Abstract
This study compares students’ opportunities to engage in transformational (rule-based) algebraic activity between 2 classes taught by the same teacher and across 2 topics in beginning algebra: forming and investigating algebraic expressions and equivalence of algebraic expressions. It comprises 2 case studies; each involves a teacher teaching in two 7th grade classes. All 4 classes used the same textbook. Analysis of classroom videotapes (15–19 lessons in each class) revealed that the opportunities to engage in transformational algebraic activity related to forming and investigating algebraic expressions were similar in each teacher’s 2 classes. By contrast, substantial differences were found between 1 teacher’s classes with regard to the opportunities to engage in transformational algebraic activity related to equivalence of algebraic expressions. The discussion highlights the contribution of the interplay among the mathematical topic, the teacher, and the class to shaping students’ learning opportunities. Specifically, the mathematical topic appeared to play a prominent role in certain situations, with the topic involving deductive reasoning generating high variation in classes of 1 teacher but not in the other’s.
Similar content being viewed by others
References
Arcavi, A. (1994). Symbol sense: Informal sense-making in formal mathematics. For the Learning of Mathematics, 14(3), 24–35.
Boero, P. (2001). Transformation and anticipation as key processes in algebraic problem solving. In R. Sutherland, T. Rojano, A. Bell & R. Lins (Eds.), Perspectives on school algebra. Dordrecht, The Netherlands: Kluwer.
Booth, L. R. (1988). Children’s difficulties in beginning algebra. In A. Coxford (Ed.), Ideas of algebra: K-12 (pp. 20–32). Reston, VA: National Council of Teachers of Mathematics.
Eisenmann, T. & Even, R. (2009). Similarities and differences in the types of algebraic activities in two classes taught by the same teacher. In J. T. Remillard, B. A. Herbel-Eisenmann & G. M. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction (pp. 152–170). New York: Routledge.
Eisenmann, T. & Even, R. (2011). Enacted types of algebraic activity in different classes taught by the same teacher. International Journal of Science and Mathematics Education, 9, 867–891.
Even, R. (1998). Factors involved in linking representations of function. Journal of Mathematical Behavior, 17, 105–121.
Even, R. & Kvatinsky, T. (2009). Approaches to teaching mathematics in lower-achieving classes. International Journal of Science and Mathematics Education, 7, 957–985.
Even, R. & Kvatinsky, T. (2010). What mathematics do teachers with contrasting teaching approaches address in probability lessons? Educational Studies in Mathematics, 74, 207–222.
Gresalfi, M. S., Barnes, J. & Cross, D. (2012). When does an opportunity become an opportunity? Unpacking classroom practice through the lens of ecological pyschology. Educational Studies in Mathematics Education, 80, 249–267.
Harel, G. & Sowder, L. (2007). Toward a comprehensive perspective on proof. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 805–842). Charlotte, NC: Information Age.
Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 707–762). Charlotte, NC: Information Age.
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, 297–312.
Manouchehri, A. & Goodman, T. (2000). Implementing mathematics reform: The challenge within. Educational Studies in Mathematics, 42, 1–34.
Nisbett, R., Krantz, D., Jepson, C. & Kunda, Z. (1983). The use of statistical heuristics in everyday inductive reasoning. Psychological Review, 90, 339–363.
Robinson, N. & Taizi, N. (1995-2002). Everybody learns mathematics. Rehovot, Israel: Weizmann Institute of Science. (in Hebrew)
Robinson, N. & Taizi, N. (1997). On algebraic expressions 1. Rehovot, Israel: Weizmann Institute of Science (in Hebrew).
Smith, J. P. & Phillips, E. A. (2000). Listening to middle school students’ algebraic thinking. Mathematics Teaching in the Middle School, 6, 156–161.
Stein, M. K., Grover, B. W. & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455–488.
Strauss, A. (1987). Qualitative analysis for social scientists. Cambridge, UK: Cambridge University Press.
Tirosh, D., Even, R. & Robinson, N. (1998). Simplifying algebraic expressions: Teacher awareness and teaching approaches. Educational Studies in Mathematics, 35, 51–64.
Usiskin, Z. (1988). Conceptions of school algebra and uses of variables. In A. F. Coxford (Ed.), The ideas of algebra, K-12 (pp. 8–19). Reston, VA: National Council of Teachers of Mathematics.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ayalon, M., Even, R. STUDENTS’ OPPORTUNITIES TO ENGAGE IN TRANSFORMATIONAL ALGEBRAIC ACTIVITY IN DIFFERENT BEGINNING ALGEBRA TOPICS AND CLASSES. Int J of Sci and Math Educ 13 (Suppl 2), 285–307 (2015). https://doi.org/10.1007/s10763-013-9498-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10763-013-9498-5