# Course Identification

## Lecturers and Teaching Assistants

## Course Schedule and Location

## Field of Study, Course Type and Credit Points

## Comments

## Prerequisites

## Restrictions

## Language of Instruction

## Attendance and participation

## Grade Type

## Grade Breakdown (in %)

## Evaluation Type

**Final assignment**

## Scheduled date 1

## Estimated Weekly Independent Workload (in hours)

## Syllabus

Goals:

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

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

- Learning algebra
- Teaching algebra
- Algebra curriculum
- Historical view on algebra

## Learning Outcomes

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

- Describe different past and present conceptions of school algebra - concepts, skills and competencies.
- Analyze students' mistakes related to algebra.
- Illustrate the complexity of teaching algebra.
- Compare opportunities for meaningful learning of algebra provided by different curriculum materials.
- Articulate roles of argumentation and proof in school algebra.
- Develop interactive applets for teaching and learning concepts in algebra.
- Explain what teachers can learn from research on algebra learning and teaching.

## Reading List

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.