Presents case study data of low- and high-achieving nine-year olds focusing on construction and analogical transfer of mathematical knowledge during novel problem solving, as reflected in strategies for dealing with isomorphic combinatorial problems presented in hands-on and written form. Results showed that achievement level does not predict…

Presents a mathematics problem involving speed of a walking student versus speed of light reflection in a high school hallway. (MKR)

Presents a classroom scenario in which a student concocts a unique solution to a standard circle exercise and the class attempts to verify if the solution works for all cases of the problem. (MKR)

Describes a study that provides information about the extent to which students actually use their mathematical resources and strategies to solve problems. Interviews were used to analyze the problem solving abilities of high school students (N=35) as they solved five problems. (DDR)

Presents a preliminary analysis from a study designed to investigate the participation of students learning English as an additional language in primary school mathematics. Concerns how students make sense of mathematics classroom interaction. Describes and uses the findings of three patterns of attention in the process of two students'…

Presents student responses to the "The Darts, Anyone?" problem that appeared in the May, 1999 issue of this journal. The problem concerned finding possible scores on dart rings. (KHR)

Examined the thinking of students who constructed personal knowledge about division of fractions. Mixed-ability fifth grade mathematics students used pictures, symbols, and words to resolve situations and communicate solutions. All strategies that the students used represented some manifestation of conceptual knowledge about addition and…

Examines the problem-solving processes of social studies and mathematics and discusses their commonalities. Considers how those processes might be taught so that students will see that there is indeed a relationship between those two seemingly discrete disciplines. (RS)

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)