When teaching mathematics with technology, the author does so in the belief that technology enables students to experience mathematical ideas in a way that might not otherwise be possible. However, teachers must be careful: Sometimes technology does not produce results in the way that they or their students expect. Rather than allowing unexpected…

Many students and adults feel that algebra is merely the shuffling of symbols. The three interrelated concepts of variable, expression, and equation are central to beginning algebra, and in recent years, helping students understand the idea of a variable has been emphasized. Although graphing calculators help students solve equations, it is also…

Procedural evaluations of limits of functions provide invariably better understanding of the limits than the approximations using a calculator. The purpose of this article is to demonstrate that better understanding can be promoted if mathematical understanding precedes the impulse to use calculators. The note clarifies the stages when the…

One problem that students have with mathematics is that they often view the topic as a series of unrelated ideas. Sometimes they are aware that they have to know one concept to move to the next, but what is done in geometry is not necessarily related to anything in algebra. This failure to recognize mathematical connections limits students'…

This paper discusses the "Curriculum and Evaluation Standards" (produced by the National Council of Teachers of Mathematics) that are of particular relevance to mildly handicapped children. Concepts discussed include curriculum and instruction, need for a broad spectrum of mathematics, problem solving, vocabulary, emphasis on understanding, and…