Mathematical practices: their use across learning domains in a tertiary environment
Date
2010-08-30
Authors
Manson, Lynette Anne
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Abstract
This research presents a case study at a South African University, involving students who had
studied mathematics in a pre-undergraduate Foundation Programme (FP) and who were currently
in their first year of study in Information Technology (IT) at the same institution. The study
investigated a possible relationship between the teaching approach used in the FP mathematics
classroom and the extent of students’ abilities to use important mathematical practices, such as
using procedures flexibly; using representation; understanding/explaining concepts; questioning;
justifying claims; disagreeing; strategising; and generalising, in an undergraduate IT context.
Focus group interviews and task-based interviews were used to answer three related questions:
“To what extent are students aware of differences in teaching approaches between FP
mathematics and undergraduate study?”; “To what extent do students believe that their
experiences of the teaching approaches in the Foundation Programme mathematics class have
helped them in undergraduate study in other courses?”; and “In what ways are the mathematical
practices taught in the Foundation Programme used in undergraduate study in IT?” A bricolage of
learning theories was used as a framework for understanding the possible relationships between
teaching approach, development of mathematical practices and learning transfer. The students in
the focus groups described the teaching approach used in the FP mathematics classes as studentcentred,
whereas many of the undergraduate IT lectures and tutorials were described as teachercentred.
The students felt that the approach used in the FP mathematics classroom was beneficial
to further study, in that it taught them how to become responsible for their own learning and
brought about deep understanding of the mathematical concepts learned in the FP. The task-based
interviews showed that all students used mathematical practices to solve IT problems to a greater
or lesser extent. The use of these mathematical practices was best understood as being influenced
by all past cognitive, social and cultural experiences, and was therefore not a case of “transfer” in
the traditional sense of the word. Instead, the use of mathematical practices could be described as
an extreme case of “cognitive accommodation” from a cognitive constructivist perspective, or a
case of “generality” from a situative perspective. Furthermore, an inter-relationship emerged between student-centred teaching, students’ productive disposition towards mathematics, and the
extent of “transfer” of mathematical practices to the IT domain. This interesting relationship
warrants further investigation.
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Keywords
mathematical practices, student-centred teaching approach, learning transfer, cognitive perspective, situative perspective