Techniques for applying mathematical concepts in the real world: six rarely taught but crucial tools for analysis, research, and problem-solving. Many young graduates leave school with a solid knowledge of mathematical concepts but struggle to apply these concepts in practice. Real scientific and engineering problems are different from those found…

The Reduced Reparameterized Unified Model (Reduced RUM) is a diagnostic classification model for educational assessment that has received considerable attention among psychometricians. However, the computational options for researchers and practitioners who wish to use the Reduced RUM in their work, but do not feel comfortable writing their own…

Gives a student-accessible proof that, in any convex polyhedron, the number of vertices plus the number of faces is always two more than the number of edges. (MKR)

Demonstrates some of the usefulness of number theory to students on the high school setting in four areas: Fibonacci numbers, Diophantine equations, continued fractions, and algorithms for computing pi. (ASK)

Argues that two problems (the mole concept and mathematical reasoning) can be reduced by carefully distinguishing betwen quantities and numbers, by replacing mole as a unit for stoichiometric calculation with a number of particles as the unit for calculation, and by introducing students to the language of quantity calculus. (JN)

Describes a method to eliminate the nonlinearity from a spring that is used in experimental verification of Hooke's Law where students are asked to determine the force constant and the linear equation that describes the extension of the spring as a function of the mass placed on it. (JRH)

Discusses the mathematical applications of weather including Fahrenheit-Celsius conversions, temperature cycles, the wind-chill factor, and a temperature-humidity index. (MKR)

Presents a class discussion about using the slope of the secant line through the vertex and the point on the parabola occurring one unit to the right as the slope of the parabola. (MKR)

Describes the use of linear equations having unique solutions and nonunique solutions in the balancing of chemical equations. (MKR)

Presents a method for solving linear equations involving the use of inverses instead of memorizing rules. (MKR)

Presents a classroom-tested, easy-to-use, multipurpose program (written in Applesoft BASIC) for graphing equations. A complete listing of the program (which is suitable for a wide range of applications in grades 7-12 mathematics classrooms) is included. (JN)

Discusses the factoring of polynomials and Fibonacci numbers, offering several challenges teachers can give students. For example, they can give students a polynomial containing large numbers and challenge them to factor it. (JN)

Geometric interpretations of algebraic statements are proposed, both to clarify the meaning of algebra and to encourage students to look for spatial or diagrammatic models. Binomial grids for several equations are illustrated. (MNS)

Explains why the isolated sphere models are physically unsound. Describes an improved model for attempting a qualitative explanation of charge concentration. (YP)

Presents a technique that helps students concentrate more on the science and less on the mechanics of algebra while dealing with introductory physics formulas. Allows the teacher to do complex problems at a lower level and not be too concerned about the mathematical abilities of the students. (JRH)