  30. Iluz-Cohen, P., & Armon-Lotem, S. (2013). Language proficiency and executive control in bilingual children. Bilingualism: Language and Cognition, 16(04), 884–899.CrossRefGoogle Scholar
  31. Imai, M., Schalk, L., Saalbach, H., & Okada, H. (2014). All giraffes have female-specific properties: influence of grammatical gender on deductive reasoning about sex-specific properties in German speakers. Cognitive science, 38(3), 514–536.CrossRefGoogle Scholar
  32. Jäger, A. O., Süß, H.-M., & Beauducel, A. (1997). Berliner Intelligenzstruktur-Test: BIS-Test Form 4. Göttingen: Hogrefe.Google Scholar
  33. 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), 147–168.CrossRefGoogle Scholar
  34. Karbach, J., & Kray, J. (2009). How useful is executive control training? Age differences in near and far transfer of task-switching training. Developmental Science, 12(6), 978–990.CrossRefGoogle Scholar
  35. 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.CrossRefGoogle Scholar
  36. Lo, Y. Y., & Lo, E. S. C. (2014). A meta-analysis of the effectiveness of English-medium education in Hong Kong. Review of Educational Research, 84(1), 47–73.CrossRefGoogle Scholar
  37. Mackworth, J. F. (1959). Paced memorizing in a continuous task. Journal of Experimental Psychology, 58(3), 206–211.CrossRefGoogle Scholar
  38. Malt, B. C., & Wolff, P. (2010). Words and the mind: how words capture human experience. CrossRefGoogle Scholar
  39. Marian, V., & Fausey, C. M. (2006). Language-dependent memory in bilingual learning. Applied Cognitive Psychology, 20(8), 1025–1047.CrossRefGoogle Scholar
  40. Martin-Rhee, M. M., & Bialystok, E. (2008). The development of two types of inhibitory control in monolingual and bilingual children. Bilingualism: Language and Cognition, 11(01), 81–93.  https://doi.org/10.1017/S1366728907003227.CrossRefGoogle Scholar
  41. Miller, K. F., & Stigler, J. W. (1987). Counting in Chinese: cultural variation in a basic cognitive skill. Cognitive Development, 2(3), 279–305.CrossRefGoogle Scholar
  42. Miller, K. F., Smith, C. M., Zhu, J., & Zhang, H. (1995). Preschool origins of cross-national differences in mathematical competence: the role of number-naming systems. Psychological Science, 6(1), 56–60.CrossRefGoogle Scholar
  43. Mishra, R. K., Hilchey, M. D., Singh, N., & Klein, R. M. (2012). On the time course of exogenous cueing effects in bilinguals: higher proficiency in a second language is associated with more rapid endogenous disengagement. The Quarterly journal of experimental psychology, 65(8), 1502–1510.CrossRefGoogle Scholar
  44. Miyake, A., Friedman, N. P., Emerson, M. J., Witzki, A. H., Howerter, A., & Wager, T. D. (2000). The unity and diversity of executive functions and their contributions to complex “Frontal Lobe” tasks: a latent variable analysis. Cognitive psychology, 41(1), 49–100.CrossRefGoogle Scholar
  45. Möller, J., Hohenstein, F., Fleckenstein, J., & Baumert, J. (2017). Formen und Effekte des Fremdsprachenerwerbs und der bilingualen Beschulung. In J. Möller, F. Hohenstein, J. Fleckenstein, O. Köller, & J. Baumert (Eds.), Erfolgreich integrieren – die Staatliche Europa-Schule Berlin. Münster: Waxmann.Google Scholar
  46. Paetsch, J., Felbrich, A., & Stanat, P. (2015). Der Zusammenhang von sprachlichen und mathematischen Kompetenzen bei Kindern mit Deutsch als Zweitsprache. Zeitschrift für Pädagogische Psychologie, 29(1), 19–29.CrossRefGoogle Scholar
  47. Piesche, N., Jonkmann, K., Fiege, C., & Keßler, J. U. (2016). CLIL for all? A randomised controlled field experiment with sixth-grade students on the effects of content and language integrated science learning. Learning and Instruction, 44, 108–116.CrossRefGoogle Scholar
  48. Saalbach, H., Imai, M., & Schalk, L. (2012). Grammatical gender and inferences about biological properties in german-speaking children. Cognitive science, 36(7), 1251–1267.CrossRefGoogle Scholar
  49. Saalbach, H., Eckstein, D., Andri, N., Hobi, R., & Grabner, R. H. (2013). When language of instruction and language of application differ: cognitive costs of bilingual mathematics learning (PSYNDEXshort). Learning and Instruction, 26, 36–44.CrossRefGoogle Scholar
  50. Saalbach, H., Gunzenhauser, C., Kempert, S., & Karbach, J. (2016). Der Einfluss von Mehrsprachigkeit auf mathematische Fähigkeiten bei Grundschulkindern mit niedrigem sozioökonomischen Status. Frühe Bildung, 5(2), 73–81.CrossRefGoogle Scholar
  51. Simon, J. R., & Rudell, A. P. (1967). Auditory SR compatibility: the effect of an irrelevant cue on information processing. Journal of applied psychology, 51(3), 300.CrossRefGoogle Scholar
  52. Spelke, E. S., & Tsivkin, S. (2001). Language and number: a bilingual training study. Cognition, 78(1), 45–88.CrossRefGoogle Scholar
  53. Turnbull, M., Hart, D., & Lapkin, S. (2003). Grade 6 French immersion students’ performance on large-scale reading, writing, and mathematics tests: building explanations. Alberta Journal of Educational Research, 49(1), 6–23.Google Scholar
  54. Verschaffel, L., Greer, B., & de Corte, E. (2002). Everyday knowledge and mathematical modeling of school word problems. In K. Gravemeijer, R. Lehrer, B. van Oers, & L. Verschaffel (Eds.), Symbolizing, modeling and tool use in mathematics education (pp. 257–276). Dordrecht: Springer.CrossRefGoogle Scholar
  55. Yan, S., & Nicoladis, E. (2009). Finding le mot juste: differences between bilingual and monolingual children’s lexical access in comprehension and production. Bilingualism: Language and Cognition, 12(03), 323–335.CrossRefGoogle Scholar
  56. Zaunbauer, A. C. M., & Möller, J. (2010). Schulleistungsentwicklung immersiv unterrichteter Grundschüler in den ersten zwei Schuljahren. Psychologie in Erziehung und Unterricht, 57(1), 30–45.CrossRefGoogle Scholar
  57. Zied, K. M., Phillipe, A., Karine, P., Valerie, H. T., Ghislaine, A., & Arnaud, R. (2004). Bilingualism and adult differences in inhibitory mechanisms: evidence from a bilingual Stroop task. Brain and cognition, 54(3), 254–256.CrossRefGoogle Scholar

Copyright information

© Springer Fachmedien Wiesbaden GmbH, ein Teil von Springer Nature 2017

Authors and Affiliations

  • Esther Volmer
    • 1
  • Roland H. Grabner
    • 2
  • Henrik Saalbach
    • 3
  1. 1.Bildungswissenschaft, Campus A5 4Universität des SaarlandesSaarbrückenGermany
  2. 2.Institut für PsychologieKarl-Franzens-Universität GrazGrazAustria
  3. 3.Erziehungswissenschaftliche FakultätUniversität LeipzigLeipzigGermany

Personalised recommendations