The Influence of Teaching on Student Learning: The Notion of Piecewise Function

This paper examines the influence of classroom teaching on student understanding of the piecewise function. The participants were two experienced mathematics teachers and their 9th grade students. Using a theoretical standpoint that emerged from an analysis of APOS theory, the paper illustrates that the teachers differ remarkably in their approaches to the essence of the piecewise function and this, in turn, affects greatly their students‟ understanding of this notion. Action-oriented teaching, which is distinguished by the communication of rules, procedures and factual knowledge, confines students‟ understanding to an action conception of piecewise function. Process-oriented teaching, which priorities the concept and illustrates it across the representations, promotes students‟ understanding towards a process conception of function.