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…

Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non-trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple…

This paper reports on the vital role that reflective thinking plays in solving problems involving the mathematics of change and variation particularly multivariable calculus. We report on how reflective thinking is one kind of self-regulatory (in the sense of metacognitive) thought mechanism. We present an outline of the results of a larger study,…

Student errors led to this exploration of the conditions under which log of x base a = x. The discussion requires only techniques contained in a first-year calculus course. (MP)

Discussed is the problem of finding the volume common to two intersecting right circular cylinders. (MP)

Concludes that writing about the executive processes of problem solving, difficulties encountered, alternative strategies that might have been used, and the problem solving process in general helped students in the treatment group learn to use executive processes more quickly and more effectively than students in the control group. (Author/NB)

What initially appears to be a standard maximum-minimum problem presents, with a particular independent variable, a wealth of calculus and algebraic subplots. Uses graphing calculator technology to reinforce the "pencil and paper" solution and open the problem to lower level mathematics courses. (Author/NB)

The article presents and discusses an optimization problem concerned with observing objects from a moving car. (MK)

A project is described where the ultimate goal is to teach students methods of problem solving through an industrial engineering environment. Students practice sharing responsibility, understanding group dynamics, using resources efficiently, meeting deadlines, using mathematics in oral and written form, and applying the appropriate mathematics.…

Presents activities designed to engage students in an experiential and theoretical application of problems in precalculus and to study geometry, coordinate systems, rates, linear applications, and the concept of function. Illustrates problem situations and includes student worksheets and a teacher's guide. (KHR)

Techniques that can be used in solving various mathematical problems are illustrated by an optimization problem and the accompanying model and solution. (MP)

Lists several problems that have proven to be successful in getting students to think about topics and notions they thought they knew. Indicates that students have not only solved the conundrums (often with help), but also developed them further into research projects. (Author/ASK)

This problem solving strategy is illustrated by examples from the fields of algebra, trigonometry, geometry, and calculus. (MP)

How min-max problems can be solved with trigonometry and without calculus is described. (MNS)

Three teaching ideas are presented: how to present changes between scientific notation and decimal form that eliminate some student confusion; an analysis of an incorrect algebra equation that produced a correct answer; and aspects of a standard calculus problem dealing with minimum and maximum values. (MP)