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

What mental computation and estimation are, what is known from research about each process, and what can help students develop these skills are discussed. (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)

Metacognition is described and suggestions for teachers about developing and improving metacognitive skills in performing mathematical tasks are given. (MNS)

Pertinent findings from research on problem solving are presented to describe how primary-level children may gain an understanding of addition and subtraction as well as practice computational skills through one-step problems. Then suggestions for teaching problem solving are given. (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)

Some research focuses on how children develop the ability to estimate computations. The theory and a research study are briefly described, followed by discussion of the study's implications and extensions into the classroom. (MNS)

Research findings on decimals and money are briefly summarized, followed by suggestions for classroom use. (MNS)

An instrumental technique is presented to help students create a symbolic representation that may aid the process of choosing an appropriate operation to solve a problem. Current research and practice are discussed; then the part-part-whole model is presented. (MNS)

Research on when and how geometric concepts are learned is briefly discussed. Several teaching suggestions are included. (MNS)

Discussed is the difference in the use of verbal explanation, identified by observations of mathematics teaching in first- and fifth-grade classrooms in Japan and the United States. The author suggests we reexamine the role of direct teaching and stress both concrete experiences and verbal explanations at the same time. (MNS)