과제 대화록에 나타난 중등수학 예비교사들의 수학적 주목하기

Abstract

The present study attempts to explore mathematical noticing of prospective secondary mathematics teachers in the area of graphing functions through analyzing the Task Dialogue which is a written script of hypothetical student-teacher conversation for a given task. Using the constant comparative method, 117 task dialogues written by 39 prospective secondary mathematics teachers were analyzed. As a result, differences were apparent in what the prospective teachers focused on and how they reasoned with the focused mathematics. Specifically, most of the prospective secondary mathematics teachers chose the time as an independent variable and focused on the formal causal relationship between the two variables without considering the problem situation. Moreover, most teachers thought of the relationship between the two variables as a change in one quantity or as a rate of change, and a few noticed the amount of change in two quantities as a way to rationalize the relationship between the two. Given that mathematics teachers would face with various levels of students in class, we argue it is important for prospective teachers to be aware of ways students might conceive of the relationship between two quantities in terms of both the amount of change and rate of change in functional situations. We finalize our discussion by providing implications for prospective secondary mathematics teacher education and for studying noticing of mathematics in a finer grain size.