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)

Explores an unexpected connection between a function, its inverse, and the arithmetic mean, algebraically and graphically. (MM)

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)

Presents worksheets for students to practice substituting whole numbers into fairly simple symbolic expressions. (MKR)

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

In posttest results, 76 prealgebra students who learned about functions in a unit emphasizing multiple formats, anchoring learning in a thematic context, and problem solving in cooperative groups were more successful at problem solving and problem representation than were 56 comparison students conventionally taught. Similar results were found for…

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)

Presents responses to a problem that appeared in the May 2000 issue. The problem was to determine different ways to divide 8 cookies between 3 people. Includes student work from grades 1, 3, and 5. (KHR)

Examines how components of the concept of function (variable, domain, and range) and the process-object duality in its nature emerge as highly relevant to student learning in various mathematical contexts related to linear and abstract algebra. (Contains 22 references.) (ASK)

Reports the results of an investigation designed to help algebra teachers and curriculum developers by providing insights into how high-performing college algebra students (N=30) develop an understanding of major aspects of the concept of function. Results revealed that these high-performing students actually possessed weak understanding. Contains…

Mathematical concepts used in modern algebra are shown to be useful in modeling syndetic structure employed in information retrieval systems. The equivalence relation can represent "see also" components of traditional library catalogs; partial orderings and mappings assist in modeling syndetics in sophisticated systems such as thesauri.…

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)

Reports on middle school students' use of dynamic physical models to interpret functions. Includes student creations of symbolic variables and function equations. (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)