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)

Argues that, though considerable difference of view is evident between Montessori and Piaget about the importance of certain concepts and level of cognitive development necessary for genuine understanding, the ideas and methods first presented by Montessori 80 years ago stand up well when evaluated through the lens of current research. (PK)

A list of heuristics for elementary school children is provided. Two examples which are viewed to demonstrate the conscientious and creative use of problem-solving strategies by fourth graders are detailed. Suggestions for teachers on how to help pupils develop their problem-solving abilities are included. (MP)

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)

Discussed is a constructivist view of mathematics education. The basic tenets and goals are described. The role of the student and teacher are highlighted. The constructivist and traditional views of instruction are compared and contrasted. (KR)

Mathematics success or failure is noted as possibly related to the way in which material is presented rather than to the subject itself. Teachers are encouraged to have pupils complete a questionnaire that is designed to measure their mathematical "state of health." Instructors are told to identify learning styles. (Author/MP)

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)

Described are graphing activities which can be instrumental in introducing the mathematics concepts of counting, sorting, grouping, and comparing on the primary level. On the intermediate level, these activites can be used to introduce collecting and sorting unorganized data, and creating graphs to represent the data. (Author/TG)

Described are activities using paper plates with dots drawn on them which place a heavy emphasis on matching and ordering sets, on developing mental images of sets, and on perceiving sets of a certain size as composed of smaller subsets. Also suggested are activities involving numerals. (Author/TG)

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)

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)