Student teachers’ pattern generalisation conceptualised through the theory of didactical situations in mathematics

Seminar with Heidi Strømskag, HiST, Norway

Title:

Student teachers’ pattern generalisation conceptualised through the theory of didactical situations in mathematics

Abstract:

Research on students’ processes of pattern generalisation suggests that it is not generalisation tasks in themselves that are difficult, but rather the way they are designed and the limitations of the teaching approaches employed. I will present results from a case study of two groups of student teachers’ engagement with tasks on algebraic generalisation of shape pattern. In this study, the theory of didactical situations in mathematics has been used to identify constraints to students’ generalisation processes. The constraints are conceptualised in terms of three analytic categories, emerging from an open coding process. The first category is about features of the milieu that imply inadequate feedback for the students in adidactical situations; the second category is about challenges the students face when they shall transform into algebraic notation relationships they have expressed informally; and, the third category is about challenges related to students’ justification of formulae they have developed. A subcategory of the first category is about the design of tasks. I will show how the tasks are not sharply focused on the target mathematical knowledge and, further, what consequences this have for the students’ mathematical activity.