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
