Incorporating problem solving as an integral part of mathematics programs in the classroom is discussed. The teacher's focus is seen as stretching pupil thinking. (MP)

Some significant components of mathematics instruction are presented and reviewed. Good instruction is viewed as a major influence on the quality and quantity of student learning. (MP)

Every student at every level is seen to learn mathematics individually and personally, putting an individual stamp on each incoming perception. (MP)

Children's difficulties remembering correct algorithms for operations with fractions are traced to difficulties in the instructional sequence. Many teachers "teach mistakes" by failing to provide sufficient referents for their pupils. (MP)

Having pupils create their own mathematical-application word problems is promoted as a powerful teaching strategy. Teachers are encouraged to make creative pupil applications an integral component of day-to-day learning in mathematics. Research is cited that strongly favors the approach presented. (MP)

Teachers are encouraged to use the results of assessments to plan specific educational programs. Information is provided about the nature of diagnostic testing, with both content and process error analysis discussed. The nature of prescriptive teaching is detailed to show how to devise remediate activities after student problems are analyzed. (MP)

Four basic types of student errors in computation are noted and described. These are: (1) mechanical, (2) careless, (3) conceptual, and (4) procedural. It is felt many teachers deal with all errors as if they were of the unhabituated procedural type, with not enough attention given to other possibilities. (MP)

Ways are identified in which typical textbook word problems can be used to better fulfill their role in the development of mathematical concepts and a sound instructional program of mathematical problem solving. (MP)

Two aspects of instructional practice in mathematics are discussed: the process of developing instructional activities and the importance of engaging students in mathematical discussion. The National Council of Teachers of Mathematics (NCTM) Standards are evaluated based on this discussion. (CW)

Discussed are "moves" in teaching mathematics that can serve as a basis for defining understanding. How to characterize and use moves is discussed, with specific examples and research evidence. (MP)

The theory of teaching the language arts is investigated for implications for teaching mathematics. Two major implications are noted and eight examples of activities designed to help teaching by addressing the various roles of the language arts are given. (MP)

Three examples of teacher and student exchanges in mathematics classes are presented which typify the qualitative difference between children's thinking and adult's thinking. The cases explored also illustrate differences caused by cultural factors. (JP)

The dynamics of success and praise are discussed. Guidelines designed to improve the chances of successful use are provided. A checklist of eight questions teachers can ask themselves about the use of praise is included. (MP)

The problems of using formalistic methods in the instruction of mathematics to elementary level children are discussed. Precision in mathematical language is not seen as a useful instructional tool, and functional modes of communication are stressed. (MP)