Computational and Inferential Orientations: Lessons from Observing Undergraduates Read Mathematical Proofs

This paper presents selected findings from an assessment of university students' moment-by-moment reading of mathematical proof. This method, adapted from an assessment of narrative reading validated by psychologists, yields novel insights into the strategies students use to construct meaning for the equations in a proof text. In particular, we present evidence that novice readers constructed meanings for the equations using mathematical practices familiar from non-proof oriented courses -- substituting and solving for variables -- while more experienced readers drew upon practices native to proof-oriented mathematics -- inferring properties of quantities. We refer to these as computational and inferential orientations, respectively. We interpret this mismatch of practices in terms of Systemic Functional Linguistic's notion of textual metafunction and briefly discuss its implications for proof-oriented instruction. [For the complete proceedings, see ED606531.]