This guide is organized around six concepts: sets, numbers and numeration; operations, their properties and number theory; relations and functions; geometry; measurement; and probability and statistics. Objectives and sample activities are presented for each concept. Separate sections deal with the processes of problem solving and computation. A…

Presented are four interpretive reports and a list of current publications of the Mathematics Work Group at the Wisconsin R&D Center. The first interpretive report gives a brief overview of their work. Reports two through four are concerned with individual interviews, carried out during a longitudinal study, in which primary children are asked to…

Thirteen research reports related to mathematics education are abstracted and critiqued in this publication. The topics of the research include counting, addition, subtraction, ratio, proportion, geometry, problem solving, and teaching strategies. Also included is an editorial comment by T. Kieren on mathematics education research. Research…

To ascertain if children's use of manipulatives and/or the teacher's presentation of the problem in parts (chunking) affect children's ability to model and/or solve addition and/or subtraction problems, 146 first-grade subjects were administered the Houston Addition and Subtraction Problem-Solving Test which provided accuracy and modeling scores…

This paper notes three objections to the use of hand-held calculators in schools: they would (1) block reasoning, (2) make individuals machine-dependent, and (3) broaden the gap between developed and underdeveloped nations. Each is addressed, with specific examples used to refute them. The belief is strongly expressed that calculators can aid in…

The need to promote mathematical creativity and suggestions for developing it are discussed in this document. The largest portion of this document consists of a collection of problem sheets, arranged according to 26 content areas. Puzzles, activities, and a variety of problems are included, with an answer key. An annotated bibliography of selected…

The material in this reprint, with minor editorial changes, is from the chapter "Doing the Impossible" in MONKEY BUSINESS by Irving Adler. This 25-page booklet contains brief accounts of historical attempts to prove impossible problems in mathematics. The mathematical recreations in this booklet of geometric constructions include the trisection…

A study was undertaken of the effects of formal education and conservation of numerousness on addition and subtraction problem types. Thirty-six kindergarten and 36 first-grade subjects randomly selected from one area of a school district were administered measures of conservation, problem-solving success, and modeling ability. Following factor…

Several activities are described for students at different elementary grade levels. Some involve estimation of quantities, and others include reasoning about permutations and combinations. (SD)

Three models are compared in terms of detail, scope, attention to individual differences, and how they deal with qualitative change and semantic processing. Two are information-processing models of arithmetical word problem-solving performance, and the third is a model of children's counting types and thinking strategies. (MNS)

Factorials are discussed, with note of the enormous size on n! even for modest values of n. A recreational problem to determine the number of zeros at the end of numbers such as 10,000! is given, with a computer program. (MNS)

In this paper we report on a case study of a university student (third year of Mathematics course). She was engaged in proving a statement of elementary number theory. We asked her to write the thoughts that accompanied her solving process. She was collaborative and her protocol is suitable to study the interrelation between affect and cognition.…

The materials and ideas in this document are intended to be used by teachers in schools in order to bring adults and children together to experience good mathematics. It features an evening of hands-on mathematics scheduled for one night a week for four weeks. Students and adults come together to share mathematics activities, solve problems, and…

The materials and ideas in this document are intended to be used by teachers in schools in order to bring adults and children together to experience good mathematics. It features an evening of hands-on mathematics scheduled for one night a week for four weeks. Students and adults come together to share mathematics activities, solve problems, and…

Multibase arithmetic blocks are used to investigate the minimum number of blocks of each size to make a square of a given size in a given base. Generalizations are made to any size and any base through pattern recognition. The problem is extended to rectangles, cubes, and rectangular solids. (LS)