In my Keynote Address to PME-NA 45, I offer an embodied framework for naming what makes mathematics powerful for mathematicians and scientists, yet intractable for many learners. The essential claim is this: Students reside in the Real World, where math is grounded, embodied and meaningful, while mathematics resides in the ungrounded, disembodied…

Many ways exist to engage students without detracting from the mathematics. Certainly some are high-tech options, such as video games, online trivia sites, and PowerPoint® presentations that follow the same model as Jeopardy; but sometimes low-tech options can be just as powerful. One exciting way to connect with students is by incorporating…

Many middle school students approach math with caution, often trepidation, and generally less-than-complete confidence. Several factors contribute to their views of what math actually is (a system of rules to follow and formulas to apply) as well as who might be good at it (people who can see the path to an answer and calculate quickly). A few say…

This article will describe two activities in which students conduct experiments with random numbers so they can see that having at least one repeated birthday in a group of 40 is not unusual. The first empirical approach was conducted by author Cauto in a secondary school methods course. The second empirical approach was used by author Flores with…

The main strand of the NRICH project is the NRICH website (http://nrich.maths.org), which was set up in 1996 to cater for secondary-aged pupils who were attending mathematics master-classes at the Royal Institution. By 1998, problems aimed at primary children were included and the site began to provide for students aged five to 18-plus. At this…

An event based on "find the rule" problems has been part of the University of Canberra Maths Day since 1985. In this paper, the authors describe the Swiss event, its context, its aims, its logistics, and gives examples of problems used in past events. The type of problems used, how they are used in an event at the maths day, and how the…

Described is an experience in assigning mathematics problems that have been purposefully selected from professional journals to assist upper level college mathematics students in developing confidence in their ability to contribute published solutions. Several examples are included. (JJK)

An exploration of a problem called solving quadratic congruences modulo p is detailed and is built around an alternate method of deriving the quadratic formula. Three practical pedagogical values that have been experienced by students and instructor when the material was presented to classes are noted. (MP)

Describes the use of math journals in one kindergarten classroom. Asserts that use of the journals, in which children record their problem-solving processes, makes them think about and use various symbols to represent their thoughts; keeps them actively involved in reasoning, comparing, counting, and other mathematical concepts; and encourages…

Describes how teachers of the gifted can make the study of mathematics dynamic, innovative, and creative through the exploration of problem-solving skills and real-life applications. Math competitions and general academic competitions that include mathematics for elementary schools, middle schools, and high schools are highlighted. (CR)

Discusses the benefits and possible side effects of learning mathematics through routine exercises. Suggests some teaching strategies including different exercises, different symbols, making examples, and counterexamples. (YP)

Describes a mathematics trail created on the campus of Exeter Academy and in the town of Exeter, New Hampshire. A series of problems and puzzles enabled teachers to teach mathematics outdoors. Novel questions were created to permit students to look at things from a different perspective. Participants were often inspired to create questions of…

A description of a planet in the shape of a cube where everything was built from squares and parts of squares is presented. The story is used as a background for several paper folding exercises that explore several geometric shapes. Solutions to the problems stated are included. (MP)

Described is a Kernel Design, used in the multiunit Discovery School in Mansfield, Ohio, to improve a general weakness in the areas of measurement and the use of monetary skills. Kernel Design is so named because it conveys the gist or core of an idea. (Author/TG)

Intended to improve mathematics education at two-year colleges and other institutions offering lower division courses as well as to encourage more students to study mathematics, this publication presents the American Mathematical Association of Two-Year Colleges' (AMATYC's) standards for revitalizing the pre-calculus mathematics curriculum and…