Presents a series of five activities that introduce division of fractions through real-world situations. Discusses problems related to resurfacing a highway, painting dividing stripes on a highway, covering one area A with another area B, looking for patterns, and maximizing the result of a division problem. Includes reproducible worksheets. (MDH)

Presents an account of the historical evolution of the definition of variable and the way the concept is currently treated in textbooks. Shares activities to promote student discussion on the use of variables as constants, as quantities that vary, and as parameters. Provides a reproducible worksheet. (MDH)

Discussed is the process of translating situations involving changing quantities into mathematical relationships. This process, called dynamical modeling, allows students to learn new mathematics while sharpening their algebraic skills. A description of dynamical systems, problem-solving methods, a graphical analysis, and available classroom…

Two studies to determine how students interact with two microworlds that reflect a constructivist view of learning investigated students' goals during interaction, strategies utilized to achieve their goals, changes in goals during interaction, and common patterns of interaction and learning. Concludes that well-designed games enable students to…

Describes a program in second-grade Dutch mathematics classes that emphasizes mental addition and subtraction of two-digit numbers up to 100. Deals with a strategy of counting by 10s from any number. (Contains 56 references.) (RLB)

Links between content knowledge in the mathematics domain and pedagogical reasoning were compared for three university mathematics professors, three mathematics-methods professors, three high school teachers, three middle school teachers, and three elementary school teachers. In general, teachers with the most training and experience produced…

Information processing researchers have assumed that algebra symbol skills depend on mastery of the abstract rules presented in the curriculum (Matz, 1980; Sleeman, 1986). Thus, students' ubiquitous algebra errors have been taken as indicating the need to embed algebra in rich contextual settings (Kaput, 1995; National Council of Teachers of…

This article deals with 12th-grade students' conceptions of a mathematical definition. Their conceptions of a definition were revealed through individual and group activities in which they were asked to consider a number of possible definitions of four mathematical concepts: two geometric and two analytic. Data consisted of written responses to…

Many students doubt that statistical distributions are of practical value. Simulation makes it possible for students to tackle challenging, understandable projects that illustrate how distributions can be used to answer "what-if" questions of the type often posed by analysts. Course materials that have been developed over two years of classroom…

In 2001, with funding of $7 million, the Australian Government implemented the "Numeracy Research and Development Initiative"--one of several initiatives introduced by the Australian Government to support literacy and numeracy improvement. Other initiatives included the "National Indigenous English Literacy and Numeracy…

Research is only beginning to show the benefits of the effective use of manipulatives with students who have disabilities. This article highlights how teachers can incorporate three manipulative instructional strategies to help students with high-incidence disabilities.

In order to prepare prospective teachers of secondary school mathematics to effectively guide the teaching and learning process using technology, a new required course was developed at Middle Tennessee State University. Technology has been integrated into mathematics courses in which these preservice teachers are enrolled. This paper discusses the…

The National Council of Teachers of Mathematics (NCTM) has articulated goals in the pursuit of mathematics literacy that include learning to value mathematics, becoming confident in one's mathematics abilities, becoming a mathematical problem solver, learning to communicate mathematically, and learning to reason mathematically. Literature that…

A basic algebra unit was developed at Utah Valley State College to emphasize applications of mathematical concepts in the work world, using video and computer-generated graphics to integrate textual material. The course was implemented in three introductory algebra sections involving 80 students and taught algebraic concepts using such areas as…

The appropriateness and feasibility of the "Curriculum and Evaluation Standards" published by the National Council of Teachers of Mathematics were examined with respect to the mathematics education of students with disabilities. Eleven experts from the areas of mathematics education, special education, and assessment were surveyed using…