The purpose of this article is to suggest ways of using research on children's reasoning and learning to elaborate on existing national standards and to improve large-scale and classroom assessments. The authors suggest that "learning progressions"--descriptions of successively more sophisticated ways of reasoning within a content domain based on…

More than a decade has passed since Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) and Professional Standards for Teaching Mathematics (NCTM 1991) were published, and the question of whether students' learning of mathematics has improved during that time has frequently been asked. Scores on the mathematics assessment of the…

This document presents activities for use by middle school teachers which show how rational numbers and proportions are present in many real-world situations, including the collection and analysis of fractions, ratios, percents, and proportions, as well as rational number connections with geometry and similarity. The activities are divided into…

A lesson plan for first-grade children beginning to learn English describes an activity using manipulatives and visual aids to develop recognition of three geometric shapes (circle, square, rectangle), their names, and a few additional words in English (e.g., "bag,""table,""door"). Students are grouped at tables of four to six and provided with…

A software tool called 3D-LAB has been developed for learning and teaching three-dimensional geometry. With this microworld, educators and students can display three dimensional solid objects, rotate them, modify them, open them up, draw points and segments, and measure lengths, areas, volumes, and angles. The major characteristics of this tool…

Geometer's Sketchpad is an interactive geometry software package used to help students learn geometry principles. Use of Sketchpad in a secondary education math course at the State University of New York (SUNY) at Oswego has allowed geometry to be taught in a dynamic manner. The paper provides three examples of how Sketchpad is used. Traditional…

This document offers instructional materials for a 60-hour course on math operations involving decimals, fractions, proportions, statistics, probability, measurement, geometry, and linear algebra as applied in the workplace. The course was part of a workplace literacy project developed by Mercer County Community College (New Jersey) and its…

The 13 leading mathematics educators who made up the task force that prepared this report were thoroughly acquainted with every major report on math education produced within the last decade. They were also thoroughly acquainted with the realities of instruction in the K-12 classrooms. Their aim, therefore, was to make appropriate compromises…

The purpose of this report is twofold. The first is to deliver an accurate portrayal of students' achievement in geometry and measurement as gleaned from the results of the 1986 Massachusetts Educational Assessment Program (MEAP). The second is to provide K-12 teachers of mathematics with activities that have proven to be helpful in encouraging…

A collection of word problems for fifth and sixth grade students are presented. The problems, which are divided into four sections and which get progressively more difficult in each section, include: (1) 38 problems on ratio and proportion; (2) 40 multistep problems (problems which require more than one calculation); (3) 40 problems on geometry…

During the Spring of 1989, the North Carolina Department of Public Instruction field-tested a geometry proof performance assessment as a component of the High School End-of-Course Testing Program (EoC). The existing geometry EoC test consisted only of multiple-choice items. The performance assessment was added to the multiple-choice component to…

Findings of a 1989 research study on LOGO-based instruction for teaching abstract concepts of geometry are reported in an effort to encourage mathematics teachers to use the LOGO language in computer-assisted instruction. Thirty-three ninth graders (19 males and 14 females) (6 white students and 27 black students) were involved in the controlled…

Since 1982, the National Council of Teachers of Mathematics has published a student periodical five times a year. Each four-page issue focuses on a single theme, developing it from a simple opening-page activity through more challenging extensions at a higher level of understanding. In this document each four-page issue published from September,…

This collection of learning activities is intended for use in reinforcing mathematics instruction as it relates to mechanical repair. Fifty activity sheets are provided. These are organized into units on the following topics: numeration, adding whole numbers, subtracting whole numbers, multiplying whole numbers, dividing whole numbers, factoring,…

This study was conducted to determine whether young children, given the experience of Logo programming, would acquire problem-solving skills and be able to transfer those skills to other areas. The study also investigated Logo's effectiveness in teaching certain fundamental geometric concepts to children who were supposedly not developmentally…