Teaching in Action: A Model to Understand the Complexity of Teachers’ Decisions in Teaching Mathematics
DOI:
https://doi.org/10.53555/nnel.v4i1.584Keywords:
teaching, inquiry, mathematics, teaching triad, modelAbstract
In this article, we focus on the teaching of mathematics in classrooms. The aim of the present study is to create, describe and test a model for teachers' decisions in action when teaching mathematics. We focused on the classroom as a very complex environment and videotaped three excellent teachers teaching mathematics. An inductive iterative research process was selected to generate theory and conclusions directly rooted in data. The model was tested in different teacher groups, and the categories changed and analyses proceeded. The model relates to Jaworski´s (1992), theory the “teaching triad”. By using the developed model “teaching in action” it is possible to analyze and describe teaching in mathematics classrooms and find examples of teachers’ decisions in action. The model “teaching in action” show the complexity of teachers’ work.
References
Artigue, M & Blomhøj, M. (2013). Conceptualizing inquiry-based education in mathematics. ZDM Mathematics Education, 45, 797-810.
Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407.
Bergqvist, E., Bergqvist, T., Boesen, J., Helenius, O., Lithner, J., Palm, T. & Palmberg, B. (2009). Matematikutbildningens mål och undervisningens ändamålsenlighet – grundskolan våren 2009, NCM, UFM.
Bernstein, B.(1990). Class, Codes and Control. Vol. 4, The Structuring of Pedagogic Discourse. London: Routledge.
Björkvall, A. (2009). Den visuella texten - multimodal analys i praktiken. Stockholm: Hallgren & Fallgren Studieförlag AB.
Boaler, J. (1999). Participation, knowledge, and beliefs: A community perspective on mathematics learning. Educational Studies in Mathematics, 40 (3), 259-281.
Boaler, J. (2002). The development of disciplinary relationships: Knowledge, practice, and identity in mathematics classroom. For the Learning of Mathematics, 22 (1), 42-47.
Clarke, C. M & Yinger, R. J. (1977). Research on teacher thinking. Curriculum inquiry, 7 (4), 279-394.
Clarke, D. (2004). Patterns of participation in the mathematichs classroom. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, Vol 2, 231-238.
Cobb, P., Confrey, J., diSessa, A. A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.
Csapó, B.,&Funke, J. (2017). The Nature of Problem Solving. OECD Publishing.
Danielsson H. (1998). Video som språk och kommunikation. Barn och unga skapar med video i skolan. Licentiatuppsats. Pedagogiska institutionen, Stockholms universitet.
Danielsson H. (2002). Att lära med media. Om det språkliga skapandets villkor i skolan med fokus på video. Doktorsavhandling. Pedagogiska institutionen, Stockholms universitet.
Danielsson H. (2004). Skolbio Stockholm– Kartläggning och utvecklingsidéer. Medioteket/Uppdragsavdelningen, Stockholms stads utbildningsförvaltning.
Darling-Hammond, L.(2009). Teacher Learning. What Matters? Research Review February 2009, Volym 66, Number 5, pp.46-53.
Darling-Hammond, L., Chung Wei, R., Andree, A., Richardson, N. & Orphanos, S. (2009). Professional learning in the learning profession. A status Report on Teacher Development in the United States and Abroad. National Staff Development Council and the School Redesign Network at Stanford University.
Dewey, J. (1916). Democracy and education. New York: Mcmillan.
Dewey, J. (1938). Logic: The theory of inquiry. New York: Holt.
Driver, R. (1986) The Pupil as Scientist? Philadelphia: Open University Press.
Glaser, B. G. & Strauss, A. L. (1967). The Discovery of Grounded Theory. Startegies for Qualitative Research. New Brunswick: Aldine Transaction.
Hattie, J. (2009). Visable learning. A synthesis of over 800 meta-analyses relating to achievement. London and New York: Routledge, Taylor & Francis group.
Hammersley, M. & Atkinson, P. (1983 ) Ethnography-Principles in practice. Routledge: London.
Hiebert, J., Carpenter, T.P., Fennema's, E., Fuson, K., Human, P., Murray, H., et al. (1996). Problem solving as a basis for reform in curriculum and instruction: The case of mathematics. Educational researcher, 25(4), 12-21.
Jaworski, B. (1992). Mathematics Teaching: What is It? For the Learning of Mathematics 12. FLM Publishing Association, White Rock, BC.
Jaworski, B. (1994). Investigating mathematics teaching. A Constructuvistic Enquiry. London. The Farmer Press.
Jaworski, B. (2004). Grappling with complexity: Co-learning in Inquiry Communities in Mathematics Teaching Development. Proceedings of the 28th Congerence of the International Group for the Psychology of Mathematics Education Vol I, 17-36.
Jaworski, B.(2008). Insiders and outsiders in Mathematics teaching development: The design and study of classroom activity. In Research in Mathematics Education 6:1, pp3-22.
Kilpatrick, J. (1985). A Retrospective Account of the Past 25 years of Research on Teaching Mathematical Problem Solving. In E. A. Silver (Ed.). Teaching and Learning Mathematical Problem Solving: Multiple Research perspectives. London: Lawrence Erlbaum Associates. pp. 1-15.
Kress, G., & Van Leeuwen, T. (2001). Multimodal Discourse: The Modes and Media of Contemporary Communication. London: Arnold.
Kress, G. (2010). Multimodality: A semiotic approach to contemporary communication. Abingdon: Routledge.
Lester, F. K. Jr. (1983). Trends and Issues in Mathematical Problem- Solving Research. In R. Lesh & M. Landau (Eds.). Acquisition of Mathematics Concepts and Processes. New York: Academic Press, Inc. (pp. 229-261).
Marton, F. (2014). Necessary Conditions of Learning. New York: Routledge.
Schoenfeld, A. H. (1985). Mathematical Problem Solving. Orlando: Academic Press.
Schoenfeld, A. H. (2012). Classroom observations in theory and practice. ZDM, Mathematics Education, Karlsruhe.
Schoenfeld, A. H. (2014). Thoughts on scale. ZDM, Mathematics Education, Karlsruhe.
Selander, S. & Kress, G. (2010). Design för lärande – ett multimodalt perspektiv. Stockholm: Norstedts.
Shulman, L.S. (1987). Knowledge and Teaching: Foundations of the New Reform. Harvard Educational Review 57 (1), 1- 21.
Silver, E; Leung, S. S. & Cai, J. (1995). Generating Multiple Solutions for a Problem: A Comparison of the Responses of U.S. and Japanese Students. Educational Studies in Mathematics. Vol. 28. (pp. 35-54).
Smith, S. M. & Stein, M. K. (2011). Five Practices for Orchestrating Productive Mathematics Discussions. NCTM.
Säljö, R. (2005). Lärande och kulturella redskap: Om lärprocesser och det kollektiva minnet.
Söderman C. (2002). Kan en mediepedagogisk undervisning stärka en elevs kommunikativa förmåga? Utvecklingsarbete - Rapport. Centrum för media och IT i grundskolan, Piteå kommun. Norstedts Akademiska Förlag.
Taflin, E. (2011). Rika matematiska problem – guldläge för bedömning. I Bartholdsson, Å. & E. Hultin (red.). Praktiknära forskning inom skola och lärande. Arbetsrapport. Högskolan Dalarna, Kultur och lärande, ISSN 1403-6878;2. s.139-153.
Taflin, E. (2007). Matematikproblem I skolan - för att skapa tillfälle till lärande. Doktorsavhandling. Institutionen för Matematik och Matematisk statistik. Umeåuniversitet.
The Swedish National Agency for education, 2009, What affects results in Swedish elementary school.
The Swedish National Agency for education, 2011, Curriculum mathematics.
Törner, G.& Schoenfeld, A.H. & Reiss, K.M. (2007). Problem solving around the world: summing up the state of the art. ZDM, Mathematics Education, Karlsruhe.
Wingstedt, J. (2012). Funktionell analys av musik i film and multimodalt berättande gestaltningar. I G. Ternhag & J. Wingstedt. (red.) På tal om musikproduktion. Elva bidrag till ett nytt kunskapsområde. Göteborg: Bo Ejeby Förlag, s.160-182.
Vygotsky, l. (1935/1999). Problems in the teaching and the intellectual development of school age. Included in g. Lafrance (eds.), Vygotsky and the school. Lund: Studentlitteratur.
Öhman-Gullberg, L. (2008). Laddade bilder. Doktorsavhandling. Institutionen för didaktik och pedagogiskt arbete, Stockholms universitet.
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
You are free to:
- Share — copy and redistribute the material in any medium or format for any purpose, even commercially.
- Adapt — remix, transform, and build upon the material for any purpose, even commercially.
- The licensor cannot revoke these freedoms as long as you follow the license terms.
Under the following terms:
- Attribution — You must give appropriate credit , provide a link to the license, and indicate if changes were made . You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
Notices:
You do not have to comply with the license for elements of the material in the public domain or where your use is permitted by an applicable exception or limitation .
No warranties are given. The license may not give you all of the permissions necessary for your intended use. For example, other rights such as publicity, privacy, or moral rights may limit how you use the material.
