Abstract:
Results are reported of a study derived from examination of constructivism and related implications that language use is a key aspect of mathematics learning. The nature and role of students' language use and in particular their use of symbols, technical and everyday language is examined. Students received instruction in one of three approaches to teaching calculus: technique-oriented, concepts-first and infinitesimal instruction. The potential impact of instruction on students' language use in relation to construction of conceptualizations is discussed. Students who received infinitesimal instruction used different symbols and technical terms than the other students. They also displayed more integration of symbols, technical terms and everyday language, making use of notions related to infinitesimal closeness and infinite magnification of a curve. Many students displayed procedural use of language as a technology by which to construct problem responses, but they did not generally use symbols to represent or think about calculus ideas. All students were able to use visual, physically oriented language to construct explanations and justifications. Implications of these findings for future instruction and research are considered.