These 14 research reports are grouped into three broad categories based on the Piagetian level concerned. The articles concerning preoperational concepts focus on problems such as: (1) finding an appropriate mathematical description of some of the primitive mathematical concepts; (2) the role of "activities" in early concept acquisition;…

This study examines the extent to which modeling facilitates transformational problem solving in mathematics for children in kindergarten and first grade. Subjects were 20 children selected from each level. They responded to two problems for each of four problem types (counting on, story problems, quantitative comparisons, and ordination) under…

This paper describes preliminary results of a study designed to explore the issue of translating geometric ideas from a diagrammatic mode to a verbal statement, and vice versa. The research model calls for comparisons of responses under 16 different conditions; these conditions are defined by question type and the nature of the translation to be…

The Minnesota School Mathematics and Science Teaching (MINNEMAST) Project is characterized by its emphasis on the coordination of mathematics and science in the elementary school curriculum. Units are planned to provide children with activities in which they learn various concepts from both subject areas. Each subject is used to support and…

A model and a computer program for performing conjoint measurement is developed. (AG)

The observations of a fifth-grade student concerning number patterns are recorded and discussed. (SD)

The project described in this article grew from the observation that many geometry students are unable to see anything in a diagram beyond a static presentation. A computerized microworld called "Motions" is described, with illustrations. (MNS)

Cut-and-try techniques that point to appropriate transformations of variables and to the selection of sets of variables for an equation that may improve understanding of a social process are illustrated. (MV)

Presents computer programs (Applesoft Basic) for: (1) 2-D rotation about any point through any angle; (2) matrix transformation for 2-D rotation; (3) 3-D translation; (4) 3-D rotation; and (5) hyperboloid rotated in 2-D space. Includes background information and sample output for the matrix transformation subroutines. (JN)

Beginning with a set of design cards and a rectangular grid, students can generate interesting and colorful designs using rotations, reflections, and translations. (SD)

Discussed is an application of number theory to cryptology that can be used with secondary school students. Background on the topics is given first, followed by an explanation for use of the topic. (MNS)

Describes a transformational geometry project in which groups of students explore symmetry, reflections, translations, rotations, and dilations to design and create one hole of miniature golf large enough to play on. Includes unit plan for transformational geometry. (MKR)

Discussed are several different transformations based on the generation of fractals including self-similar designs, the chaos game, the koch curve, and the Sierpinski Triangle. Three computer programs which illustrate these concepts are provided. (CW)

Function Probe is a multi-representational software for Apple Macintosh computers. It was designed to allow students to approach problems in different ways and/or use different representations. This case study describes a 16-year-old student as he creates a path among a variety of representations of transformations of functions while using the…