Introduces a problem that can be used to help children develop graph sense. Involves two graphs of which students must determine which one applies to which situation. (KHR)

Poses a practical woodwork problem in which maximizing the perimeter of a square-based pyramid is required. The pyramid is constructed from four identical trapezia to be cut from a given rectangle of wood. A simple mathematical analysis suggests a number of different strategies for the solution of the problem. (Author/NB)

Compared the performance of grade 9 mathematics students trained to use a self-explanation procedure during study of a new theorem in geometry to that of students using their usual study procedures. Results for 47 high school students reinforce the view that a self-explanation procedure can be seen as a simple but potentially powerful technique…

Presents a way of using counterintuitive mathematics problems to help keep students actively involved in mathematics education. (KHR)

Describes the use of a purposefully designed set of problems borrowed from a variety of critical thinking activity books and selected to motivate, excite, and engage students in the learning process. Helps students develop a deeper, more conceptual understanding of mathematics by incorporating these problems into a beginning algebra course.…

The values of a polynomial with integer coefficients can be computed using a graphing calculator, but it is impossible to see the formula itself. Suggests finding this formula from numerical data and describes the unusual way to solve this problem with one calculation only. (Author/NB)

Concludes that writing about the executive processes of problem solving, difficulties encountered, alternative strategies that might have been used, and the problem solving process in general helped students in the treatment group learn to use executive processes more quickly and more effectively than students in the control group. (Author/NB)

Discusses an algorithm from Vedic mathematics that has similarities to FOIL and the standard algorithm for multiplication. (Author/NB)

Students use the relationship between the speed of a ball and the time that a player has to react to it to understand uniform motion problems. Includes activity sheets. (Author/NB)

Five primary-grade students identified as learning-disabled benefited from instruction that focused on making sense of mathematics word problems. Examples of student work demonstrate the students' ability to solve a variety of problem types and justify their solutions. (Author/NB)

Describes three types of mathematics problems that are useful in promoting algebraic reasoning in the elementary school. (Author/NB)

Investigates mathematical problem-solving processes from the viewpoint of the solver's structures representing a problem situation. Analysis shows that the solver's structures were modified during the solution process in a global restructuring based on certain characteristics of the solver's mental representations. (53 references) (Author/MKR)

Presents examples of the use of open-ended problems in Australia and discusses assessment of open-ended problem solving. (MKR)

Cobb's Cusp Surface Analysis Program (CUSP) provides a way to estimate empirically and test a nonlinear cusp catastrophe model. A model of emotion during problem solving is used to introduce catastrophe theory modeling and is discussed in conjunction with how to run and interpret CUSP. (SLD)

The National Council of Teachers of Mathematics has called for sweeping changes in mathematics instruction, arguing that knowledge should emerge from experience with problems. Deborah Ball's third grade class in East Lansing, Michigan, is a community of youthful mathematicians who argue, concur, and theorize about odd and even numbers. Instituting…