Minding the nouns and verbs: definitions that respect knowledge development

The definition of function varies from textbook to textbook at the introductory level. Though the definitions are often mathematically equivalent, there are linguistic features that may make some definitions more accessible to beginning learners. In particular, students who see functions as actions or processes rather than objects may be better served by definitions which facilitate the use of meaningful verbs. This study examines the impact of definition choice on the mathematics work of graduate students, all of whom were mathematics majors and pre- or in-service mathematics teachers. Their work with three definitions of function is interpreted within the commognitive framework and frames a discussion of features of mathematical definitions that may help learners.