Teachers’ Knowledge about Language in Mathematics Professional Development Courses: From an Intended Curriculum to a Curriculum in Action

Maaike Hajer; Eva Norén

doi:10.12973/eurasia.2017.00808a

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Maaike Hajer ¹ ², Eva Norén ³ ^*

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¹ Malmö University, Sweden² Utrecht University of Applied Sciences, the Netherlands³ Stockholm University, Sweden^* Corresponding Author

Abstract

Explicit language objectives are included in the Swedish national curriculum for mathematics. The curriculum states that students should be given opportunities to develop the ability to formulate problems, use and analyse mathematical concepts and relationships between concepts, show and follow mathematical reasoning, and use mathematical expressions in discussions. Teachers’ competence forms a crucial link to bring an intended curriculum to a curriculum in action. This article investigates a professional development program, ‘Language in Mathematics’, within a national program for mathematics teachers in Sweden that aims at implementing the national curriculum into practice. Two specific aspects are examined: the selection of theoretical notions on language and mathematics and the choice of activities to relate selected theory to practice. From this examination, research on teacher learning in connection to professional development is proposed, which can contribute to a better understanding of teachers’ interpretation of integrated approaches to language and mathematics across national contexts.

Keywords

content and language integrated learning
curriculum implementation
knowledge about language
mathematics teachers
Pedagogical Content Knowledge
professional development

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 13, Issue 7b, July 2017, 4087-4114

https://doi.org/10.12973/eurasia.2017.00808a

Publication date: 21 Jun 2017

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References

Adler, J. (1998). A language of teaching dilemmas: Unlocking the complex multilingual secondary mathematics classroom. For the Learning of Mathematics, 18(1), 24–33.
Adler, J. (2001). Teaching Mathematics in Multilingual Classrooms. Dordrecht: Kluwer Academic Publishers.
Alrø, H., & Skovsmose, O. (2004). Dialogue and learning in mathematics education: Intention, reflection, critique (Vol. 29). Dordrecht, Boston, New York, London Dialogue and learning in mathematics education: Intention, reflection, critique: Kluwer Academic Publishers.
Arnó-Macià, E. (2009). Knowledge about language in English language Courses for future language professionals. Nordic Journal of English Studies, 8(1), 5–39.
Australian Curriculum and Reporting Authority (ACARA) (2015). The Shape of the Australian curriculum, version 4. Retrieved the 15th of August from http://www.acara.edu.au/curriculum.
Bakkenes, I., Vermunt, J. D., & Wubbels, T. (2010). Teacher learning in the context of educational innovation: Learning activities and learning outcomes of experienced teachers. Learning and Instruction 20, 533–548. DOI:10.1016/j.learninstruc.2009.09.001.
Civil, M., & Planas, N. (2004). Participation in the mathematics classroom: Does every student have a voice? For the learning of mathematics 24(1), 8–14.
Cleghorn, A., Mtetwa, D., Dube, R., & Munetsi, C. (1998). Classroom language use in multilingual settings: mathematics lessons from Quebec and Zimbabwe. International Journal of Qualitative Studies in Education, 11(3), 463–477. DOI:10.1080/095183998236610.
Coyle, D. (2009) Promoting cultural diversity through intercultural understanding. A case study of CLIL professional development at inservice and preservice level. In M. Carrió-Pastor, Content and language integrated learning: cultural diversity, pp. 105–124. Bern: Peter Lang.
Davison, C. (2016). Collaboration between English language and content teachers: Breaking the boundaries. In A. Tajino, T. Stewart, & D. Dalsky (Ed.), Team Teaching and Team Learning: Collaboration for Innovation in Language Classrooms, pp. 51–66. New York: Routledge.
Deen, J., Hajer, M., & Koole, T. (Eds.). (2008). Interaction in two multicultural mathematics classrooms: Mechanisms of inclusion and exclusion. Amsterdam: Aksant.
den Brok, P., van Eerde, D., & Hajer, M. (2010). Classroom interaction studies as a source for teacher competencies: the use of case studies with multiple instruments for studying teacher competencies in multicultural classes. Teachers and Teaching: theory and practice, 16(6), 717–733. DOI: 10.1080/13540602.2010.517689.
Derewianka, B. (2003). Trends and issues in genre-based approaches. RELC Journal, 34(2), 133–154. DOI: 10.1177/003368820303400202.
Elbers, E., Hajer, M., Koole, T., & Prenger, J. (2008). Instructional dialogues: participation in dyadic interactions in multicultural classrooms. In J. Deen, M. Hajer, & T. Koole (Eds.), Interaction in Two Multicultural Mathematics Classrooms. Mechanisms of Inclusion and Exclusion, pp. 141–171. Amsterdam: Aksant, NWO-reeks.
Ferrini-Mundy, J., Floden, R., McCrory, R., Burrill, G., & Sandow, D. (2005). Knowledge for teaching school algebra: Challenges in developing an analytic framework. American Education Research Association. Montreal, Quebec, Canada.
Gibbons, P. (2002). Scaffolding language, scaffolding learning: teaching second language learners in the mainstream classroom. Portsmouth, NH: Heinemann.
Gibbons, P. (2009). English learners, academic literacy, and thinking. Learning in the Challenge Zone. Portsmouth, England: Heinemann.
Goodlad, J. I. (1979). Curriculum inquiry. The study of curriculum and practice. New York, McGraw Hill.
Goodlad, J. I. (1986). The learner at the world's center. Social Education, 50(6).
Hajer, M. (2006) Inspiring teachers to work with content-based language instruction – stages in professional development. In I. Lindberg & K. Sandwall (Eds.) Språket och kunskapen – att lära på sitt andraspråk i skola och högskola, pp. 27–46. Gothenburg: Institutet för Svenska som Andraspråk, Rosa-serien.
Hajer, M., & Meestringa, T. (2014). Språkinriktad undervisning: en handbok. Stockholm: Hallgren & Fallgren.
Hammond, J. (2014). An Australian perspective on standards-based education, teacher knowledge, and students of English as an additional language. TESOL Quarterly, 48(3), 507–532. DOI: 10.1002/tesq.173.
Hammond, J. & Gibbons, P. (2005). Putting scaffolding to work: The contribution of scaffolding in articulating ESL education. Prospect, 20(1), 6–30.
Hattie, J. (2012). Visible learning for teachers: Maximizing impact on learning. London, New York: Routledge.
Hattie, J., & Timperley, H. (2007). The power of feedback. Review of educational research, 77(1), 81–112.
Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372–400.
Jahnke, A. (2015). Hur högt kan ett lyft ta oss? Pedagogiska Magasinet, 3.
Jouber, M., & Sutherland, R. (2009). A perspective on the literature: CPD for teachers of mathematics. National Centre for Excellence in the Teaching of Mathematics. Retrieved from https://www.ncetm.org.uk/files/387553/RECME_Literature_Review.pdf.
Joubert, M., Back, J., De Geest, E., Hirst, C., & Sutherland, R. (2010). The researching effective CPD in mathematics education (RECME) research project. Research in Mathematics Education, 12(1), 77–78.
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. National Research Council. Mathematics Learning Study Committee.
Kling Sackerud, L. A. (2009). Elevers möjligheter att ta ansvar för sitt lärande i matematik: En skolstudie i postmodern tid (Doctoral dissertation, Institutionen för matematik, teknik och naturvetenskap, Umeå universitet).
Lee, O. (2004). Teacher change in beliefs and practices in science and literacy instruction with English language learners. Journal of Research in Science Teaching, 41(1), 65–93. DOI: 10.1002/tea.10125.
Liljestrand, J., & Runesson, U. (2006). Interaction, organisation, tasks and possibilities for learning about mathematical relationships: A Swedish classroom compared with a US classroom. In D. Clarke, E. Emanuelsson, E. Jablonka, & I. A. Chee Mok (Eds.). Making connections: Comparing mathematics classrooms around the world, pp. 165–184). Rotterdam, Taipei: Sense Publishers.
Little, D. (2007). The common European framework of reference for languages: Perspectives on the making of supranational language education policy. The Modern Language Journal, 91, 645–655. DOI:10.1111/j.1540-4781.2007.00627_2.x.
Loucks-Horsley, S., Stiles, K. E., Mundry, S., Love, N., & Hewson, P. W. (2009). Designing professional development for teachers of science and mathematics. Thousand Oaks, CA: Corwin Press.
Love, K., & Humphrey, S. (2012). A multi-level language toolkit for the Australian Curriculum: English. Australian Journal of Language and Literacy, 5(2), 173.
Marsh, D. (2002). Language awareness and CLIL. In J. Cenoz & N. H. Hornberger (Eds.), Encyclopedia of Language and Education, 2nd Edition, Volume 6: Knowledge about Language, pp. 233-246. New York: Springer.
Marsh, D. P., Mehisto, D., Wolff, M. J., & Frigols, M. (2009). European framework for CLIL teacher training. Strasbourg: Council of Europe.
McIntosh, A. (2006). Nya vägar i räkneundervisningen. In J. Boesen (Ed.), Lära och undervisa matematik – internationella perspektiv. Göteborg: NCM.
Moschkovich, J. N. (2002). A situated and sociocultural perspective on bilingual mathematics learners. In N. Nassir & P. Cobb (Eds.), Mathematical Thinking and Learning, Special issue on Diversity, Equity, and Mathematical Learning, 4(2&3), 189–212. DOI: 10.1207/S15327833MTL04023_5.
Moschkovich, J. (2007). Using two languages when learning mathematics. Educational studies in Mathematics, 64(2), 121–144. DOI: 10.1007/sl0649-005-9005-l.
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.
Norén, E. (2015). Agency and positioning in a multilingual mathematics classroom. Educational Studies in Mathematics, 89(2), 167–184. DOI 10.1007/s10649-015-9603-5.
Norén, E., Ramsfeldt, S., & Österling. L. (2016). Tentative evaluation of the module Language in mathematics. Unpublished evaluation, built on interviews, surveys and observations in classrooms. Stockholm University.
Novak, J. D. (1990). Concept maps and Vee diagrams: Two metacognitive tools to facilitate meaningful learning. Instructional science, 19(1), 29–52.
OECD (2010). OECD Reviews of Migrant Education - Closing the Gap for Immigrant Students: Policies, Practice and Performance. Retrieved the 17th of August 2016 at: http://www.oecd.org/edu/school/oecdreviewsofmigranteducation-closingthegapforimmigrantstudentspoliciespracticeandperformance.htm#W.
Österholm, M., & Bergqvist, E. (2013). What is so special about mathematical texts? Analyses of common claims in research literature and of properties of textbooks. ZDM, 45(5), 751–763. DOI: 10.1007/s11858-013-0522-6.
Prediger, S., Clarkson, P., & Bose, A. (2016). Purposefully relating multilingual registers: Building theory and teaching strategies for bilingual learners based on an integration of three traditions. In R. Barwell, P. Clarkson, A. Halai, M. Kazima, J. Moschkovich, N. Planas, . . . M. Villavicencio Ubillús (Eds.), Mathematics education and language diversity: The 21st ICMI study, pp. 193–215). Heidelberg: Springer.
Ramböll (2015). Delutvärdering Matematiklyftet Läsåret 2014/15. Stockholm. Retrieved the 15th of August 2016 https://www.skolverket.se/polopoly_fs/1.249368!/Slutlig%20version %20delutv%C3%A4rdering%20Matematiklyftet%20150904%20Pdf.pdf.
Regeringen [the Government] (2012). Government decision I 44. Stockholm: Utbildningsdepartementet [Department of Education].
Rezat, S., & Rezat, S. (2017). Subject-specific genres and genre awareness in integrated mathematics and language teaching. Eurasia Journal of Mathematics, Science and Technology Education, 3585-3606. doi: 10.12973/eurasia.2017.00805a.
Rose, D., & Martin, J. R. (2012). Learning to write, reading to learn: Genre, knowledge and pedagogy in the Sydney School. Sydney: Equinox.
Schleppegrell, M. J. (2004). The language of schooling: A functional linguistics perspective. Mahwah, NJ: Lawrence Erlbaum Associates Inc.
Schleppegrell, M. (2007). The Linguistic Challenges of Mathematics Teaching and Learning: A Research Review. Reading & Writing Quarterly, 23, 139–159. DOI: 10.1080/10573560601158461.
Schleppegrell, M. J., & O'Hallaron, C. L. (2011). Teaching academic language in L2 secondary settings. Annual Review of Applied Linguistics, 31, 3–18. DOI: https://doi.org/10.1017/S0267190511000067.
Schnellert, L. M., Butler, D. L., & Higginson, S. K. (2008). Co-constructors of data, co-constructors of meaning: Teacher professional development in an age of accountability. Teaching and Teacher Education, 24(3), 725–750. DOI: 10.1016/j.tate.2007.04.001.
Short, D. (2013). Training and sustaining effective teachers of sheltered instruction. Theory Into Practice, 52(2), 118–127. DOI: 10.1080/00405841.2013.770329.
Short, D., & Echevarria, J. (2004). Teacher skills to support English language learners. Educational leadership, 62(4), 8–13.
Short, D., & Echevarria, J. (2016). Developing academic language with the SIOP Model. Boston: Pearson Allyn & Bacon.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational researcher 15(2), 4–14.
Simon, M. (2014). Hypothetical Learning Trajectories in Mathematics Education. In S. Leman (Ed.), Encyclopedia of Mathematics Education, pp. 272-275. The Netherlands: Springer.
Simon, M., & Tzur, R. (2004). Explicating the role of mathematical tasks in conceptual learning: an elaboration of the hypothetical learning trajectory. Mathematical Thinking and Learning 6(2), 91–104. DOI: 10.1207/s15327833mtl0602_2.
Sjöberg, G. (2006). Om det inte är dyskalkyli-vad är det då? En multimetodstudie av eleven i matematikproblem ur ett longitudinellt perspektiv. Doctoral dissertation, Umeå universitet.
Skolverket [National Agency for Education] (2004). Nationella utvärderingen av grundskolan 2003 – Huvudrapport – svenska/svenska som andraspråk, engelska, matematik och undersökningen i årskurs 5, Skolverkets rapport 251.
Skolverket [National Agency for Education] (2011). Kommentarmaterial till kursplanen i matematik. Stockholm: Skolverket.
Skolverket [National Agency for Education] (2012). Matematiklyftet. Beslut 2012-08-24. Retrieved from http://www.skolverket.se/polopoly_fs/1.204676!/Menu/article/attachment/Programbeskrivning_Matematiklyftet240802013.pdf.
Skolverket (2016a). Video: Skolvägen, texten i uppgiften analyseras. Retrieved from https://matematiklyftet.skolverket.se/matematik/faces/training/newlink8190/newlink6604?_afrLoop=565647300864336&_afrWindowMode=0&_adf.ctrl-state=9gtodxui4_144.
Skolverket [National Agency for education] (2016b). Redovisning av Regeringsuppdrag. Retrieved from http://mb.cision.com/Public/481/2130927/aa1e7a4e159cb8ea.pdf.
Smit, J. (2013). Scaffolding language in multilingual mathematics classrooms. Utrecht University: Utrecht.
Smit, J., & van Eerde, D. (2011). A teacher’s learning process in dual design research: learning to scaffold language in a multilingual mathematics classroom. ZDM, 43(6–7), 889–900. DOI: 10.1007/s11858-011-0350-5.
Timperley, H., & Phillips, G. (2003). Changing and sustaining teachers’ expectations through professional development in literacy. Teaching and Teacher Education 19(6), 627–641. DOI:10.1016/S0742-051X(03)00058-1.
Timperley, H., Wilson, A., Barrar, H., & Fung, I. (2008). Teacher professional learning and development. Educational Practises Serie – 18. Brussels: The International Academy of Education (IAE).
Turkan, S., de Oliveira, L., Lee, O., & Phelps, G. (2014). Proposing a knowledge base for teaching academic content to English language learners: Disciplinary linguistic knowledge. Teachers College Record, 116(1), 1–30.
Van den Akker (2003) Curriculum perspectives: An introduction. In J. van den Akker, W. Kuiper, & U. Hameyer (Eds.), Curriculum landscapes and trends, pp. 1–10. Dordrecht: Kluwer Academic Publishers.
Van den Akker, J. (2010). Building bridges: How research may improve curriculum policies and classroom practices. Beyond Lisbon, 201(0), 175–195.
van Eerde, H. H. A., & Hajer, M. (2008). The integration of mathematics and language learning in multiethnic schools. In M. Cesar, & K. Kompulainen (Eds.) Social Interactions in multicultural settings, pp. 269–296. Rotterdam: Sense Publishers.
Vogt, M. E., Echevarria, J., & Short, D. (2010). The SIOP Model for Teaching English Language Arts to English Learners. Boston: Pearson Allyn & Bacon.
Wenger, E. (1998). Communities of Practice. Learning, Meaning and Identity. Cambridge: Cambridge University Press.
Wiseman, A. W. (2008). A culture of (in) equality? A cross-national study of gender parity and gender segregation in national school systems. Research in Comparative and International Education, 3(2), 179–201. DOI: 10.2304/rcie.2008.3.2.179.

How to cite this article

APA

Hajer, M., & Norén, E. (2017). Teachers’ Knowledge about Language in Mathematics Professional Development Courses: From an Intended Curriculum to a Curriculum in Action. Eurasia Journal of Mathematics, Science and Technology Education, 13(7b), 4087-4114. https://doi.org/10.12973/eurasia.2017.00808a

Vancouver

Hajer M, Norén E. Teachers’ Knowledge about Language in Mathematics Professional Development Courses: From an Intended Curriculum to a Curriculum in Action. EURASIA J Math Sci Tech Ed. 2017;13(7b):4087-114. https://doi.org/10.12973/eurasia.2017.00808a

AMA

Hajer M, Norén E. Teachers’ Knowledge about Language in Mathematics Professional Development Courses: From an Intended Curriculum to a Curriculum in Action. EURASIA J Math Sci Tech Ed. 2017;13(7b), 4087-4114. https://doi.org/10.12973/eurasia.2017.00808a

Chicago

Hajer, Maaike, and Eva Norén. "Teachers’ Knowledge about Language in Mathematics Professional Development Courses: From an Intended Curriculum to a Curriculum in Action". Eurasia Journal of Mathematics, Science and Technology Education 2017 13 no. 7b (2017): 4087-4114. https://doi.org/10.12973/eurasia.2017.00808a

Harvard

Hajer, M., and Norén, E. (2017). Teachers’ Knowledge about Language in Mathematics Professional Development Courses: From an Intended Curriculum to a Curriculum in Action. Eurasia Journal of Mathematics, Science and Technology Education, 13(7b), pp. 4087-4114. https://doi.org/10.12973/eurasia.2017.00808a

MLA

Hajer, Maaike et al. "Teachers’ Knowledge about Language in Mathematics Professional Development Courses: From an Intended Curriculum to a Curriculum in Action". Eurasia Journal of Mathematics, Science and Technology Education, vol. 13, no. 7b, 2017, pp. 4087-4114. https://doi.org/10.12973/eurasia.2017.00808a