We examine the long term history of the development of fundamental representational infrastructures such as writing and algebra, and how they were physically implemented via such devices as the printing press and computers, in order to (1) gain insight into what is occurring today both in terms of representational infrastructure change and in…

Small-group cooperative learning provides an alternative to both traditional whole-class expository instruction and individual instruction systems. The procedures described in this volume are realistic, practical strategies for using small groups in mathematics teaching and learning with methods applicable to all age levels, curriculum levels, and…

This packet contains 29 lesson plans for integrated academic and vocational education courses. Lesson plans for the following courses are included: algebra, health occupations education, English, biology, laboratory mathematics, and health care sciences. Some of the topics covered are as follows: statistics, vital signs, graphing, ethics, special…

MathView is a computer algebra system designed to foster interactive exploration of mathematics. MathView is designed so that mathematics, both symbolic and graphic, is highly interactive. Change to a proposition in a MathView notebook produces a cascade of changes to the conclusions that are tied to the proposition. This structure helps to create…

This paper reviews an approach for finding optimal solutions to the traveling salesman problem, a well-known problem in combinational optimization, and describes implementing the approach using the MAPLE computer algebra system. The method employed in this approach to the problem is similar to the way ant colonies manage to establish shortest…

The purpose of this study was to evaluate the effects of manipulatives on student achievement in a high school Algebra I class. The study was conducted during the third nine weeks grading period in the spring of 1997 at a high school in Lewisburg, West Virginia. The study groups used in the study were two Algebra I classes. One class had an…

Describes a method for teaching Euler's line, the co-linearity of the circumcenter, centroid, and orthocenter of a triangle. Discusses teaching results. (KHR)

A study investigated the effects of an instructional strategy within a graduated teaching sequence on the representation and solution of problem-solving skills encompassing integer numbers for six secondary students with learning disabilities. Results indicate problem-solving skills dramatically improved following instruction at the concrete,…

As almost every state revises its mathematics frameworks or develops new ones, current testing practices remain almost unchanged. The National Council of Teachers of Mathematics (NCTM), in its "Professional Standards for Teaching Mathematics," argues for greater emphasis on application, reasoning, and conceptual understanding, but the…

Evidence is presented from an ethnographic study of an eighth grade pre-algebra teacher's classroom in support of the idea that teachers' beliefs about the ontology and epistemology of math profoundly influence how they teach and thus what students learn. Specifically, beliefs based on a traditional view of mathematics as procedurally-based are…

This paper introduces a multi-dimensional, multi-level framework for analyzing students' social interaction and individual action during collaborative problem solving. Crossing the dimensions of problem knowledge distribution and degree of cooperation yields six possible social interactions: piecemeal guessing, joint construction, lecture,…

The generic workplace curricula in this document were developed in a workplace education project conducted in Pima County, Arizona, which served 524 workers (58 percent from minority groups) at 14 worksites. Generic curriculum and competencies were developed for each subject area rather than each specific worksite. Of 374 workers who completed the…

This module for a 1-semester Total Quality Management (TQM) course for high school or community college students contains a brief overview of problem solving and offers a practical approach along with some of the tools that can be used. The following components are included: (1) narrative of the problem-solving process; (2) the problem-solving…

Today's technology gives us a great opportunity to complement the subtlety of human thought with the power and accuracy of modern computers. In this presentation I consider fundamental modes of human thinking to see how enactive, visual and symbolic methods can be used in a versatile way with the support of well-designed software. My analysis…

The purpose of this revised syllabus/guide is to help teachers and administrators plan and implement Course I in the State of New York Three-Year Sequence for High School Mathematics for Regents credit. Course I builds upon the State mathematics curriculum outlined in the Department's mathematics K-6, Grade 7, and Grade 8 publications. This guide…