Of the most universal applications in integral calculus are those involved with finding volumes of solids of revolution. These profound problems are typically taught with traditional approaches of the disk and shell methods, after which most calculus curriculums will additionally cover arc length and surfaces of revolution. Even in these visibly…

Mathematics teachers constantly encourage their students to think independently. The study of integration in calculus provides an excellent opportunity to encourage inventive investigation. In contrast to differentiation, which is predominately mechanical, integration is a more creative process. One such possibility is offered by the study of the…

Students' experience in using formulas for volumes is often limited to substituting numbers into given formulas. An activity presented in this article may help students make connections between the formulas for volumes of prisms and volumes of pyramids. In addition, some interesting facts from number theory arise, demonstrating strong connections…

The great gorilla jump is an activity designed to allow calculus students to construct an understanding of the structure of the Riemann sum and definite integral. The activity uses the ideas of position, velocity, and time to allow students to explore familiar ideas in a new way. Our research has shown that introducing the definite integral as…

Mathematical fallacies have an embedded sense of awe and mystery that can be used effectively in a classroom to inspire students to tackle a fallacy and find the "hidden" violation. In doing so, the student may discover the consequence of a rule violation in a stimulating manner, thus making a lasting impact of the rule as well as providing the…

This paper describes student response, as indicated by an anonymous questionnaire, given by the author to her remedial algebra students at a community college that is part of a large East Coast open-admissions university. The course in question is aimed at the university-wide exit mathematics test necessary to graduation and college-level…

One of the often overlooked aspects of modern statistics is the analysis of time series data. Modern introductory statistics courses tend to rush to probabilistic applications involving risk and confidence. Rarely does the first level course linger on such useful and fascinating topics as time series decomposition, with its practical applications…

Imagine a mathematics instructor and English instructor sharing an office; scribbled equations litter one desk, snatches of poetry the other. Our learning community, "Space on Earth," grew from conversations in just such an office where we bridged our own disciplinary gap and discovered a shared passion for helping students apply the concepts and…

Recommendations and standards from various stakeholders in the mathematical preparation of teachers, such as "The Mathematical Education of Teachers" (http://www.cbmsweb.org/MET_Document/chapter_2.htm) and "Beyond Crossroads" (http://beyondcrossroads.amatyc.org/doc/CH6.html), call for courses that emphasize connections within topics in…

When properly implemented, the vision of "Beyond Crossroads" will result in classrooms where students are actively engaged and responsible for their learning. They are able to share their thinking and the teacher, in turn, can use the emerging understanding as a foundation for learning. According to "Beyond Crossroads," students will be expected…

I recently had the opportunity to teach a developmental mathematics class at a community college, something a little different from what I usually do as a mathematics teacher educator at a university. I welcomed the chance to examine the curriculum and try some new approaches. In particular, I wanted to explore the development of some fundamental…

Each year, well over a million students take college algebra and related courses. Very few of these students take the courses to prepare for calculus, but rather because they are required by other disciplines or to fulfill Gen Ed requirements. The present article discusses what the current mathematical needs are in most of those disciplines,…