Page 8 - Professorial Lecture - Prof Kasanda

how these criteria, as well as the knowledge evidence upon which
the decision is based, may change with time and thus may cause
mathematicians to revise some of their assumptions, definitions,
and/or results (p. 205 -206).

For Siegel and Borasi mathematics is changeable and not absolute. New
mathematics is being created all the time and theories are being proven or
discarded. Aaboe (1967, p. 2) indicates that “…Mathematics is cumulative,
that is, it never loses territory, and its boundaries are ever moving
outwards.” These views of mathematics point to mathematics as
“changing” and as such not an absolute truth. This aspect should be
mentioned when we teach mathematics to our students. The views of
mathematics indicated by Ernest (1971) seem to suggest to mathematics
teachers that they should be aware of their own view of the nature of
mathematics knowledge, since this is likely to determine the way they
teach mathematics (Mtetwa, 2000). A teacher who holds the absolutist
view of mathematical knowledge is most likely to transmit this knowledge
as rules and principles to be learned “parrot like” by the students in its
“finished and polished form”. Mathematics teachers should strive to show
the “non-linear process” in which mathematical knowledge is produced
(Siegel, & Borasi, 1996, p. 207) for students to realize that they can learn
mathematics. Nonetheless, Rowlands (2007) disputes the view that an
absolutist teacher will always present mathematics in a “transmission”
mode (p. 96). He suggests that such a teacher could present mathematics
in a meaningful way and not necessarily in a manner which will lead to
rote learning. In support of absolutist view of mathematics knowledge,
Rowland, Graham and Berry (2011) suggest that fallibilism as propagated
by Ernest (1991) is an attempt to push the agenda for “a child-centred
pedagogy” and “downplays mathematics as a formal, academic system of
knowledge” (p. 625).

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