Primary students’ participation in school based mathematical reasoning practices: Coordinating reciprocal teaching and systemic functional linguistics to support reasoning in the Swedish context
The foreign language (FL) classroom can be an anxious environ- ment where students feel uncomfortable having to communicate in a language in which they feel inadequate and have little practice. Low self-efficacy in skill-specific tasks is oftentimes the culprit. While there are a number of factors involved in successful language learning, this study examines how practice affects students’ sense of self-efficacy in the foreign language classroom. Using self-efficacy theory and design-based research, this qualitative study ‘flipped’ the classroom to focus on student input and output practice in class with grammar instruction video-recorded for homework. Data were recursively collected and analyzed from ten courses over three semesters. Classroom observations and reflection were triangulated with interviews and focus groups. Findings suggest that practice and self-efficacy in the FL classroom are indeed linked and that other factors such as peer familiarity and grading also play a role. The paper concludes with implications for language learning and teaching.
Barton, M. L., & Heidema, C. (2002). Teaching reading in mathematics (2nd ed.). Aurora, Co: Mid-continent research for education and learning.
Baxter, J. A., Woodward, J., & Olson, D. (2005). Writing in mathematics: An alternative form of communication for academically low-achieving students. Learning Disabilities Research & Practice, 20(2), 119-135.
Bishop, J., Lamb, L., Philipp, R., Withacre, I., Schappelle, B., & Lewis, M. (2014).Obstacles and Affordances for Integer Reasoning: An Analysis of Children's Thinking and the History of Mathematics. Journal for Research in Mathematics Education, 45(1), 19-61.
Boesen, J., Helenius, O., Bergqvist, E., Bergqvist, T., Lithner, J., Palm, T., & Palmberg, B. (2014). Developing mathematical competence: From the intended to the enacted curriculum. The Journal of Mathematical Behavior, 33(0), 72-87.
Brehmer, D., Ryve, A., & Van Steenbrugge, H. (2015). Problem solving in Swedish mathematics textbooks for upper secondary school. Scandinavian Journal of Educational Research.
Brinkmann, A. (2003). Mind mapping as a tool in mathematics education. Mathematics Teacher, 96(2), 96-101.
Budd, J.W. (2004). Mind maps as classroom exercises. The journal of economic education 35(1), p. 35-46.
Buzan, T. (1991). Mind mapping. Executive excellence 8(8), 3-4.
Carter, A. T., & Dean, O. E. (2006). Mathematics intervention for grades 5-11: Teaching mathematics, reading, or both? Reading Psychology, 27, 127-146.
Chronaki, A. (submitted).
Cobb, P. (2002) Reasoning With Tools and Inscriptions, Journal of the Learning Sciences, 11(2-3), 187-215.
Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.
Collen, M. H. (2011). Fifth Grade Children's Use of Reciprocal Teaching to Solve Word Problems in Mathematics. Doctoral thesis, state university of New York at Albany.
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in mathematics, 61, 103-131.
Ebbelind, A., & Segerby, C. (2015). Systemic Functional Linguistics as a Methodological Tool in Mathematics Education. Nordic Studies in Mathematics Education, 20(1), 33-54.
Gibbons, P. (2002). Scaffolding language, scaffolding learning: teaching second language learners in the mainstream classroom. Portsmouth, NH: Heinemann
Gravemeijer, K., & Cobb, P. (2006). Design research from a learning design perspective. In J. Van den Akker and K. Gravemeijer, S. McKenney and N. Nieveen (Eds.), Educational design research, 17-51. London: Routledge.
Halliday, M. A. K. (1973). The functional basis of language. In Basil Bernstein (ed.) Applied Studies towards a Sociology of Language, Vol. 2, Class, Codes and Control. Routledge and Kegan Paul, 343–66.
Halliday, M. A. (1993). Towards a language-based theory of learning. Linguistics and education, 5(2), 93-116.
Halliday, M. A. K., & Hasan, R. (1985). Language, context, and text: Aspects of language in a social-semiotic perspective. Oxford: Oxford University Press.
Halliday, M. A. K., & Matthiessen, C. (2004). An Introduction to Functional Grammar. London: Arnold.
Hanna, G. (2000). Proof, explanation and exploration: An overview. Educational Studies in Mathematics, 44 (1), 5-23
Herbel-Eisenmann, B. A. (2007). From intended curriculum to written curriculum: Examining the" voice" of a mathematics textbook. Journal for Research in Mathematics Education, 38, 344-369.
Huber, C. W. (2010). The Impact of Reciprocal Teaching on Mathematics Problems Solving for Grade 4 Students. Doctoral thesis, Central Connecticut State University, New Britain.
Kilpatrick, J. (2001). Understanding mathematical literacy: The contribution of research. Educational Studies in Mathematics, 47(1), 101-116.
Larsson, M. (2015). Orchestrating mathematical whole-class discussions in the problem-solving classroom: theorizing challenges and support for teachers. Diss. Västerås: Mälardalens högskola, 2015. Västerås.
Lederer, J. M. (2000). Reciprocal teaching of social studies in inclusive elementary classrooms. Journal of Learning Disabilities, 33(1), 91-106.
Liberg, C. (2008). Skrivandet i olika ämnen- lärares textkompetens. In R. T. Lorentzen and J. Smidt (Eds.), Å skrive i alle fag [To write in every subject]. Oslo: Universitetsforlaget.
Lithner, J. (2006). A framework for analysing creative and imitative mathematical reasoning. Rapportserie, Matematik, Umeå: Umeå universitet.
Lundberg, I., & Sterner, G. (2006). Räknesvårigheter och lässvårigheter under de första åren - hur hänger de ihop? [Counting disabilities and reading disabilities during the first Years- how are they connected]. Stockholm: Natur och Kultur.
Makar, K. (2014). Young children's explorations of average through informal inferential reasoning. Educational Studies in Mathematics, 86(1), 61-78.
Minsono, T. & Takeda, K. (2012). An investigation of the mathematical writing abilities of students in public elementary school in Japan. Paper presented at the 12th international congress on mathematical education, July 8-15, Seoul, Korea.
Morgan, C. (1998). Writing Mathematically: The discourse of investigation. London: Falmer Press.
Myndigheten för skolutveckling (the Swedish Agency for School Improvement) (2008). Mer än matematik: om språkliga dimensioner i matematikuppgifter [More than mathematics: the language dimensions in mathematics tasks]. Stockholm: Myndigheten för skolutveckling.
Möllehed, E. (2001). Problemlösning i matematik - en studie av påverkansfaktorer i årskurserna 4-9 [Problem solving in mathematics- a study of influencing factors in Year 4-9]. (Doctoral dissertation, Malmö University, Sweden). Malmö: Reprocentralen Lärarutbildningen.
National council of teachers of mathematics (NCTM) (2003). Programs for Initial Preparation of Mathematics Teachers. National Council of Teachers of Mathematics Reston, VA: NCTM.
NCF (2005). National curriculum framework. Retrieved from: http://www.ncert.nic.in/rightside/links/pdf/framework/english/nf2005.pdf
Niss, M. (2003). Mathematical competencies and the learning of mathematics: The Danish KOM project. In 3rd Mediterranean conference on mathematical education (pp. 115-126).
Nunes, T., Bryant, P., Evans, D., Gottardis, L., & Terlektsi, M. E. (2015). Teaching mathematical reasoning: Probability and problem solving in Primary School. Nuffield Foundation.
Palinscar, A. S., & Brown, A. L. (1984). Reciprocal teaching of comprehension-fostering and comprehension-monitoring activities. Cognition and Instruction, 1(2), 117-175.
Palinscar, A. S. (2003): Collaborative Approaches to Comprehension instruction. In A. Sweet and C. E., Snow (Eds.), Rethinking reading comprehension (pp. 99-114). New York: The Guilford Press.
Pimm, D. (1987). Speaking mathematically: Communication in mathematics Classrooms. London: Routledge.
Pressley, M. (2000). What should comprehension instruction be the instruction of? In M.L. Kamil, P. B. Mosenthal, P.D. Pearson, & R. Barr (Eds). Handbook of reading research, 545-560.Mahway, NJ: Erlbaum.
Quirk, P. J. (2010).Using reciprocal teaching and learning methods to enhance comprehension in mathematics word problems: a thesis presented in partial fulfillment of the requirements for the degree of Master of Education, Massey University, Palmerston North, New Zealand (Doctoral dissertation, Massey University).
Ratekin, N., Simson, M. L., Alvermann, D.E., & Dishner, E. K.(1985). Why teachers resist content reading instruction. Journal of Reading, 30, 432-437.
Riccomini, P. J., Smith, G. W., Hughes, E. M., & Fries, K. M. (2015). The language of mathematics: The importance of teaching and learning mathematical vocabulary. Reading & Writing Quarterly, 31(3), 235-252.
Rojas-Drummond, S., & Zapata, M. P. (2004). Exploratory talk, argumentation and reasoning in Mexican primary school children. Language and education, 18(6), 539-557.
Rosenshine, B., & Meister, C. (1994). Reciprocal teaching: A review of the research. Review of educational research, 64(4), 479-530.
Schleppegrell, M. J. (2004). The language of schooling – A functional linguistics perspective. London: Lawrence Erlbaum Associates.
Segerby, C. (2014). Reading strategies in mathematics: a Swedish example. In S. Pope (Ed.) Proceeding at BSLRM conference in Nottingham (pp. 311-318). Nottingham: British Society for Research into Learning Mathematics. Available from https://bsrlm.org.uk/BCME8/BCME8-Full.pdf
Segerby, C. (2016). Writing in mathematics lessons in Sweden. Proceedings of the ninth Congress of the European Society for Research in Mathematics Education, pp. 1490-1496. Prague: Czech Republic. Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education. Available from: https://hal.archives-ouvertes.fr/hal-01287787/document
Segerby, C. (submitted). Four Grade students’ comprehensions strategies for reasoning when reading their mathematics textbook.
Shepherd, M. D., Selden, A., & Selden, J. (2012). University Students' reading of Their First-Year Mathematics Textbooks. Mathematical Thinking and Learning, 14(3), 226-256.
Skolverket (the Swedish National Agency for Education (2011). Läroplan för grundskolan, förskoleklassen och fritidshemmet 2011 [Curriculum for elementary school, presechool and youth leisure centre 2011]. Stockholm: Fritzes
Stahl, S. A., & Fairbanks, M. M. (1986). The effects of vocabulary instruction: A model-based meta-analysis. Review of educational research, 56(1), 72-110.
Sterner, H. (2015). Problematisera "görandet": lärares lärande om kommunikation och resonemang i matematikundervisningen i en organiserad praktikgemenskap. Licentiatavhandling Växjö: Linnéuniversitetet, 2015. Växjö.
Stylianides, G. J. (2009). Reasoning-and-proving in school mathematics textbooks. Mathematical Thinking and Learning, 11(4), 258–288.
Sullivan, P., & Lilburn, P. (2002). Good questions for math teaching: why ask them and what to ask, K-6. Sausalito, CA: Math Solutions Publications Thomsen & Fleming
Thompson, D. R. (2014). Reasoning-and-proving in the written curriculum: Lessons and implications for teachers, curriculum designers, and researchers. International Journal of Educational Research, 64, 141-148.
Toulmin, S. E. (2003).The Uses of Argument. Cambridge, U.K.: Cambridge University Press.
Wagner, D. (2012). Opening mathematics texts: Resisting the seduction. Educational Studies in Mathematics, 80(1-2), 153-169.
Weinberg, A., Wiesner, E., Benesh, B., & Boester, T. (2012). Undergraduate students' self-reported use of mathematics textbooks. Primus, 22(2), 152-175.
Österholm, M. (2006). Kognitiva och metakognitiva perspektiv på läsförståelsen inom matematik [Cognitive and metacognitive perspectives on reading comprehension in mathematics]. Doctoral dissertation, Linköping University, Sweden. Linköping: Uni Tryck.
Authors contributing to EDeR agree to publish their articles under the Creative Commons Attribution 4.0 International license.