Our research programme (Nardi, Biza & Zachariades, 2012) examines teachers’ priorities when they make decisions in the secondary mathematics classroom. We use tasks in which we invite teachers to consider a mathematical problem and typical student responses to the problem. Tasks are in the format of fictional classroom situations. We collect written responses to the tasks and conduct follow-up interviews. The task we discuss here aims to elicit perspectives on a key issue (e.g. Jaworski, 1994): classroom management often interferes with commendable learning objectives. The task is as follows. A class is asked to solve the problem: “When p=2.8 and c=1.2, calculate the expression: 3c2+5p-3c(c-2)-4p”. Two students reach the result (10) in different ways: Student A substitutes the values for p and c and carries out the calculation; Student B simplifies the expression first and then substitutes the values for p and c. When Student A acknowledges her difficulty with simplifying expressions, Student B retorts offensively (“you are thick”) and dismissively (“what can I expect from you anyway?”). Both solutions are correct and Student B’s approach particularly demonstrates proficiency in important algebraic skills. But Student B’s behaviour is questionable. Respondents to the task (21 prospective mathematics teachers) were asked to write, and then discuss, how they would handle this classroom situation. Responses were analysed in terms of: balance between mathematical (arithmetic vs algebraic solution) and behavioural (verbal mischief verging on offensive treatment of a peer) aspects; and, social and sociomathematical norms (Cobb & Yackel, 1996) which participants intended to prioritise in their classroom. While most participants discussed social (e.g.: peer respect; value of discussion) and sociomathematical (e.g., value of different solutions in mathematics) norms, 10 of the 21 focused almost exclusively on behavioural aspects and made limited or no reference to mathematical aspects. We credit this type of tasks with allowing this insight into teachers’ intended priorities and we posit that this lack of balance between mathematical and behavioural aspects merits further attention both in teacher education and research.
|Title of host publication||Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education (PME) and the 36th Conference of the North American Chapter of the Psychology of Mathematics Education (PME-NA)|
|Publication status||Published - 2014|
|Event||PME 38/PME-NA 36 - Vancouver, Canada|
Duration: 15 Jul 2014 → 20 Jul 2014
|Conference||PME 38/PME-NA 36|
|Period||15/07/14 → 20/07/14|