Students and teachers use language to communicate mathematical knowledge and understanding. This communication is compounded by the underlying requirement for students to acquire language with specialized meaning and to have facility with this meaning as a member of a mathematics discourse community. The lecture format is a long-standing means of communicating knowledge in the university mathematics classroom.

Instructors and students approach the mathematics classroom with cultural meaning systems that contain diverse and divergent assumptions, histories, personalities, and social and cultural norms. The instructor assembles a lecture from a perspective that includes a deep understanding of mathematics that may not match the perspective and mathematical knowledge of the student audience. Given the multiple and complex concepts in mathematics, assigning a precise meaning can be difficult for students, producing a high likelihood that connotation, implication, and relevance can be confused. Even with precise mathematical definitions, students' interpretation of the meaning of a definition being taught is very much dependent on the precision with which the student assigns connotation, implication, and relevance to each symbol, picture, metaphor and word within the framework of the definition.

This study examines the question of how students assign meaning to terms in the mathematics register and how these assigned meanings determine the ways in which students understand mathematical concepts. The students in this study are drawn from a college-level remedial mathematics course. The depth of students' pre-existing knowledge of mathematics determined the complexity and breadth of their current meaning-making. The students' use of language and meaning in an "everyday" context influenced the ways meaning was assigned to terms in the mathematics register and the lack of precision in understanding and assigning mathematical meanings. The subtle variations in meanings and the seemingly reasonable connections students made to arrive at these meanings suggests instructors need to take cultural meanings that students bring to the classroom into account when teaching the mathematics course. Instructional planning should include ways for instructors to decipher previous student meaning-making about and understanding of mathematical concepts in order to correct students' misunderstandings and to help students develop more precise meanings assigned to terminology and concepts.