Abstract:
To avoid feeling ashamed or embarrassed in class, students employ avoidance strategies, such as withdrawing from challenging tasks they might get wrong, covering up their errors, or need for help, that, although protecting them from negative emotions, also inhibit their ability to learn. One problem with such avoidance behaviours is that they are likely to be self-reinforcing in that withdrawing from opportunities to learn reinforces students’ state of confusion, which in turn reinforces students’ need to withdraw, trapping students in a negative cycle. Another problem is that encouraging errors in low-stakes situations, provided they are sufficiently analysed, understood, and corrected, is actually an effective means of reducing their recurrence when the stakes are high.
In this thesis, I employed an action science approach to reframe errors in high school mathematics classrooms. Across three empirical studies, I came to understand what made errors appear ‘risky’ from students’ point of view and experimented with strategies for reducing the risks and increasing the benefits students associated with errors. In the first study, I found that high school mathematics students who avoided help seeking when they needed it did so rationally by employing a form of mental calculus to weigh up the socio-emotional risks and learning benefits of speaking up when confused. In the second study, I drew connections between the patterns of interaction high school mathematics teachers and students engaged in to manage errors and the psychological frames they drew on to make sense of those interactions. I found that the recursive and self-reinforcing nature of teachers’ and students’ framing of errors and their interactions made it difficult for them to see and thus alter the pattern of error avoidance they co-created. In the third study, I drew on the findings of the previous two studies to test whether or not strategic changes to teachers’ error-management behaviour could prompt students to reframe errors as less threatening and more beneficial for learning, and thus lead to error-engaging interactions. Taken as a whole, these studies provide a basis for understanding and altering patterns of error-avoidance in high school mathematics classrooms. In particular, they highlight the role teachers’ management of errors and associated pedagogical strategies can play in reframing errors in non-threatening ways from students’ point of view.