Based on insights into the nature of vocational mathematical knowledge, we designed a computer tool with which students in laboratory schools at senior secondary vocational school level could develop a better proficiency in the proportional reasoning involved in dilution. We did so because we had identified computations of concentrations of…

Reports survey results on proof conceptions. Presents an overview of responses at the end of year 8 (age 13 years) and year 9 (age 14 years). Distinguishes three strategies--empirical, focused-empirical, and focused-deductive--that represent shifts in attention from an inductive to a deductive approach. Indicates some progress from year 8 to year…

In recent years, semiotics has become an innovative theoretical framework in mathematics education. The purpose of this article is to show that semiotics can be used to explain learning as a process of experimenting with and communicating about one's own representations (in particular "diagrams") of mathematical problems. As a paradigmatic…