Learning to reason spatially is increasingly recognized as an essential component of geometry education. Generally taken to be the "ability to represent, generate, transform, communicate, document, and reflect on visual information," "spatial reasoning" uses the spatial relationships between objects to form ideas. Spatial thinking takes a variety…

Teams, pit stops, clues, time limits, fast forwards, challenges, and prizes are all components of the CBS hit show "The Amazing Race." They were also elements of the Amazing Mathematical Race sponsored by the Math and Stats Club at Northern Kentucky University in April 2009. Held in recognition of Math Awareness Month, which is advocated…

Technology impacts students' learning experiences. The increased use of calculators, computer algebra systems, and computer-based and Web-based assessments opens up new opportunities and challenges for teaching and learning mathematics. Students' lives are becoming busier, and they have less time to dedicate to homework outside the classroom.…

Take a minute and imagine the ideal classroom learning environment. What would it be like? How would students learn? What would they be doing? Certainly, each student would be actively engaged in the lesson, exploring and discovering the key points. Perhaps students would work collaboratively, discussing various concepts and figuring out central…

As a college mathematics teacher for six years, the author has learned his share of pedagogical techniques through research, practice, and reflection. He adopts new theories into classroom practice, differentiates instruction when necessary, and remains open to the diversity his students bring with respect to academic readiness, cultural norms,…

This article describes the authors' attempts to make a college mathematics class more hands-on and interactive. The authors challenge other college mathematics instructors to try similar approaches to enhance the learning and understanding of their students.

The mathematics that students see in their textbooks is highly polished. The steps required to solve a problem are all clearly laid out. Thus, students are denied what could be a valuable learning experience. Often when students meet a problem that differs only slightly from the ones in the book, they are unable to proceed and afraid to "play…

The garlic problem presented in this article develops several themes related to dimensional analysis and also introduces students to a few basic statistical ideas. This garlic problem was used in a university preparatory chemistry class, designed for students with no chemistry background. However, this course is unique because one of the primary…

The Fundamental Theorem of Calculus is discovered based on the use of data analysis techniques applied to a variety of common families of functions. (Contains 8 figures and 6 tables.)

Fantasy baseball, a game invented in 1980, allows baseball fans to become managers of pretend baseball teams. In most fantasy baseball leagues, participants choose teams consisting of major league players who they believe will do well in five offensive categories (batting average, home runs, runs batted in, stolen bases, and runs scored) or in…

To create an environment in which all students have opportunities to notice, describe, and wonder about variability, this article takes a context familiar to many teacher--sampling colored chips from a jar--and shows how this context was used to explicitly focus on variation in the classroom. The sampling activity includes physical as well as…

Under the backdrop of the investigation of rational functions and their respective curved asymptotes, the reader is invited to experience the mathematical process alongside the authors and observe the application of the NCTM Process Standards and the use of multiple representations in the investigation and solution of a problem. (Contains 9…

University mathematics education courses do not always provide the opportunity to make connections between advanced topics and the mathematics taught in middle school or high school. Activities like the ones described in this article invite such connections. Analyzing concrete or particular examples provides a better grasp of abstract concepts.…

If students are to understand inferential statistics successfully, they must have a profound understanding of the nature of the sampling distribution. Specifically, they must comprehend the determination of the expected value and standard error of a sampling distribution as well as the meaning of the central limit theorem. Many students in a high…

The article focuses on engaging students in algebra through modeling real-world problems. The technique of least squares is explored, encouraging students to develop a deeper understanding of the method. (Contains 2 figures and a bibliography.)