Provides examples which suggest the importance of giving children opportunities to create their own arguments and of allowing them the opportunity to verbalize these arguments in clinical interviews. Also indicates that if time is spent interviewing children individually, instruction can be matched to the way they think. (JN)

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

An awareness of negative effects of mind set is promoted, and ways to minimize harmful sets are suggested. Visual perception, Eistelung effect, and functional fixedness are discussed as categories of potentially negative mind sets, with several examples given of each. Fixation combinations are noted as well. (MP)

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)

Reasons for using manipulative materials in mathematics instruction are discussed: motivation, stimulation to think mathematically, and introduction of big ideas in mathematics. (MNS)

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)

Instruction in estimation is proposed as a natural context to develop and practice important thinking skills. These skills are described and estimation activities are proposed for each. (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)

Research on the characteristics of individuals who have demonstrated a high level of ability in mathematics is presented. The importance of structure in mathematical thinking is stressed and implications for teaching are detailed. (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)

Indicates how thinking strategies help children learn the basic facts for whole numbers, listing several strategies involved in addition, subtraction, multiplication, and division. Also lists books and articles for illustrations of the strategies and how to teach them, and two sources for research findings on thinking strategies for basic facts.…

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)

"Capture" is a game that requires players to perform several computations on each turn and to choose an optimal move, thus promoting higher-order thinking and probability notions. Rules are given, playing is described, and extension activities are noted. (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)