Relates research findings on the way primary-grade students communicate mathematical ideas through the use of symbols to a framework for students to investigate the part-whole relationship of quantity. Discusses children's problem-solving abilities, linking word problems and symbols, the importance of context for understanding symbols, and the…

Describes "talk-through" model of peer teaching in which student pairs are asked to verbalize their thinking processes as they work through a mathematical problem. Lists five benefits of using this method. (MDH)

Presents a series of activities developed from the "Arithmetic Teacher's" regular feature entitled "Problem Solving: Tips for Teachers" to help students develop skills in each of the four steps of Polya's problem-solving process: (1) Understanding the Problem; (2) Making a Plan; (3) Carrying Out the Plan; and (4) Reflecting…

Describes seven problems designed to enhance the development of four types of student communication in mathematics: (1) describing observations; (2) justifying solutions and solution processes; (3) documenting thinking; and (4) completing or creating mathematical problems. (MDH)

The use of logical reasoning is illustrated with a problem and its solution process. Other suggestions for teaching problem solving are included. (MNS)

Presents the results of a survey of 165 seventh grade students asked to respond yes, no, or maybe to 21 metacognitive statements about their cognitive activity on a mathematical word problem. Suggests how to use the responses as a basis for developing classroom activities. (MDH)

Recommendations for teaching problem solving stem from a discussion of the differences in the functioning of the left and right hemispheres of a person's brain. (JT)

Using questions to help students think mathematically and solve problems is discussed. The teacher's role is described, with a classroom example involving questions about a specific problem. (MNS)

One view of mathematical thinking is described, followed by detailing of the characteristics of a problem-solving program necessary to develop this kind of thinking. (MNS)

A problem-solving strategy that appears to be highly successful is having children write their own word problems. The stages of prewriting, writing, rewriting and revising, and publication are each discussed. (MNS)

When the words "problem" and "answers" are used in connection with computational exercises, students think they are solving problems. Distinguishing between computational forms and problems is illustrated with a variety of topics. (MNS)

Evidence is presented that many primary-age children are good at solving word problems. The data comes from three years of observation of about 100 pupils from grades one through three. It is noted that instances of total failure were relatively rare. The individual interview method is recommended to teachers. (MP)

Presents a study of 87 second graders to demonstrate that achievement tests in primary mathematics emphasize pupil's lower-order thinking by comparing answers to interview questions from constructivist and traditionally instructed groups. Results indicated that constructivist instructed students demonstrated superior higher-order thinking on tasks…