Abstract
Mathematical modelling (MM) and its importance in teaching and learning are reflected
in its growing incorporation in mathematics curricula internationally (Blum & Ferri,
2009). MM, as a teaching and learning approach, has consistently shown not only to
improve students’ conceptual understanding, but also their problem-solving and
application competencies (Buchholtz & Mesrogli, 2013). It is on this basis that the
South African Curriculum and Assessment Policy Statement (CAPS) prescribes MM
as a teaching and learning approach. Therefore, the purpose of this study was to
explore the experiences of 21 fourth-year mathematics pre-service teachers (PSTs)
during a mathematical modelling week at a South African public university.
This study was underpinned by the Mathematical Knowledge for Teaching (MKT)
framework of Ball, Thames, and Phelps (2008) and the Attitudes Towards
Mathematical Modelling Inventory (ATMMI), adapted from Tapia (2002). The paradigm
employed for this study was pragmatism, appropriate for a mixed-methods inquiry
geared towards a practical, problem-solving approach that integrated both quantitative
and qualitative methods. This was in line with the engagement of pre-service teachers
in authentic mathematical modelling tasks with the intention of uncovering changes to
their knowledge and attitudes towards MM.
Quantitative data were collected in the form of pre- and post-attitude surveys. A
statistical analysis of the quantitative data was conducted based on four
predetermined attitude constructs (value, self-confidence, enjoyment, and motivation).
The qualitative data were collected from a semi-structured focus group interview that
was conducted after the modelling week. An inductive approach to the analysis of
qualitative data was employed, with the intention of establishing changes in PSTs’
knowledge of MM.
Findings from the quantitative analysis revealed a general negative change across all
four attitude constructs, with some showing correlations while others occurred
independently. The findings from the qualitative analysis showed a positive change in
the PSTs’ knowledge of MM. However, the students’ low levels of preparedness to
implement MM in their emerging practice, and their need for ongoing support, were
also important findings...