Comparing the Textbook with Professors’ Intended and Enacted Potential Intellectual Need for Infinite Series in Calculus II

ABSTRACT Infinite series are known to be challenging for Calculus II students, perhaps because they lack intellectual need for the content. In their analysis of Calculus textbooks found few instances of potential intellectual needs for infinite series. This study combines a textbook analysis with interviews of four professors and observations of their video-taped lectures. We compared the intellectual need in the textbook with what the professors intended to present and what they presented in lecture. The professors collectively intended to present the same potential intellectual needs that are found in the textbook, and they enacted presentations of these needs in their lectures. However, the professors incorporated more application problems than were found in the sections of the book. We outline implications for instructors, textbook authors, and course coordinators. In particular, reordering the topics to better show the intellectual need for power series and including more activities to engage students in problematic situations that power series can resolve. We noted that the instructors were presenting intellectual needs for power series in their own ways and were not reliant on the textbook.