Describes an approach to the initial teaching of composite functions that relies primarily on mapping representations. (MKR)

Explores the effects of varying the coefficients in the general quadratic function using graphing calculators. (MKR)

The concept of function is considered as foundational in mathematics. Yet, it proves to be elusive and subtle for students. A generic image that can act as a cognitive root for the concept is the function box. This is not a simple pattern-spotting device, but a concept that embodies the salient features of the idea of function, including process…

Discussion of the nature of the algebraic and graphical representations of functions focuses on a study integrating cognitive research and the development of an intelligent tutoring system (ITS), the Function Characteristics Tutor, to evaluate the effects of pairing representations of mathematical functions on high school students. (Author/LRW)

Four noncommutative groups are given, to be used by students to construct the operation tables and verify that each structure is noncommutative. (MNS)

Suggests that, for some classes of functions, an algebraic method is available that provides a nonstandard application of the discriminant conditions as well as an exact method of optimization for precalculus students. Examples are given, and students should compare these methods with others regarding generality, ease, and efficiency. (AIM)

Researchers and educators are calling for increased use of technology and attention to function concepts in school mathematics. Students often have considerable difficulty gleaning pointwise and global information from Cartesian (R squared) representations of functions, whether they are hand- or machine-produced. Described here is an interactive…

Recent reports have pointed to the need for teachers to have "deep understanding" of concepts and procedures in school mathematics, particularly those related to functions. However, previous research has demonstrated that many students, including preservice teachers, have limited understanding of functions. This paper describes a set of nonroutine…

Presents a classification of factorable cubics and shows how the associated factor graphs determine domains of disconnected branches and furnish a skeletal framework for the number and shape of the branches. Illustrates three dimensional visualization and examines level curves and spikes of surfaces. (KHR)

Computer algebra systems have great potential uses, but learning the basic concepts of algebra is itself a mathematical activity. Explores theoretical concepts that may be seen as essential enabling skills for computer algebra systems users. (Author/ASK)

Develops and tests a function-based approach to algebra called the Visual Mathematics curriculum in grades 7-9. Presents a theoretical framework for a systemic investigation of the structures of algebra word problems and their relationship to function-based solutions. Suggests new insights into categorizing word problems. (Contains 19 references.)…

Much can be learned from a study of rational functions and the behavior of their graphs, so their inclusion in secondary school mathematics textbooks is urged. Analysis of reciprocal relationships and when they don't apply, asymptotes, and the graphing technique are each included in the discussion. (MNS)

Describes an activity in which students are given a set of designs and are required to use their electronic grapher to reproduce the designs. The activity reinforces students' understanding of lines and of the formula for a linear function. (MKR)

Presents a method for introducing students to broken-line functions with unbroken domains. Concludes that a unit on broken-line functions should enhance students' understanding of the function concept. (ASK)

A drill-and-practice game called "Digits Delight"; the story of Parabella (and Hyp and Elli); and a method for finding inverse functions, using Rubik's cube and algebra, are included. (MNS)