# Introduction to Mathematics Education and Research in Mathematics Education

**Contents: **

Note 1: This is a shortened version of the normal course. Additional two credits is likely to be offered as a continuation next semester.

Note 2: The list of readings is tentative and may be modified as the course progresses **Unit 1: The nature of mathematics and its history.**

This unit is aimed at getting an overview of the origin and development of elementary mathematics. It will also introduce students to the key features of mathematics: modelling, abstraction and generalization, the use of symbols, the place of proof.

**Readings **

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

2. Davis, P.J. and Hersh, R. The Mathematical Experience, 1999, Selected Chapters.

3. Stein, Sherman (1999) Archimedes – what did he do besides cry eureka, America: Mathematical Association of America. (2. The law of the lever)

4. 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). *Unit 2: Teacher education and preparation. *

This unit aims to elaborate the kind of knowledge that is required to teach mathematics. Further, it tries to develop an understanding of the culture of the teaching activity and the organizational structures that are required to enhance the kind of knowledge that is needed for teaching

mathematics and to become reflective practitioners. **Readings **

1. Ma, L. (1999) Knowing and teaching Elementary mathematics, London: Lawrence Erlbaum Associates publisher, (Forward, introduction, and chapters 1, 2, 3, 5, 6)

2. Stigler, J. W., Hiebert, J. (1999) The teaching gap, The Free Press. (Chapters 7, 8, 9)

3. Ball, D. L., Hill, H. C. and Bass, H. (Fall 2005) Knowing mathematics for teaching. American educator. *Unit 3: Understanding how children learn mathematics *

This unit will focus on how cognitive studies of mathematical learning, largely inspired by Piaget, have provided detailed and specific insights that are useful for designing teaching and learning. A large area of focus will be the learning of whole number arithmetic. The ‘learning trajectories’ perspective, which integrates the results of many studies, and provides a framework for using them in education will be discussed. The unit will also aim at understanding how constructivist, ethnomathematical and socialconstructivist perspectives have emerged from cognitive studies. **Core readings ****1. Van den Heuve Panhuizen (Ed.), M. (2001). Children learn mathematics. Utrecht:**

**2. Stigler, J. W., Hiebert, J. (1999) The teaching gap, The Free Press. (Chapters 7, 8, 9) 3. Ball, D. L., Hill, H. C. and Bass, H. (Fall 2005) Knowing mathematics for teaching. American educator. **