We study the turning point problem of a spherical pendulum. The special cases of the simple pendulum and the conical pendulum are noted. For simple initial conditions the solution to this problem involves the golden ratio, also called the golden section, or the golden number. This number often appears in mathematics where you least expect it. To…

This article suggests the introduction of the concepts of areas bounded by plane curves and the volumes of solids of revolution in Pre-calculus. It builds on the basic knowledge that students bring to a pre-calculus class, derives a few more formulas, and gives examples of some problems on plane areas and the volumes of solids of revolution that…

The effectiveness of problem solving as a learning tool is often diminished because students typically use only an algorithmic approach to get to the answer. We discuss a way of encouraging students to reflect on the solution to their problem by requiring them--after they have arrived at their solution--to draw solution maps. A solution map…

"Case Studies for Educational Leadership" gives educational leadership students an opportunity to project themselves into real-life administrative situations and prepare for their future positions in the field. Each case study contained in this practical first edition book asks students to analyze complex problems, consider the moral ramifications…

We present a study of the ascending vertical motion of a self-propelled body under a uniform gravitational field suffering the action of two different types of air friction forces: linear on the velocity, which is valid for slowly moving bodies, and quadratic on the velocity. We study the special case where the thrust force is a decreasing…

This story is a chemical mystery with an emphasis on qualitative analysis, descriptive chemistry, and forensics. It is as well yet another article in the continuing series, first presented by Thomas Waddell and Thomas R. Rybolt, which presents a scientific problem in mystery format in the context of the popular and beloved characters of Sherlock…

For many years, the author has been involving his students in classroom teaching of their own classes. The day-to-day practice is described, and the advantages and disadvantages for both the instructor and the students are discussed. Comparisons with the Moore Method of teaching are made.

Just as comprehension strategies have helped millions of students learn to read like proficient readers, they can also help students think like effective test-takers. The authors show how students can use background knowledge, mental images, synthesizing, monitoring, inferring, questioning, and determining of importance to understand the genre of…

Middle and High school students of the twenty-first century possess surprising powers of spatial reasoning. They are assisted by technologies not available to earlier generations. Both of these assertions are demonstrated by students who are challenged with George Polya's classic Five Planes Problem. (Contains 5 figures.)

This article shows how to use six parameters describing the International Space Station's orbit to predict when and in what part of the sky observers can look for the station as it passes over their location. The method requires only a good background in trigonometry and some familiarity with elementary vector and matrix operations. An included…

Using sticky notes and number lines, a hands-on activity is shared that anchors initial student thinking about absolute value. The initial point of reference should help students successfully evaluate numeric problems involving absolute value. They should also be able to solve absolute value equations and inequalities that are typically found in…

Computer algebra systems (CAS) have been around for a number of years, as has dynamic geometry. Symbolic geometry software is new. It bears a superficial similarity to dynamic geometry software, but differs in that problems may be set up involving symbolic variables and constants, and measurements are given as symbolic expressions. Mathematical…

A little imagination, a little drama, a little mystery. Using the guided inquiry model in this updated, second edition, students become detectives at Information Headquarters. They solve a mystery-and enhance their problem-solving and literacy skills. Middle school is a crucial time in the development of problem-solving, critical-thinking, and…

There is need to reform teacher education programs through the creation of active learning environments that support and improve the depth and scope of student learning. Specifically, teachers should provide intellectually powerful, learner-centered, and technology-rich environments for students without undermining sound pedagogical practices.…

This guide was written for children, to help them handle problems they might encounter, learn about other children and how they have handled similar problems, and learn what to do when things go wrong or when they feel misunderstood. In the introduction, children are assured that, even when they have problems, they can be happy again. The body of…