Exploring and deriving proofs of closed-form expressions for series can be fun for students. However, for some students, a physical representation of such problems is more meaningful. Various approaches have been designed to help students visualize squares of sums and sums of squares; these approaches may be arithmetic-algebraic or combinatorial…

In mathematics, developing a conceptual understanding and observing properly modeled methods rarely lead to successful student performance. The student must participate. As with bike riding, participation with monitoring and guidance makes initial efforts meaningful and beneficial. In this article, the authors share a bike riding experience and…

Describes a modified version of the tree diagram used to make probability more meaningful. (MKR)

Examines ways in which students can learn about computational discrepancies that arise as a result of a calculator's limited ability to store numbers accurately. Suggests ways in which such discrepancies can be avoided. (Author/NB)

An introduction to hypothesis testing using a mathematician's claim that his dog knows calculus and can intuit a minimum path.

A number of different solutions are presented and discussed for the problem of constructing a unit segment given the length of the square root of X. (DT)

Recounts a high school teacher's recognition of forces that impede the success of high school students in higher-level mathematics courses. (Author/NB)

Discusses the merits of cooperative learning in the classroom and the effects of implementing cooperative learning in a high school geometry classroom. (Author/NB)

Students use the Law of Cosines and tools of construction, the quadratic formula, and graphing parabolas to explore the ambiguous case of the Law of Sines. (Author/NB)

Gives several proofs of the converse of the Pythagorean Theorem. (MKR)

Discusses how to set the size of the viewing window for a graphing calculator so that it is "user friendly" for all levels of students. Visually correct graphs, numerical interpretation, determining screen size, and setting friendly windows are addressed. (AIM)

Emphasizes the importance of problem-solving attitudes when the problem solver is waiting for a breakthrough. Discusses the classroom use of five components of "mathematical disposition" from the chapter on "Evaluation" in the "Curriculum and Evaluation Standards for School Mathematics." Nine references are listed.…

Explores logarithms of negative numbers spurred by an unanticipated result given by a calculator. Shares the perspectives of the teacher and the teacher-as-learner. (Author/NB)

Explores the use of a study group as a form of professional development for high school mathematics teachers. (Author/NB)

Shows the connections between Sherlock Holmes's investigative methods and mathematical problem solving, including observations, characteristics of the problem solver, importance of data, questioning the obvious, learning from experience, learning from errors, and indirect proof. (MKR)