Abstract
In this chapter, video recorded episodes occurring in three Swedish-speaking Grade 6 classrooms in Finland constitute the empirical material. The focus of the instruction is the introduction of basic principles of equation solving. The analysis focuses on the classroom interactions, and the role of the textbooks in co-determining the structure of the lessons and the challenges students encounter. Through interviews with teachers on how they account for their approaches to equation solving, it is possible to discern different emphases on how to teach equation solving procedures.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The term arithmetic equation here used as proposed by Filloy and Rojano (1989).
References
Anthony, G., & Burgess, T. (2014). Solving linear equations: A balanced approach. In F. K. S. Leung, K. Park, D. Holton, & D. Clarke (Eds.), Algebra teaching around the world (pp. 17–37). Rotterdam: Sense.
Asikainen, K., Fälden, H., Nyrhinen, K., Rokka, P., Vehmans, P., Törnroos, S., et al. (2007a). Min matematik 5 [My mathematics 5]. Helsingfors: Schildts Förlag.
Asikainen, K., Fälden, H., Nyrhinen, K., Rokka, P., Vehmans, P., Törnroos, S., et al. (2007b). Min matematik 5. Lärarhandledning [My mathematics 5. Teacher’s study guide]. Helsingfors: Schildts Förlag.
Asikainen, K., Fälden, H., Nyrhinen, K., Rokka, P., Vehmans, P., Törnroos, S., et al. (2008a). Min matematik 6 [My mathematics 6]. Helsingfors: Schildts Förlag.
Asikainen, K., Fälden, H., Nyrhinen, K., Rokka, P., Vehmans, P., Törnroos, S., et al. (2008b). Min matematik 6. Lärarhandledning [My mathematics 6. Teacher’s study guide]. Helsingfors: Schildts Förlag.
Balacheff, N. (2001). Symbolic arithmetic vs algebra the core of a didactical dilemma. Postscript. In R. Sutherland, T. Rojano, A. Bell, & R. Lins (Eds.), Perspectives on school algebra (pp. 249–260). Dordrecht: Kluwer.
Black, L., Mendick, H., & Solomon, Y. (Eds.). (2009). Mathematical relationships in education. Identities and participation. London: Routledge.
Carraher, D. W., Schliemann, A. D., Brizuela, B. M., & Earnest, D. (2006). Arithmetic and algebra in early mathematics education. Journal for Research in Mathematics Education, 37(2), 87–115.
Falkner, K. P., Levi, L., & Carpenter, T. P. (1999). Children’s understanding of equality: A foundation for algebra. Teaching Children Mathematics, 6(4), 232–236.
Filloy, E., & Rojano, T. (1989). Solving equations: The transition from arithmetic to algebra. For the Learning of Mathematics, 9(2), 19–25.
Herscovics, N., & Linchevski, L. (1994). A cognitive gap between arithmetic and algebra. Educational Studies in Mathematics, 27, 59–78.
Hiebert, J. (Ed.). (1986). Conceptual and procedural knowledge: The case of mathematics. Hillsdale, NJ: Lawrence Erlbaum.
Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12(3), 317–326.
Kieran, C. (2014). The false dichotomy in mathematics education between conceptual understanding and procedural skills: An example from algebra. In K. Leatham (Ed.), Vital directions in mathematics education research (pp. 153–172). New York, NY: Springer.
Knuth, E. J., Alibali, M. W., McNeil, N., Weinberg, A., & Stephens, A. C. (2011). Middle school students’ understanding of core algebraic concepts: Equivalence & variable. In J. Cai & E. Knuth (Eds.), Early algebraization. A global dialogue from multiple perspectives (pp. 259–276). Berlin: Springer.
Knuth, E. J., Stephens, A. C., McNeil, N. M., & Alibali, M. W. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 37(4), 297–312.
National Board of Education. (2004). The curriculum for basic education. Helsinki: National Board of Education.
Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93(2), 346–362.
Rittle-Johnson, B., & Star, J. R. (2009). Compared with what? The effects of different comparisons on conceptual knowledge and procedural flexibility for equation solving. Journal of Educational Psychology, 101(3), 529–544.
Schliemann, A. D., Carraher, D. W., & Brizuela, B. M. (2013). Bringing out the algebraic character of arithmetic. London: Routledge.
Stacey, K., & MacGregor, M. (2000). Learning the algebraic method of solving problems. Journal of Mathematical Behavior, 18(2), 149–167.
Törnroos, J. (2001, June). Finnish mathematics textbooks in grades 5-7. Presentation at the Second Scandinavian Symposium on Research Methods in Science and Mathematics Education, Helsinki, Finland.
Vieira, L., Gimenez, J., & Palhares, P. (2013). Relational understanding when introducing early algebra in Portuguese schools. In B. Ubuz, C. Haser, & M. A. Mariotti (Eds.), Proceedings of the Eight Congress of the European Society for Research in Mathematics Education (pp. 550–557). Manavgat, Side: Middle East Technical University, Turkey on behalf of the European Society for Research in Mathematics Education.
Vlassis, J. (2002). The balance model: Hindrance or support for the solving of linear equations with one unknown. Educational Studies in Mathematics, 49, 341–359.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Röj-Lindberg, AS., Partanen, AM. (2019). Learning to Solve Equations in Three Swedish-Speaking Classrooms in Finland. In: Kilhamn, C., Säljö, R. (eds) Encountering Algebra. Springer, Cham. https://doi.org/10.1007/978-3-030-17577-1_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-17577-1_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-17576-4
Online ISBN: 978-3-030-17577-1
eBook Packages: EducationEducation (R0)