Describes two investigations suitable for grades seven and eight that explore the properties of the figure created when the midpoints of an equilateral triangle or square are joined. (MDH)

Describes a problem to challenge students as they come back from summer vacation. Working in small groups, students discover Pick's Theorem, the formula to calculate the area of a polygon constructed on a geoboard. A writing assignment evaluates the students' efforts. (MDH)

Concrete experience should be a first step in the development of new abstract concepts and their symbolization. Presents concrete activities based on Hyde and Nelson's work with egg cartons and Steiner's work with money to develop students' understanding of partitive division when using fractions. (MDH)

Over a 10-month period, normal children showed an increased reliance on memory retrieval and a decreased reliance on counting when they solved addition problems. There was an increase in speed of counting and of retrieving addition facts from long-term memory. Children with a mathematical learning disability showed no change in problem-solving…

Discusses the limitations in the explain-practice and active learning methods of teaching mathematics. Proposes that problem-centered learning is a teaching method that encourages student reflection, and presents examples demonstrating that encouraging reflection results in greater mathematics achievement. (MDH)

Results from 40 high school students on the mathematics subtest of the Scholastic Aptitude Test (SAT) support the prediction that successful students would have more prior knowledge and would be better at defining problems, assembling strategies, and avoiding computational errors. Results are discussed in terms of a cognitive processing model.…

Responses of students in grades K-10 (42 interviewed; 98 written) to 4 common fractions problems were analyzed for iconic mode processes in relationship to concrete symbolic mode development. Concludes that progress in the latter, without development of complementary iconic support, limits both understanding and flexibility in solving problems.…

Describes a mathematics course for prospective elementary teachers that has teaching and learning mathematics via problem solving at its core. Presents a problem-solving activity involving number theory and reactions by the students and teacher to the activity. (MDH)

As part of Alberta's provincial initiative, teacher-researchers in two Calgary school districts developed and field-tested quality indicators for assessment of student artwork and mathematical problem solving. The resulting qualitative materials depend on informed professional judgment and student involvement in self-assessment; celebrate…

The task seemed straightforward enough: Students taking part in a recent international test were asked to review drawings of five triangles with varying angles and midpoints. Then those teenagers were to read over a paragraph describing the characteristics of a particular triangle and, finally, choose the triangle that fit the description. Of the…

This article describes a mathematical model that connects mathematics with social studies. Students use mathematics to model independent versus convoyed ship deployments and sinkings to determine if the British should have convoyed their merchant ships during World War I. During the war, the British admiralty opposed sending merchant ships grouped…

This is the first of two papers that develop a framework and encourage discussion of research and programmatic concerns on arithmetic word problem solving. The two papers include a comprehensive framework for expanding the traditional three to five sentence word problem into a scheme that assures problems will be of a variety of structures and…

This research examines how primary school children exhibit uncertainty in their spoken responses to mathematics assessment tasks. Students displayed uncertainty about: what was expected of them in a task; what information was provided; the correctness of their answers, and the exactness of their answers. The use of uncertainty devices and…

Described is a study concerned with the mode of presentation of printed mathematical word problems. Tenth grade students were given twenty word problems to solve, presented in one of three ways: (1) prose only, (2) prose with an accurate picture included, or (3) prose with a distorted picture. Experimental results showed that the group with an…