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

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

1. Describe different past and present conceptions of school algebra - concepts, skills and competencies.
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. Articulate roles of argumentation and proof in school algebra.
6. Develop interactive applets for teaching and learning concepts in algebra.
7. Explain what teachers can learn from research on algebra learning and teaching.

This is a tentative bibliographical list:

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

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

Clement, J. (1982). Algebra word problem solutions: Thought processes underlying a common misconception. Journal for Research in Mathematics Education, 13(1). 16-30.

Cooper, J., & Pinto, A. (2017). Mathematical and pedagogical perspectives on warranting: approximating the root of 18. For the Learning of Mathematics, 37(2), 8-13.

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

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

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

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

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.

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

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