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…

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…

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…

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 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…

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…

For a period of four semesters, the possibility was explored of using a "group quiz" as a learning activity that provides a collaborative learning environment, a review of the previous week's material, and a formative assessment for both the student and the instructor. Using both quantitative (i.e., student surveys) and qualitative (i.e., student…

In this paper, students used problem-solving skills to investigate what patterns exist in the Pascal triangle and incorporated technology using Geometer's Sketchpad (GSP) in the process. Students came up with patterns such as natural numbers, triangular numbers, and Fibonacci numbers. Although the patterns inherent in Pascal's triangle may seem…

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…

Based on the results of a prior case-study analysis of mathematics placement at one university, the mathematics department developed and piloted a mathematics placement test. This article describes the implementation process for a mathematics placement test and further analyzes the test results for the pilot group. As an unexpected result, the…

A mixed-method study was conducted during the Fall 2008 semester to better understand the experiences of students participating in computer-aided instruction of College Algebra using the software MyMathLab. The learning environment included a computer learning system for the majority of the instruction, a support system via focus groups (weekly…

We will first recall useful formulas in integration that simplify the calculation of certain definite integrals with the quadratic function. A main formula relies only on the coefficients of the function. We will then explore a geometric proof of one of these formulas. Finally, we will extend the formulas to more general cases. (Contains 3…