I, You and It: Pronouns and Students' Understanding of Introductory Algebra

Some studies suggest that teachers make inferential judgements about students’ understanding based on the ways in which they use language. One aspect of language use is that of pronouns. Students’ use of first, second, or third person pronouns indicates the extent of commitment to the truth-value of their utterances. This paper discusses a study that investigated students’ use of pronouns as they explained their understanding of introductory algebraic expressions and equations. The evidence suggested that pronoun use can act as an indicator of the level of students’ conceptual development in this context, which might also be aligned with a theoretical model. Teachers listening to students, or reading their work, make judgements about their understanding based on the way students explain their thinking. Elements of that judgement include not only the students’ use of appropriate (or inappropriate) mathematical terminology, but also more subtle features that operate in any discursive environment. Studies by Bills and Gray (2001) and Bills (2002) investigated the language used by primary students discussing their arithmetic understanding. Boero, Douek, and Ferrari, (2002), conducted studies into the written mathematical explanations of students entering university science and computing courses. Their findings indicated that the quality of students’ understanding of mathematical ideas might be inferred from ways in which they use the language. Rowland (2002), in a broad study of students’ language use, identified linguistic features such as modality, pronouns, and tense that serve to indicate quality of students’ understanding. Some of the findings from these studies are summarised in the following. Explanations given by successful students tend to be propositional in nature ‐ generalised statements that make little or no reference to specific mathematical examples. Such generalisation tends to be marked by the use of the simple present tense and the impersonal you (instead of the archaic one). Generalisation by students implies a confident understanding of the topic, an ability to see and articulate mathematical similarities between examples, and to see individual examples as representative of a class of mathematical objects (Sfard, 2002). Less-successful students tend to make more specific statements that use the first person pronoun, I, and explain their thinking in terms of recounting procedures with particular examples. Particularity implies that students cannot make explicit their perceiving of class characteristics that might be shared by sets of mathematical objects, although such knowledge might be implicit in their responses to several examples. Rowland (2002) noted that where students struggle with inaccessible concepts, they make vague statements, characterised by the third person pronoun, it. Vagueness suggests that students are far less certain of their knowledge; that they are “operating in a conjecturing environment” (p.67). In contrast to generalisation and particularity, vagueness leaves the listener, or reader, uncertain as to the subject of the utterance. The studies cited above have focused on young students in primary school, and older students of greater mathematical experience entering university. The study outlined in this paper focuses on students in the intervening years, investigating language use by students