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

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)

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)

The importance of understanding is stressed. Understanding the task is as vital as knowing the basic meaning. (MNS)

The informal subtraction strategies that children develop are discussed in detail, with the role of the counting-down strategy described. Problems and remedies for difficulties caused by counting backward and the double count are also presented. (MNS)

Concerns about how mathematics should be taught are discussed. Considered are operational and conceptual domains of thought, with many explicit examples. Educational implications, with premises, are noted, and an alternative is described. (MNS)

Two successful procedures for evaluating problem-solving performance in the classroom are shared. Five goals for teaching problem-solving are noted, followed by a discussion of evaluating a child's performance through joint use of: (1) analyzing written work; and (2) observing and questioning students. (MP)

Establishing and maintaining the desirable kind of balance between meaning and computational competence is the subject of this reprint from a 1956 issue of the journal. Sources of the dilemma and suggestions for solution are discussed. (MNS)

The history of mental computation in the elementary school curriculum is briefly described, followed by discussion of the benefits of mental computation. How thinking skills are enhanced is then illustrated. (MNS)