Discusses the implications of a research study of more than 2000 students aged 11 to 15 that explored why the students interpret algebra in certain ways. Recommends strategies that can help teachers deal with prior knowledge that students may bring to their study of algebra. (DDR)

Proposes activities that promote students' awareness of the structure of the information involved in their everyday activities, and builds the concept of function from students' mental representations of phenomena. Recommends the use of spreadsheets to provide external representations of these functions. (DDR)

Describes a game used in precalculus that builds interest and confidence in the uses of inverse functions. The game is preceded by a worksheet that enables students to discover that f(x) and f-1(x) are mirror images of the line y=x. (DDR)