One goal of a mathematics education is that students make significant connections among different branches of mathematics. Connections--such as those between arithmetic and algebra, between two-dimensional and three-dimensional geometry, between compass-and-straight-edge constructions and transformations, and between calculus and analytic…

Encouraging students to reason with quantitative relationships can help them develop, understand, and explore mathematical models of real-world phenomena. Through two examples--modeling the motion of a speeding car and the growth of a Jactus plant--this article describes how teachers can use six practical tips to help students develop quantitative…

In January 2006 the Billings (Montana) Public Schools adopted a computer-assisted instruction (CAI) intervention aimed at helping students recover credits that they had attempted but had not attained. The author volunteered to teach the algebra component in his high school. Through the following seven semesters, he came to better understand the…

Describes the Recognizing and Recording Reform in Mathematics Education Project created to monitor the implementation of the NCTM Standards and monitor a broader program of research and development. Discusses key issues in mathematics reform and describes the methodology of the project. (Contains 10 references.) (MKR)

The probability and statistics portion of an optional comprehensive mathematics sequence offered at the secondary level in New York public schools is presented. (MP)

The objectives, content, and intent of an undergraduate mathematics course at the University of Northern California. The course focuses on gambling and bets, with the focus of ideas on probability, expected value, computers, and the mathematics of finance. (MP)

The nature of an investigation into numbers termed Nearly Isosceles Pythagorean Triples (NIPTs) is detailed. The exploration, even though it is stated to have no practical value, is defended as helping pupils see the beauty of patterns in mathematics. Two questions regarding the pattern of generating NIPTs are noted. (MP)

Examples of answers college students studying to be elementary teachers gave to sample student errors and questions in mathematics are presented. The bulk of the prospective answers are judged to have serious flaws. The analysis of such "poor" answers is suggested as a useful vehicle in teacher training programs. (MP)

Described is a two-week summer residential program designed for students who have been identified through one of several middle school talent searches. Discussed are the assumptions and goals, course content and pedagogy, evaluation, and materials of the program. (CW)