This study investigates prospective elementary and secondary school mathematics teachers' ways of reasoning about differentiability at a point and corner points while working on a mathematical modelling activity. Adopting a multiple-case study design, the participants of the study were 68 prospective elementary school mathematics teachers enrolled…

Graphing techniques are used to demonstrate the inverse function theorem and that the graph of the inverse function can be obtained by flipping the graph about the line y=x. (MP)

Reviews recent research into the effectiveness of the graphing calculator as a tool for instruction and learning within precalculus and calculus, specifically in the study of functions, graphing, and modeling. Contends that much research fails to provide clear guidance or informed debate regarding the role of graphing calculators in mathematics…

The graph of this function is analyzed by using calculus methods and the computer. The graph in most texts is shown to be misleading. (MP)

An alternative approach is described for presenting the idea of the derivative through the use of chords of a graph. (MP)

This booklet contains a representative sample of the efforts of colleagues at 11 institutions to use graphing calculators to enhance the teaching of calculus and precalculus. The first section contains examples of graphs for teachers to choose from for presentations, including: simple examples to illustrate some standard ideas in precalculus,…

This is part one of a three-part SMSG calculus text for high school students. The aim of the text is to develop some of the concepts and techniques which will enable the student to obtain important information about graphs of elementary functions. Chapter topics include: (1) polynomial functions; (2) the derivative of a polynomial function; and…

This is part three of a three-part SMSG calculus text for high school students. The aim of the text is to develop some of the concepts and techniques which will enable the student to obtain important information about graphs of elementary functions. Chapter topics include area and the integral, differentiation theory and technique, mathematical…

A magazine article is shown to contain material that could lead to discussions of several topics in mathematics. The article and the related mathematics are discussed in detail. (MP)

Illustrates the contrasting thinking processes of two beginning calculus students' geometric and analytic schemes for the derivative function. Suggests that teachers can enhance students' understanding by continuing to demonstrate how different representations of the same mathematical concept provide additional information. (KHR)

Illustrates exploration of composition of functions, translations, and inverse functions on a graphing calculator. Includes reproducible student worksheets. (MKR)

Presents a strategy for graphing conic sections on the polar plane without using a table of values by beginning with information gained from the graphs of circular functions. (MKR)

Attempts to answer and generalize the question: When is the numerical derivative obtained on the graphing calculator greater than the actual derivative, and when is it smaller? Discusses symmetric difference. (MKR)

Three activities with Knuth functions are discussed and illustrated, with sample computer programs listed. (MNS)