Another way to divide a line segment discovered by Nathan Besteman is described along with Euclid's and the GLaD construction. The related projects and problems that teachers of geometry can assign to their students are also presented.

The method of integration by parts is one of the most useful in integral calculus. Among the most important applications is the integration of differentials involving products, differentials in involving logarithms, and differentials involving inverse circular functions.

Available research supports a belief that a high-quality mathematics education for high school students cannot be accomplished unless a highly qualified mathematics teacher is in the classroom. This author primarily addresses the need for small, rural schools in Missouri to employ such highly-qualified mathematics teachers, although he also states…

Students learn more when they attempt to make sense of a mathematical situation they face. For example, a question like why square root of 25 is not + or - 5. Providing the intermediate steps and the reasoning of a technique with graphs can help make better sense of mathematics.

The challenges in developing discursive classrooms in high-poverty, rural schools motivate less verbal students to communicate. Students tend to resist mathematics education reforms and classroom discourses.

Mathematical contests should be decentralized to allow access to non competitive activities so as to enable students to participate and succeed in Mathematics. These activities should be compellingly interesting so that students enjoy learning about proofs and abstract structures rather than just solving problems.

The greatest benefit of including leap year in the calculation is not to increase precision, but to show students that a problem can be solved without such presumption. A birthday problem is analyzed showing that calculating a leap-year birthday probability is not a frivolous computation.

The factors responsible for the shortage of middle and secondary mathematics teachers in the U.S. are discussed. Seven strategies are suggested to reach out and recruit more mathematics teachers in the future.

Teachers often wrongly presume that all students would interpret a three-dimensional image presented in a two-dimensional manner in the same way. They need to be specific as to how questions are stated especially in real-life situations, where alternative interpretations are possible.

While helping high school students develop statistical thinking, teachers need to engage them in all phases of investigative cycle. Students should master some of the nonmathematical elements of the cycle involved in identifying a problem, creating a plan of attack and gathering necessary data.

Media Clips aims to offer readers contemporary, authentic applications of quantitative reasoning based on print or electronic media. Clips may be in text or graphic format, and clip sources may be either print or electronic media.

Analysis of students' work on tasks relating to reflections, translations and rotations is discussed. Findings from research with regard to students' understanding of a subject would help teachers prepare for the class.

A few problems to dispel the notion that mathematics today admits no unsolved problem are presented. The vast area of the unknown and challenges that befit a twenty-first-century attack are discussed.

A dynamic program for geometry called Cabri Geometry II is used to examine properties of figures like triangles and make connections with other mathematical ideas like ellipse. The technology tip includes directions for creating such a problem with technology and suggestions for exploring it.

Describes constructivism as an educational theory promoted by the National Council of Teachers of Education (NCTM), the ideals of NCTM's standards, the validity of NCTM's approach, and the research behind NCTM's recommendations. Includes examples of what teachers can do to promote student construction of knowledge in the classroom and resources…