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Enacting challenging tasks : maximising opportunities for students' mathematical learning : a thesis presented in partial fulfilment of the requirements for the degree of Master of Education at Massey University, Palmerston North, New Zealand
Three teachers of year 7 and 8 learners explored pedagogical approaches that exemplified
current research on maximising opportunities for students to engage with and learn from
challenging mathematics tasks. This study examined the learning opportunities afforded by
the task enactments in the teachers’ classrooms. The study also considered teachers’
perspectives on a planning and lesson structure that exemplified explored approaches, and
the challenges teachers experienced in implementing the tasks and approaches.
Reforms in mathematics education that have called for change in how teachers view
mathematical knowledge, the value and purpose of social interaction in the classroom, and
teachers’ role as participants in classroom discourse, have influenced pedagogical
approaches to the enactment of classroom tasks. Relevant literature was reviewed that
illustrated the importance of tasks in affording opportunities for students to engage in
meaningful mathematical practices and discourse, and construct conceptual mathematical
understanding. Evidence was provided that teachers’ pedagogical decisions and actions play
a significant role in optimising opportunities for student learning from tasks, and that
teachers’ task implementations are mediated by their intentions, goals, knowledge, attitudes
The qualitative methodology chosen for this study aligned with case study and design-based
research approaches. Multiple data sources were collected, and systematic analysis and
triangulation of data alongside collaboration between the researcher and participant teachers
strengthened the research findings.
The study revealed the influence of task selection on the type of mathematical activity
afforded value in classrooms. The planning template and lesson structure prompted
purposeful decision-making that strengthened teachers’ task enactments, including explicit
consideration of mathematical ideas inherent in tasks, students’ prior understandings, and the
role of task variations in supporting students’ access to tasks. The study demonstrated that
different enactments from the same planning resulted in contrasting opportunities for student
learning. A noteworthy difference was the extent to which the mathematical ideas inherent
in the task were explicitly addressed by teachers.