This article presents two classroom episodes in which students were exposed to the value of asking questions and to the different roles played by proof in mathematics. The conversation in the two episodes is outlined in the article. The setting was a classroom of fifteen good high-school students, who were studying calculus. These episodes…

The present research study investigates how undergraduate students in an integrated calculus and physics class use physics to help them solve calculus problems. Using Zandieh's (2000) framework for analyzing student understanding of derivative as a starting point, this study adds detail to her "paradigmatic physical" context and begins to address…

Free, open, online homework help sites appear to be extremely popular and exist for many school subjects. Students can anonymously post problems at their convenience and receive responses from forum members. This mode of tutoring may be especially critical for school subjects such as calculus that are intrinsically challenging and have high…

Calculators used widely by students, teachers, scientists, engineers and many others provide an interesting case study of a compelling technology that has helped change the way many professionals work. They not only help in enhancing problem solving skills of most individuals, but also help visualise solutions to problems in a better way. Research…

This article describes how a presentation from the point of view of differential operators can be used to (partially) unify the myriad techniques in an introductory course in ordinary differential equations by providing students with a powerful, flexible paradigm that extends into (or from) linear algebra. (Contains 1 footnote.)

Several examples are given of a variety of nonstandard problems, not ordinarily found in texts or courses, now accessible to students who have programmable calculators. These include: (1) finding limits; (2) evaluating infinite series; (3) calculating finite series; (4) computing variable length products; (5) solving equations; (6) searching for…

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)

A discussion of the mathematics of rugby is related to an earlier article about mathematics and the physical world. (MP)

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)

Four of the author's favorite calculus word problems are presented. These aid students in recognizing and applying concepts in contexts unlike those in typical textbook problems. (MNS)

Discussed is the method of substitution of variables within the framework of precalculus level extremum problems, both maximum and minimum. Many examples with graphical representations are provided. (JJK)

Presents a murder mystery in the form of six Calculus II review problems. Students must solve the six problems to determine the murderer, murder weapon, and time and location of the murder. (AIM)

The cross-product is a mathematical operation that is performed between two 3-dimensional vectors. The result is a vector that is orthogonal or perpendicular to both of them. Learning about this for the first time while taking Calculus-III, the class was taught that if AxB = AxC, it does not necessarily follow that B = C. This seemed baffling. The…