Teachers’ perception of mathematical tasks. An exploration of what teachers ‘saw’ in a published task, and how this changed as a result of experience of enactment of the same task. - Lewis, M (2016)
What do teachers perceive when presented with a mathematical task? This study reviewed the literature on tasks, teachers’ use and relationship with tasks, perception and teachers’ pedagogical decision making. Three teachers’ submitted written planning notes, and interview responses were analysed to identify lesson images representing their intended use of a particular task. Teachers’ beliefs, knowledge and goals were related to these lesson images, and the impact of the teachers’ observation of an enactment of the task was discussed. The three teachers had distinct plans for how they intended to use the same task, as shown in lesson images inferred from their written scripts and interviews. This difference in intended use reflected variation in how the task was perceived, and in how teachers’ beliefs, knowledge and goals informed pedagogical decision making. Teachers adapted the task better to align with their own beliefs, knowledge and goals, but the design of the task also allowed and constrained teachers’ decisions. Teachers formed a relationship with this particular task, which they either developed, challenged or acquiesced to, based on their differing perception of the task. Some teachers’ experience of enactments of the task – observation of another teacher’s lesson, and teaching their own lesson – led to changes in teacher’s goals as reflected in their revised plans. Useful revisions to teachers’ plans were made after teaching using the task, which was too late for students in those lessons. An implication for future practice is to investigate ways in which teachers might refine lessons prospectively by more effectively anticipating student learning. The established Japanese practice of kyozai kenkyuu is offered as one such practice which offers this prospect.