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Introduction to Mathematics Education


Outline of the course:

 

Mondays- Afternoon and Friday - 11.00am to 12.30pm

 

The course aims to cover essential ground in mathematics education at the school level. Issues of content and pedagogy will be discussed in an integrated manner. The course will draw perspectives from history and psychology, but will have a strong grounding in the practice of curriculum development and teacher development in mathematics. The bulk of the course will focus on mathematics education at the elementary level. The units on algebra and geometry will also include issues relevant at the secondary level. The course will consist of lectures, tutorials and student presentations. Grading will be through assignments, presentations and a term paper.

 

  1. 1.Elementary Mathematics - a historical-structural overview; Readings: Gowers, Davis and Hersh, Bunt et al. 

  2. 2.Knowledge of Elementary Mathematics for Teaching; Organizing teacher professional development; Readings: Schulman, Ma, Ball et al., Stigler and Hiebert 

  3. 3.Analysis of the knowledge structure of key topics: whole numbers, measurement, multiplicative structures and rational numbers, shape and space 

  4. 4.Psychological perspectives on mathematics learning : Readings: Resnick, Anderson, Cobb 

  5. 5.Approaches to the School Mathematics Curriculum: Mathematization, 'Realistic Mathematics Education', Constructivism, Maths standards, NCTM curriculum, National Curriculum Framework 

  6. 6.Algebra Education: transition from arithmetic to algebra, 'theories' of reification, algebra in the primary school, key issues in the teaching and learning of algebra, use of ICT in learning algebra. Readings: Bell, Stacey, Artigue The teaching and learning of Geometry: Deductive structure of geometry, van Hiele's account of the stages of geometry learning, role of proof in geometry, visualization and geometry, dynamic geometry software, Readings: Battista and Clements in Grouws handbook, Herskowitz  

  7. 7.Mathematics education and equity  Readings: D'Ambrosio 

 

Reading list (somewhat incomplete, additions and modifications may be made):

Gowers, T. (2002) Mathematics - a very short introduction. OUP.

Davis, Philip J., and Reuben Hersh, (1981). The Mathematical Experience, Houghton

Mifflin (Selected chapters)

Bunt, L.N.H., Jones, P.S., & Bedcent J.D. (1988) The historical roots of elementary

mathematics, NY: Dover Publications. (1. Egyptian Mathematics, 2. Babylonian

Mathematics).

Resnick, L. B. and Ford, A. W. (1981) Psychology of mathematics for instruction.

NJ: LEA. (Selected Chapters and sections)

Cobb, Paul (2004) Perspective on constructivist, emergent and sociocultural

perspective in the context of developmental research. In T.P. Carpenter, J.A.

Dossey, & J. Kochler (eds.) Classics in mathematics education research, Reston, VA:

NCTM.

D. A. Grouws (ed.) Handbook of research in mathematics teaching and learning,

MacMillan: NCTM. (Selected Chapters)

Ma, L. (1999) Knowing and teaching Elementary mathematics, London: Lawrence Erlbaum

Associates publisher,

Stigler, J. W., Hiebert, J. (1999) The teaching gap, The Free Press.

Ball, D. L., Hill, H. C. and Bass, H. (Fall 2005) Knowing mathematics for teaching.

American educator.

Anderson, J.R. (1999) Learning and Memory, an integrated approach, 2nd edition,

John Wiley. (Chapter on mathematics education)

Bell, A. (1995). Purpose in school algebra. Journal of Mathematical Behavior, 14,

41-73.


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