Durer's method for drawing an ellipse is used to explain why some people think an ellipse is egg shaped and to show how this method can be used to derive the Cartesian form of the ellipse. Historical background and suggestions for further reading are included. (KR)

Described is a way that elemental mathematics can be applied to explain an astronomical phenomenon. The fact that the extreme of sunrise and sunset do not occur on the shortest or longest days of the year is analyzed using graphs and elementary calculus. (KR)

A question-answering strategy for problem solving is described, and the effects of instruction in that strategy on student learning are examined in a computer-assisted context involving 46 fifth graders. The reasons students trained in guided questions performed better are discussed. (SLD)

Presents a study to determine whether computer use in guided-discovery learning episodes would enhance the problem-solving ability of secondary school students (n=147). Results indicate interaction between low- and middle-level students' mathematical achievement and treatment groups, while high-level students performed well regardless of approach.…

Kindergarten students' (n=7) thought processes were investigated during a problem-solving task to gain insight into students' problem-solving strategies and to guide students toward a closer awareness of their own mathematical thinking. Outlines some of the processes and problems of implementing a constructivist approach by an experienced teacher.…

Examined the quality of responses of six classes of grade six students to four questions requiring multiple and generalized solutions posed under varying conditions. Results indicated that this type of question can be useful in classrooms because students can respond at a variety of levels. (13 references) (MDH)

Discusses the process of mathematical iteration, its benefits as a problem-solving technique, and how to teach it. Presents a selection of mathematical ideas and problems that can be solved and explored using iteration, along with related BASIC computer programs. (MDH)

Short essay questions are introduced into the calculus course as a technique to involve students with their own learning. Provides (1) instructions to the student for writing the report; (2) results of using the technique; and (3) reasons for using writing in mathematics classes. (MDH)

Presents three teaching strategies requiring active student participation in which students (1) create and solve their own word problems; (2) generate trigonometric expressions to be solved by their classmates; and (3) act as points to model a basic locus of points. (MDH)

This study examined the effectiveness of peer collaboration in assisting 48 special education and 43 regular classroom teachers in developing and implementing alternative interventions for students with mild learning and behavior problems. Teachers using peer collaboration were found to have increased tolerance for the range of students' cognitive…

The forces and torques experienced by the spine are examined to understand, and possibly avoid, low back pain. The structure, degrees of freedom, forces and torques when lifting objects, an experimental study, and other factors affecting the back are discussed. (KR)

Thirteen 8- to 10-year-old students participated in a Lego-LOGO learning environment, coupling Lego building-block activities with Logo computer programming, to evaluate whether this learning environment was conducive to metacognitive awareness and cooperation. Results suggested positive cognitive and affective outcomes, especially for the younger…

Describes problems in teaching problem solving and summarizes research in this area. Presents Guided Design or Guided Decision Making as a problem-solving approach in which groups of students work their way through a model of the problem-solving process as they wrestle with a discipline-specific situation. (PR)

The paper describes the details and use with primary school teachers of a problem-solving activity known as the King Alfred's College Maths Game. The game demonstrates to teachers that problem solving needs to be approached through structured learning experiences that provide material for reflection and questioning. (Author/MDH)

Describes a study of factors in the development of reasoning on the balance beam (n=34 nonscience majors in a Physical Science class). From this study and others, the author developed a model of problem solving and problem-solving behaviors. The implications of this model for instruction are discussed. (PR)