Presented are five scenarios of how division might be introduced to a class of third graders using experiences with the concept, process, and symbolism of division rather than algorithms. Instruction that makes problem solving the emphasis of students' learning is described. (KR)

Recounts a teacher's experiences with a small group of elementary school students as they explore different forms of the combinatorics problem of choosing two out of five objects. Describes how students examine the connections between the problems and a proof of the relationship. (MDH)

Presents an experiment carried out at the University of Groningen where pretest-posttest design was used including two experimental conditions with the graphics calculator (TI-81) and one control condition without the calculator. Results point toward a change in teacher instructional behavior and in pupils' problem-solving approaches. Contains 14…

Mathematics plays an exceptionally important role in biological education and the history of biology. Ten equations and descriptions of their historical importance are presented to draw students' and faculty's attention to mathematical models that have been intrinsic to many of the significant discoveries in biology in the 20th century. Each…

Describes two problem-solving activities for small groups that motivate through the use of sundials. Includes practical work. (ASK)

Evaluates the use of modern CAD methods to solve geometric problems. Solves descriptive geometry problems using the layout and position of the successive auxiliary views from the projection of three-dimensional figures onto a two-dimensional plane of paper. (CCM)

Investigates the effects of an instructional intervention derived from the Garofalo and Lester cognitive-metacognitive framework on the problem-solving performance of year six students with different ability levels. Concludes that there was significant improvement in problem-solving performance for the experimental class compared to the control…

Shares two lessons in which students help teachers pose problems and discover the importance of posing problems properly. Presents a fifth-grade lesson in which students found a mistake in a proportion problem, and an eighth-grade lesson that discusses a geometry problem with insufficient information. (ASK)

Describes a typical fifth-grade mathematics lesson as taught in a Japanese elementary school, followed by a reflective commentary focused on problem solving, using manipulative aids, and multiple solutions. (ASK)

States that writing has become a major component of mathematics as a teaching, learning, and assessing mechanism of mathematical understanding. Presents some writing activities for mathematics classes and their advantages. (ASK)

Describes how successful study of mathematics requires a set of problem-solving processes that help students reason mathematically, offers a context in which students can communicate their reasoning, and provides opportunities for students to link their learning to prior mathematical contexts. Discusses the three basic processes of Krutetskii's…

Presents suggestions for integrating mathematical problem solving into all aspects of an elementary school classroom. This includes taking data from such areas as attendance and lunch counts, numbers of seats needed for an open house, amount of money needed for field trips, and many more. The article offers tips for powerful problem solving. (SM)

Analyzes student construction of function-based problem solving methods in introductory algebra. Describes longitudinal observation of a pair of students that studied algebra for three years using the function approach including intensive use of graphing technology. Offers terms for describing and explaining what and how do learners appreciate and…

Matrix organization can be used to construct math word problems for children with mild disabilities. Matrix organization specifies the characteristics of problems, such as problem theme or setting, operations, level of computation complexity, reading vocabulary level, and need for classification. A sample scope and sequence and 16 sample word…

Contends that the context of children's literature affords opportunities for solving varied and authentic mathematics problems. Suggests that the problem-solving process in mathematics is often linked with that involved in comprehending children's literature. Consequently the teacher is provided meaningful information about students' thinking that…