"Math is language, too," Phyllis and David Whitin (2000) remind everyone in their informative book about reading and writing in the mathematics classroom. This means that students in elementary school math classes are learning two distinct, yet related languages--one of numbers, the other of words. These languages of numbers and words…

FIFTEEN DAILY DRILLS EMPHASIZING MASTERY OF BASIC NUMBER FACTS, SUCH AS ARITHMETIC OPERATIONS AND UNITS OF MEASUREMENT WERE CONSTRUCTED TO ENCOMPASS 7 PREVIOUSLY REPORTED ATTRIBUTES OF AN EFFECTIVE DRILL. ATTRIBUTES ARE MIXED DRILL, TIME LIMIT, INCREASINGLY DIFFICULT EXAMPLES, THOROUGH COVERAGE, FREQUENT AND SMALL AMOUNTS, VERBAL PROBLEMS,…

The author of this article, while recently working through some problem sets on determining volumes by triple integrals in cylindrical and spherical coordinate systems, realized that, although the textbook he was using included many interesting problems involving spheres, cylinders and cones and the increasingly complex solids that arose from the…

This study investigates the use of using complexity theory--the study of nonlinear dynamical systems of which chaos and catastrophe theory are subsets--in the analysis of a non temporal data set to derive valuable insights into the functioning of university schools of business. The approach is unusual in that studies of nonlinearity in complex…

Presented are the six problems that were given to 120 secondary school students representing 15 countries at the 12th International Olympiad in Budapest, June, 1970. (JG)

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 results of an experimental study investigating the influence of problem familiarity on learning in a problem-based psychology course are presented. Participants worked with either a "familiar" or an "unfamiliar" version of the same problem. The following measurements were taken (1) a measure of problem quality as perceived by students, (2)…

For more than twenty years, the Richmond, Virginia Public Schools' program for gifted students has conducted an interscholastic competition similar to the nationally known competition, Destination Imagination. In the featured contest of this yearly event, teams of five students present solutions to engineering problems that they have worked on for…

Presented are more than 300 problems of varying difficulty along with answers and solutions. These problems were initially given to participants in mathematics contests among high school students. With each problem a time factor is included as well as a percentage of participants who successfully solved that problem. (CT)

Two approaches are discussed for calculating the work necessary to pump water from a conical or parabolic container. The direct method derived from the definition of work is easy to misuse, as illustrated by a student's incorrect solution. (JP)

Seven articles present: 1) a solution to a force equilibrium problem, 2) a magic square, 3) a characteristic of right triangles, 4) a family tree of Pythagorean triples, 5) a misunderstanding which may be cleared through modern mathematics, 6) a technique for solving conversion problems, and 7) a special permatation problem. (RS)

Presents some examples of drill problems turned into thinking problems. Examples include fraction problems, stretching simple problems, cone problems, and area problems. (KHR)

Describes the electronic homework system that provides individual students with a disk of programs that they can use to generate personalized problem sets. Discusses the advantages of this approach and the nature of computerized problems. (JRH)