This paper, one of a series considering eight disciplines, describes historical developments and current thinking in mathematics concerning what ought to be included in the elementary school mathematics curriculum. The first part of this paper is devoted to a discussion of the previous involvement of mathematicians in curriculum reform projects.…

This unit is designed to help middle school students care for a real or imaginary horse while they review basic mathematics skills. Sections in this unit include: (1) "Statistics of Your Horse"; (2) "A Home for Your Horse"; (3) "Feeding Your Horse"; (4) "Equipping Your Horse"; (5) "Showing at Halter"; (6) "Working Hunter"; (7) "Open Jumping"; (8)…

Assuming guided inquiry as a pedagogical ideal in mathematics education implies that teaching must connect students' thinking about a subject with curricular agendas and instructional goals. Because students are not typically inclined to consider their active inquiry as a route to acquiring the knowledge that is valued in school, such teaching…

This material assumes the user has the background provided by a good undergraduate course in applied probability. It is felt that introductory courses in calculus, linear algebra, and perhaps some differential equations should provide the requisite experience and proficiency with mathematical concepts, notation, and argument. The document is…

This document deals with basic statistical concepts and operations used in the social sciences. The book was written under the philosophy that students enter statistics courses with a variety of aptitudes and experiences, and that traditional teaching approaches can do little to accommodate individual needs. It sets up an individualized course,…

This is the teacher's guide for Matematica 1, an introduction to numbers for Portuguese-speaking students. The teacher's guide contains corresponding material to the 15 chapters in the student's book. The guide also contains for each lesson suggestions for presentation, a statement of objectives, and instructions for evaluating student learning.…

This handbook was developed to help the vocational teacher aid students in solving mathematical problems in vocational education classes. Most of the examples in the handbook were derived from metal-working and industrial mechanics classes; however, the procedures explained through them will work in any vocational class. The handbook is divided…

This is the first unit of a 15-unit School Mathematics Study Group (SMSG) mathematics text for high school students. Topics presented in the first chapter (Structuring Space) include: lines and points; planes; intersections; intersections of lines and planes; betweenness and segments; separation; angles; locating positions and points; coordinates;…

The Comprehensive School Mathematics Program (CSMP) is described as a complete elementary mathematics curriculum that provides a natural place for probability and statistics. The CSMP approach of innovative, pictorial techniques is summarized here, with emphasis on methods and activities seen as proven successful through the enthusiastic reception…

This work studies the difficulties children have solving two-step word problems of a given structure (e.g., 7 lollypops/2 chocolate bars X 6 chocolate bars). Thirty-six children between the ages of 9 and 14 years were individually observed solving problems of the above type. Other tasks, repetition of the problem and model recognition, were used…

The effects of negative instances on the acquisition of the mathematical concepts of commutativity and associativity were examined. Also investigated were possible transfer effects that might result from the use of negative instances. For 64 ninth-grade subjects, results favored the treatments containing mixed instances and supported the transfer…

This article is a continuation of SE 514 442. The use of learning hierarchies in analyzing and planning changes in the teaching of mathematics is discussed. (SD)

Noting that ratios can be used to great advantage in scoring informal reading tests, such as the cloze procedure and the informal reading inventory, this paper explains the procedures for calculating cross-ratios and percentages when computing scores for informal reading assessments. Examples are provided for using ratios to determine scores for…

A group is viewed to be one of the simplest and most interesting algebraic structures. The theory of groups has been applied to many branches of mathematics as well as to crystallography, coding theory, quantum mechanics, and the physics of elementary particles. This material is designed to help the user: 1) understand what groups are and why they…