Emphasizes the importance of proofs and offers examples and ideas that might help educators develop students' mathematical reasoning skills. (ASK)

The Optimizer in Quattro Pro and the Solver in Excel software programs make solving linear and nonlinear optimization problems feasible for business mathematics students. Proposes ways in which the Optimizer or Solver can be coaxed into solving systems of linear equations. (ASK)

That the principal axis theorem does not extend to any finite field is demonstrated. Presented are four examples that illustrate the difficulty in extending the principal axis theorem to fields other than the field of real numbers. Included are a theorem and proof that uses only a simple counting argument. (KR)

Presented is a lesson in which the patterns that occur within and between sequences of polygonal numbers present an opportunity for students to analyze, represent, and generalize relationships. Materials, objectives, levels, and directions for this activity are discussed. Worksheets to accompany the activities are provided. (CW)

Discussed is an application of the computer software package, "Mathematica," to solve typical optimization problems from freshman calculus. An example of the use of this method is provided. (CW)

Presents a brief definition and examples of residue designs while sharing some of the algebraic thought that a student used to form generalizations about the patterns discovered during the investigations of residue designs. (ASK)

Demonstrates how graphing calculators can be used by students to solve equations involving absolute value. Allows students to make connections between the algebraic and graphical representations of the problem. (MDH)

High school students (n=295) were administered variants of the student-professor problem to ascertain whether errors could be traced to implicit versus explicit relationships between the variables. Concludes that implicit variable relationship problems were harder than explicit variable relationship problems. A follow-up study to explore why is…

This article explores the multiple representations (verbal, algebraic, graphical, and numerical) that can be used to study the golden ratio. Emphasis is placed on using technology (both calculators and computers) to investigate the algebraic, graphical, and numerical representations. (JAF)

EQUALS is a teacher education program that helps elementary and secondary educators acquire methods and materials to attract minority and female students to mathematics. It supports a problem-solving approach to mathematics which has students working in groups, uses active assessment methods, and incorporates a broad mathematics curriculum…

This study examines teachers' mathematical understanding of various representations of slope and their knowledge for teaching the concept of slope. Specifically examined in this research are the concept images and concept definitions of slope held by both preservice (N=18) and inservice (N=21) secondary mathematics teachers. Data collected include…

Provided is an example of the use of the Pythagorean Theorem to give learners experience in applying mathematical rules. A proof for the theorem is included. Precautions and alternatives are discussed. (CW)

Discussed is the use, importance, and availability of programmed algebraic manipulation packages. The general power summation formula is presented and an example using a programed numerical verification package is provided. (KR)

Describes a Calculus I project in which students discover the formula for the derivative of an exponential function. The project includes two targeted writing assignments and leads to several additional problems. Together these tasks provide a basis for an algebraic approach to the exponential function. (AIM)

Presented is a scheduling algorithm that uses all the busses at each step for any rectangular array. Included are two lemmas, proofs, a theorem, the solution, and variations on this problem. (KR)