Course Identification

Goals:

1. Get acquainted with, and better understand, research, theory and practice of algebra teaching and learning.
2. Develop knowledge of, and practice in, the scholarly discipline of mathematics education

The course will deal with the following topics (sometimes in parallel):

1. Historical view on algebra
2. Learning algebra
3. Teaching algebra
4. Algebra curriculum

Upon successful completion of the course- the students should be able to:

1. Describe different past and present conceptions of school algebra.
2. Analyze students' mistakes related to algebra.
3. Illustrate the complexity of teaching algebra.
4. Compare opportunities for meaningful learning of algebra provided by different curriculum materials.
5. Explain what teachers can learn from research on algebra learning and teaching.

Harper, E. (1987). Ghosts of Diophantus. Educational Studies in Mathematics, 18, 75-90.

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.

Arcavi, A. (1994). Symbol sense: informal sense-making in formal mathematics. For the Learning of Mathematics 14, 24?35.

Gray, E. & Tall, D. (1992). Success and Failure in Mathematics: Procept and Procedure - Secondary Mathematics, Workshop on Mathematics Education and Computers, Taipei National University, 216-221. http://www.warwick.ac.uk/staff/David.Tall/pdfs/dot1992l-secondary-procept.pdf

Tirosh, D., Even, R., & Robinson, N. (1998). Simplifying algebraic expressions: Teacher awareness and teaching approaches. Educational Studies in Mathematics, 35, 51-64.

Even, R. (1998). Factors involved in linking representations of functions. Journal of Mathematical Behavior, 17(1), 105-121.

Yerushalmy, M. (2005). Challenging known transitions: learning and teaching algebra with technology, For the Learning of Mathematics, 25(3), 37-42.

Vinner, S., & Dreyfus, T. (1989). Images and definitions for the concept of function. Journal for Research in Mathematics Education, 20, 356-366.

Ayalon, M. & Even, R. Students? opportunities to engage in transformational algebraic activity in different beginning algebra topics and classes. International Journal of Science and Mathematics Education.

Palatnik, A., & Koichu, B. (2017, online first). Sense making in the context of algebraic activities. Educational Studies in Mathematics, 95, 245-262.