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…

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 the development of the contextualized math, the course design, student teaching and daily interaction with the students, and the implementation aspects of the research project designed to develop contextualized mathematics and integrate it into the Auto Technician courses. The applied math curriculum was integrated into…

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…

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…

This article is the result of a comprehensive research study investigating the impact of computer-learning technology as well as the impact of a synergistic teaching approach (Keystone Method) on developmental mathematics classes at the college level. The study focused on mathematics skills of elementary and intermediate algebra students and…

The "Beyond Crossroads" document (American Mathematical Association of Two-Year Colleges, 2006) contains the Standard for Assessment of Student Learning. Its implementation standard requires that faculty use results from assessment to improve instruction. In doing this, each faculty member is expected to employ multiple assessment techniques.…

A facility with signed numbers forms the basis for effective problem solving throughout developmental mathematics. Most developmental mathematics textbooks explain signed number operations using absolute value, a method that involves considering the problem in several cases (same sign, opposite sign), and in the case of subtraction, rewriting the…

Technology permeates our daily lives; education has not been untouched. Liaw (2002) points out that "teachers, trainers, and instructional designers of computer-based or Web-based instruction would benefit by being more attentive to learners' perceptions toward Web-based environments." Reviewing the earlier research into student perceptions toward…

Basic brain function is not a mystery. Given that neuroscientists understand the brain's basic functioning processes, one wonders what their research suggests to teachers of developmental algebra. What if we knew how to teach so as to improve understanding of the algebra taught to developmental algebra students? What if we knew how the brain…