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It is to investigate the instructional performance of a
mathematics student-teacher. The focus is on the teaching of
function, where the role, effect, and development of
pedagogical mathematics knowledge is analyzed from the
operational aspect of knowledge representation in mathematics
lessons. The data is collected through classroom observations,
interviews, It is found that: (1) The instructional performance
has been much constrained with past schooling experience and
present epistemology. The concept of function is introduced
through everyday knowledge. There are misconceptions: "The
expression of a function must be in polynomial form",
"Polyomials are not necessarily functions". (2) On the part of
pedagogical knowledge, there are convictions: repeated
explanation promotes text-comprehension, drill and practice
helps conceptual understanding; corporal punishment is
effective in urging pupils to work hard. (3) On the knowledge
of learners: it is not easy to make sense of algebra; the
difficulty in learning the concept of function lies in the
confusion of symbolism. (4) The standard textbook is regarded
not suitable for average students, and supplementary texts are
employed. Causing inconvenience is an excuse for not using
teaching aids. (5) After a semester, there are apparent
changes: The teacher pays less attention to underachievers than
highachievers. There shows better connexions among concepts and
more awareness of curricular integrity and the occasions of
difficulties in learning. The aim of teaching transits from
"happy learning at one''s own will" to "the attainment of high
scores", and therefore more emphasis on mathematics content.
Overall, the student teacher has striven to optimize and any
shortcoming in teaching is due to the divorce of pedagogical
knowledge and mathematics knowledge in teacher preparation
program. It is imperative that innovative experiments on
pedagogical mathematics knowledge for beginning teachers are
developed.
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