Abstract
A critical element in the introduction of algebra is to focus student attention on the basic ideas of algebraic reasoning including the use of concepts such as variable and algebraic expression. In the Norwegian classrooms, representing a student-centered instructional philosophy, the teachers utilized examples and problems that they themselves had designed, and the examples involved resources such as concrete objects and body movements in order to make algebra accessible to students. When designing these examples, teachers thus used their own previous experiences of teaching algebra in an attempt to articulate the passage from arithmetic to algebra.
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Notes
- 1.
Based on Wertsch (1991) who highlighted these three themes: social sources of development, semiotic mediation and genetic analysis (the method for investigating the former).
- 2.
Not to be confused with the unit foot in the U.S. customary system of measurement.
References
Berg, C. V. (2009). Developing algebraic thinking in a community of inquiry: Collaboration between three teachers and a didactician. Diss., The University of Agder, Kristiansand, Norway.
Bills, L., Dreyfus, T., Mason, J., Tsamir, P., Watson, A., & Zaslavsky, O. (2006). Exemplification in mathematics education. In J. Novotna, H. Moraova, M. Kratka, & N. Stehlikova (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 126–154). Prague: Charles University.
Carlsen, M. (2010). Appropriating geometric series as a cultural tool: A study of student collaborative learning. Educational Studies in Mathematics, 74(2), 95–116.
Davydov, V. V., Gorbov, S. F., Mikulina, G. G., & Savaleva, O. V. (1999). Mathematics class 1 (J. Schmittau, Trans.). Binghamton, NY: State University of New York.
Derry, S. J., Pea, R. D., Barron, B., Engle, R. A., Ericson, F., Goldman, R., et al. (2010). Conducting video research in the learning sciences: Guidance on selection, analysis, technology, and ethics. Journal of the Learning Sciences, 19, 3–53.
Fried, M. N. (2009). Similarity and equality in Greek mathematics: Semiotics, history of mathematics and mathematics education. For the Learning of Mathematics, 29(1), 2–7.
Hjardar, E., & Pedersen, J.-E. (2006). Faktor 1 [Factor 1]. Oslo: Cappelen Damm.
John-Steiner, V., & Mahn, H. (1996). Sociocultural approaches to learning and development: A Vygotskian framework. Educational Psychologist, 31(3/4), 191–206.
Kieran, C. (2007a). What do we know about the teaching and learning of algebra in the elementary grades? (NCTM Brief). Retrieved from http://mason.gmu.edu/~jsuh4/impact/research.algebra.pdf
Leont’ev, A. N. (1981). Problems of the development of the mind (M. Kopylova, Trans.). Moscow: Progress Publishers.
Linell, P. (1998). Approaching dialogue. Talk, interaction and contexts in dialogical perspectives. Amsterdam: John Benjamins Publishing Company.
Mason, J. (1996). Expressing generality and the roots of algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra. Perspectives for research and teaching (pp. 65–86). Dordrecht: Kluwer.
Ministry of Education and Research. (2013). Curriculum for the common core subject of mathematics (MAT1-04). Retrieved from http://www.udir.no/kl06/mat1-04/Hele/?lplang=eng
Myhill, D., & Dunkin, F. (2005). Questioning learning. Language and Education, 19(5), 415–427.
Pepin, B. (2011). Pupils’ attitudes towards mathematics: A comparative study of Norwegian and English secondary students. ZDM: The International Journal on Mathematics Education, 43(4), 535–546.
Radford, L. (2003). On the epistemological limits of language. Mathematical knowledge and social practice during the Renaissance. Educational Studies in Mathematics, 52(2), 123–150.
Reinhardtsen, J. (2012). The introduction of algebra: Comparative studies of textbooks in Finland, Norway, Sweden and USA (Master’s thesis at the University of Agder). Kristiansand: University of Agder.
Rissland-Michner, E. (1978). Understanding mathematics. Cognitive Science, 2(4), 361–383.
Rowland, T. (2008). The purpose, design and use of examples in the teaching of elementary mathematics. Educational Studies in Mathematics, 69(2), 149–163.
Säljö, R. (2006). Læring og kulturelle redskaper; om læreprosesser og den kollektive hukommelsen [Learning and cultural tools: On processes of learning and the collective memory]. Oslo: Cappelen Akademiske.
Schmittau, J., & Morris, A. (2004). The development of algebra in the elementary mathematics curriculum of V. V. Davydov. Mathematics Educator, 8, 60–87.
Schoenfeld, A. (1989). Explorations of students’ mathematical beliefs and behavior. Journal for Research in Mathematics Education, 20(4), 338–335.
Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.
Wertsch, J. V. (1991). Voices of the mind: A sociocultural approach to mediated action. Cambridge, MA: Harvard University Press.
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Wathne, U., Reinhardtsen, J., Borgersen, H.E., Cestari, M.L. (2019). Designed Examples as Mediating Tools: Introductory Algebra in Two Norwegian Grade 8 Classrooms. In: Kilhamn, C., Säljö, R. (eds) Encountering Algebra. Springer, Cham. https://doi.org/10.1007/978-3-030-17577-1_5
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