Exploring practices and beliefs that shape the teaching of mathematical ways of thinking and doing at university

This study examined two lessons taught in parallel in a real analysis course by two different teaching assistants. The lessons were based on a single lesson-plan but decisions the instructors made prior to and during class took the lessons in substantially different directions. In this paper we focus on one instructor and describe some of the ingenious ways by which he adapted the written curriculum and introduced mathematical practices and ways of thinking in his lesson. We apply Schoenfeld's resources, orientations and goals framework to highlight relationships between the instructors' beliefs and practices, and to propose explanations as to why this instructor implemented the written curriculum and addressed the mathematics the way he did. On the basis of this analysis we suggest a new perspective on the nature of the process by which university instructors make sense of the curriculum, derive and prioritize goals and form their lesson-images.