Research on direct instruction in mathematics is briefly summarized, with key procedures listed. (MNS)

Research on the use of manipulative materials in teaching mathematics is briefly reviewed. Lessons using manipulative materials have a higher probability of producing greater mathematics achievement than do lessons in which materials are not used. (MNS)

Cassette tapes were prepared to provide drill in multiplication facts. Pre-test and post-test scores were recorded. (MP)

This brief review of research on calculators indicates that they will not harm achievement and that they are helpful in problem solving and for teaching other mathematical ideas. (MNS)

Research on the amount of questioning and the types of questions teachers ask are briefly discussed. (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)

Research on how teachers treat low-achieving students is briefly noted. It seems apparent that these students are being given a poor self-image. (MNS)

Research appears to support one major conclusion: problem-solving strategies should be taught. Sections presented are: Why doesn't research tell us what to do? What do we know about problem solving? What can teachers do to help children learn to solve problems? What has recent research affirmed? (MP)

A study to determine if "random" or "careless" errors in multiplication made by individual students take on discernible patterns is described. Implications for teaching are discussed. (MK)

One-third of the kindergarten teachers in Kansas were surveyed by questionnaire as to the competencies in mathematics achievement by kindergarten children and trends evident in the methods used by teachers of kindergarten mathematics. (MN)

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)

After research on problem solving is briefly summarized, an in-service program on problem types and solution strategies is described. Teachers must know how pupils solve problems; they can use activities designed for both instruction and assessment. Key aspects of assessment are summarized. (MNS)

Research on effective teaching is described. Comparisons of expert and novice teachers reveal a profile of expertise in elementary mathematics instruction. How lessons are planned and presented is discussed. (MNS)

Research on the use of review is briefly summarized. Some guidelines for planning review work are listed, and five types of effective review are noted: outlines, questions, varied grouping, varied content, and games. (MNS)

Research on the attitudes of elementary school pupils toward mathematics is briefly summarized. Included are the points that most elementary school children like mathematics and that few differences are found between the attitudes of boys and girls. Some suggestions on what teachers can do to improve attitudes are given. (MNS)