Calculators are seen to shift the student focus in problem-solving situations from "how to do it" to "what to do," by keeping computation from standing in the way when pupils write or solve problems. (MP)

A review of several studies on the role of concrete and symbolic models in facilitating the learning of mathematical ideas, and a discussion of their implications for instruction are presented. (DT)

Activities that allow students to represent patterns concretely before showing the patterns in color on paper are presented. Three basic activities are described, with suggestions made for extensions that allow further pupil exploration of multiples. Student discovery of relationships not found by the teacher is expected. (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)

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)

A description is given of several theories of learning styles. The implications for mathematics education are discussed; special attention is given to corrective teaching. (MK)

Children's perception and understanding of three-dimensional figures and of operations on them is discussed. Piaget's findings are reviewed and more current research is described. Classroom implications are explored. (SD)

A series of learning activities used in grades one and two to teach number conservation and arithmetic are presented in detail. The activity sequence is based on working with one-to-one correspondences for a lengthy period before introducing arithmetic operation. The author claims the approach is very successful. (SD)

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 is research which shows, in contrast to the dominant impression given by Piaget's work, that before the onset of schooling the young child possesses several kinds of fundamental "intuitions" concerning numbers. (Author/TG)

If the principles of languages are applied to the learning of arithmetic, it appears that elementary grade pupils are being introduced to mathematical symbols at too early an age. (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)

Advocated is the use of everyday games and situations instead of the traditional use of textbooks, workbooks, and worksheets. New goals and principles for the beginning arithmetic student are presented. Modifications of activities that promote the constructivist ideal are included. (KR)