This study explored how students develop meaning of functions by building on their understanding of expressions and equations. A teaching experiment using design research was conducted in a sixth-grade classroom. The data was analyzed using a grounded theory approach to provide explanations about why events occurred within this teaching episode…

This paper is about the development of a task sequence to help overcome the fragmented understanding of the "function" concept that students often bring with them into the initial stage of upper secondary school level. Our aim is to make the students' use of functions more flexible in certain respects, for example when functions are…

Two problems from high school mathematics on finding minimum or maximum are discussed. The focus is on students' approaches and difficulties in identifying a correct solution and how dynamic geometry systems can help.

This study evaluates the effects of an intervention aimed at improving representational flexibility in linear-function problems. Forty-nine students aged 13-16 participated in the study. A pretest-intervention-posttest design with an experimental and control group was used. At pretest, both groups solved a choice test, where they could freely…

Nonroutine function tasks are more challenging than most typical high school mathematics tasks. Nonroutine tasks encourage students to expand their thinking about functions and their approaches to problem solving. As a result, they gain greater appreciation for the power of multiple representations and a richer understanding of functions. This…

A statistical method is described and illustrated which provides confidence envelopes around item response functions. Examples of 95 percent confidence envelopes for the one-, two-, and three-parameter logistic response models are given. In addition, the authors describe N-line plots, which show the genesis of the envelope as well as the density…

Proposes a new definition of the nuclear zone of a Bradford or Leimkuhler curve. The mathematical rationale is outlined, and examples of the application of this technique to citation analysis are given. (15 references) (CLB)

Presents simple experiments using the flow of water from bell jars that can provide an easily visualized introduction to exponential decay. (Author)

Describes the use of step-functions in modelling instruction. Classifies modelling into three categories: direct, analogical, and creative application. Provides and discusses modelling postal rates and other problems as examples. (YP)

This section provides mathematical activities in reproducible formats appropriate for students in grades 8-10. The activity is designed to provide an experience in model building while developing the concept of slope. (PK)