Introduction to Mathematics Education
Outline of the course:
The Introduction to Mathematics Education course will start from 29th Oct 2007. The course will consist of daily contact sessions for three weeks (29th Oct to 16th Nov). There may be minor adjustments in these dates taking into view other programs.
The course will consist of approximately 15 contact sessions and 4-5 tutorial sessions. Assessment will be through classroom discussion/ presentation, one assignment and one term paper. The course description given below is taken from the previous year's course. There may be some modification in the course which will be announced before the course begins. However the description below generally holds and will give an idea of the course.
Course description:
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.
Course Outline:
1. Elementary Mathematics - a historical-structural overview; Readings: Gowers, Davis and Hersh, Bunt et al.
2. Knowledge of Elementary Mathematics for Teaching; Organizing teacher professional development; Readings: Schulman, Ma, Ball et al.,
Stigler and Hiebert
3. Analysis of the knowledge structure of key topics: whole numbers, measurement, multiplicative structures and rational numbers, shape and space
4. Psychological perspectives on mathematics learning : Readings: Resnick, Anderson, Cobb
5. Approaches to the School Mathematics Curriculum: Mathematization, 'Realistic Mathematics Education', Constructivism, Maths standards, NCTM curriculum, National Curriculum Framework
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
7. 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
8. Mathematics education and equity Readings: D'Ambrosio
Reading list:
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.
