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.
