Students’ definitions of lexically ambiguous mathematical vocabulary

Fifty-five students in three high school geometry classes participated in a vocabulary survey asking them to write out, exemplify, and/or illustrate with drawings their definitions for fifteen mathematical vocabulary words: acute, area, coordinate, diagonal, difference, exponent, factor, irrational, mean, multiple, prime, product, reduce, square, and variable. All of these terms are characterized by lexical ambiguity, meaning that they have different meanings in different contexts. The students' responses were analyzed qualitatively, driven by the following research questions. First, in light of past studies in which findings seem consistently to reveal that a large portion of the participants have inadequate comprehension and/or inability to articulate their understanding of "basic" mathematical vocabulary, what are students' ideas about the meanings of certain vocabulary words? What strands or themes of meaning attributed to the words are evident from students' responses? Do students' responses seem to indicate that lexical ambiguity causes confusion for them in their definitions? A variety of ideas and interpretations emerged from the students responses for each of the words. Some of the students' ideas conformed to conventional mathematical definitions of the terms, but many were also characterized by vagueness or confusion. Interference from the lexical ambiguity of some of the words did appear in the data, particularly with the terms diagonal, irrational, and prime. A secondary purpose of this research was driven by the question: what forms of written expression do the students use to communicate their meanings for the vocabulary words posed to them? After a preliminary analysis of the data from the surveys through systematic theoretical sampling, nine students were selected to participate in follow-up interviews in which supplementary information was gathered. The interview method utilized stimulated recall, and the interviews were video-taped and transcribed. Because students construct their own individual meanings for mathematical terminology, their ideas about specific words do reflect a spectrum of interpretations. Through focused discussion and articulation of meaning where lexical ambiguity exists, students can more confidently enter into mathematical communication and discourse.Education, Faculty ofCurriculum and Pedagogy (EDCP), Department ofGraduat