Many developmental mathematics programs emphasize computational fluency with the assumption that this is a necessary contributor to student success in general studies mathematics. In an effort to determine which skills are most essential, scores on a computational fluency test were correlated with student success in general studies mathematics at…

During the last 20 years, there has been an increasing awareness that the U.S. is falling behind in its mathematics education of primary and secondary school students. For those who teach mathematics at the community college level, the deficiencies in mathematics education are painfully evident by the number of students requiring remedial math…

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…

It is common for both algebra and calculus instructors to use power functions of various degrees as well as exponential functions to examine and compare rates of growth. This can be done on a chalkboard, with a graphing calculator, or with a spreadsheet. Instructors often are careful to connect the symbolic and graphical (and occasionally the…

When this author first began to take classes in theater and comedy improvisation, his motives were largely creative and social, though there was some supposition that his mathematics teaching (at a community college) could benefit as well. Students are known to tout their favorite teachers as "funny." Taking improv classes would presumably loosen…

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…

This article describes how to design program assessment for mathematics departments, in two-year and four-year colleges across the Midwest, based on a set of components that was generated from a Delphi survey. An example is provided to illustrate how this was done at a small four-year college. There is an alignment between these components and a…

In this paper, the authors examine a property that holds for all cubic polynomials given two zeros. This property is discovered after reviewing a variety of ways to determine the equation of a cubic polynomial given specific conditions through algebra and calculus. At the end of the article, they will connect the property to a very famous method…

This paper justifies the need for, and offers some suggestions on, the selection and implementation of mathematical problems known as dynamic solution exercises (DSEs). The intent of this article is to help provide insight into how mathematics teachers can go about making "vertical articulation" a cooperative and tangible part of the mathematics…

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…

As the coauthor (with Susan Dean) of a formally for-profit and now open (i.e., free on the web) textbook, "Collaborative Statistics," this author has received many questions about open educational resources (OER), which can be summarized as follows: (1) What are OER?; (2) Why do you support, actively promote, and speak about OER?; (3) If a book is…

Learning is obviously a student responsibility... the learning environment is obviously the responsibility of faculty (supported by the institution). "Beyond Crossroads" (Chapter 4) lists recommendations and standards in both areas. Current approaches to developmental mathematics offer methodologies that address those standards and bring a…

As noted in "Beyond Crossroads" (AMATYC, 2006), for today's students, learning mathematics is participatory and depends on the active involvement of students (p. 53). The National Council of Teachers of Mathematics shares the point of view that the teaching and learning of mathematics should include giving students ample opportunity to think…

A couple of years ago, I gave a presentation to a group of secondary-school girls who were attending a workshop at a community college. The workshop's purpose was to encourage the girls to keep taking mathematics courses while in high school and beyond, in order to increase their future opportunities. The presentation was titled, "Where Can I Find…