Abstract
M.Ed. (Subject Didactics)
Research shows that "the aims of secondary school's teaching of mathematics are
often not realized with many pupils leaving the school with passive knowledge of
mathematics" (H.S.R.C. 1981:8). This means that knowledge of mathematical facts
are reproduced on demand, instead of active mathematical knowledge " which is
congruent with the aims of teaching secondary mathematics" (Crooks, 1988 : 6/7).
Active knowledge of mathematics implies and characterised by the understanding of
concepts, principles that underlie facts and ideas and principles and concepts that are
connected to each other" (Entwistle & Entwistle, 1992 : 2). Active knowledge also
enables pupils to act intellectually independently.
One reason for the previously mentioned predicament is that "teaching often
encourage passive knowledge because the teaching practice of mathematics teachers
are often not in accordance with their educational aims" (Gravett, 1994 :6). Thus, a
discrepancy exists between teacher's intentions of teaching mathematics and their
conduct during teaching. It can be argued also that teachers teach mathematics in the
classroom but that the pupils not always effectively learn.
It is from the perception above that a constructivistic view of learning as a conceptual
change underlies the idea that teaching "as the creation of a classroom context
conducive to learning" (Strike & Posner, 1985:117). Biggs (1993 : 74) thus argues
that "if knowledge is constructed, rather than recorded as received, it does not make
sense to think of teaching as imparting knowledge, but rather as creating learning
environments that enhance the process of mathematical knowledge construction".
Russell (1969: 14) mentions that "mathematics is a subject in which we never know
what we are talking about, nor whether what we are saying is true". The views,
amongst others Oosthuizen, Swart and Gildenhuys (1992:2) see mathematics as "an
essential language of a creative but deductive process which has its origins in the
problems of the physical world", In the light of this, the origin of mathematics in the
real world, it can be argued that from a "constructivistic perspective, mathematical
learning is an active process by which pupils construct their own mathematical
knowledge in the light of their existing knowledge and through interaction with the
world around them" (Gravett, 1994 : 6/7). "Construction, not absorption or
unfocused discovery, enables learning" (Leder, 1993 : 13). Mathematics is not
something discovered by mankind, mathematics is a creation of mankind and is
transmitted and changed from one generation to the next.