•  1464
    Unpacking the logic of mathematical statements
    Educational Studies in Mathematics 29 123-151. 1995.
    This study focuses on undergraduate students' ability to unpack informally written mathematical statements into the language of predicate calculus. Data were collected between 1989 and 1993 from 61students in six small sections of a “bridge" course designed to introduce proofs and mathematical reasoning. We discuss this data from a perspective that extends the notion of concept image to that of statement image and introduces the notion of proof framework to indicate the top-level logical struct…Read more
  •  666
    We report on an exploratory study of the way eight mid-level undergraduate mathematics majors read and reflected on four student-generated arguments purported to be proofs of a single theorem. The results suggest that mid-level undergraduates tend to focus on surface features of such arguments and that their ability to determine whether arguments are proofs is very limited -- perhaps more so than either they or their instructors recognize. We begin by discussing arguments (purported proofs) r…Read more
  •  678
    Teaching proving by coordinating aspects of proofs with students' abilities
    with John Selden
    In Despina A. Stylianou, Maria L. Blanton & Eric J. Knuth (eds.), Teaching and Learning Proof Across the Grades: A K-16 Perspective, Routledge. pp. 339--354. 2009.
    In this chapter we introduce concepts for analyzing proofs, and for analyzing undergraduate and beginning graduate mathematics students’ proving abilities. We discuss how coordination of these two analyses can be used to improve students’ ability to construct proofs. For this purpose, we need a richer framework for keeping track of students’ progress than the everyday one used by mathematicians. We need to know more than that a particular student can, or cannot, prove theorems by induction or c…Read more
  •  599
    Affect, behavioural schemas and the proving process
    with John Selden and Kerry McKee
    International Journal for Mathematical Education in Science and Technology 41 (2): 199-215. 2010.
    In this largely theoretical article, we discuss the relation between a kind of affect, behavioural schemas and aspects of the proving process. We begin with affect as described in the mathematics education literature, but soon narrow our focus to a particular kind of affect – nonemotional cognitive feelings. We then mention the position of feelings in consciousness because that bears on the kind of data about feelings that students can be expected to be able to report. Next we introduce the idea…Read more