The relation between social and conceptual conventions in everyday mathematics teaching
The paper analyzes the specific epistemological role of mathematical symbols by using and comparing the Odgen and Richards' triangle of meaning with the epistemological triangle of "Symbol, Concept and Object". The micro-analysis of a teaching episode about the meaning of the decimal point and the role of appended zeros to decimal numbers illustrates the dominating tendency in classroom interaction to conceive of mathematical symbols and signs as pure names for concrete objects. This denotation function of mathematical signs hinders the conceptual development of symbols. The adequate understanding of the symbols role requires to interpret single mathematical symbols as systems of signs with their operations. The construction of such systems depends on the interplay between social and conceptual conventions and conditions.