The first document in this set is a final report titled "Preparation for the Mathematics GED Test: A Computer Based Program," which describes a project to develop a General Educational Development (GED) mathematics preparation program for the adult learner at the 9-12 grade level. The other two documents are a teacher's guide and a…

The aim of this study was to investigate and validate the use of a computerized testing program for the diagnosis of arithmetic difficulties experienced by primary school children. The basic research question was whether a microcomputer could be used to diagnose difficulties in addition, subtraction and multiplication as well as a paper-and-pencil…

A home-based Spanish literacy program for Spanish-speaking parents in Elgin, Illinois, which began as a project of the Elgin school district, is described. The program originated with a search for literacy instructional materials for this group. The curriculum was designed to focus on functional Spanish literacy and basic arithmetic skills, the…

This module is the second in a series of 12 learning modules designed to teach occupational mathematics. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are found at the end of the module. Specific topics covered include rounding off, precision of measurement, and the…

Open-ended individually administered questions can ascertain whether students can reason about arithmetic problems. Free response test items are useful in assessing students' thought processes as they solve mathematics story problems. Since story problems do not state explicitly which arithmetic operations are required for solution, students must…

An overview is first given of some main theoretical frameworks underlying current European research in mathematical thinking, learning, and teaching. Together with the information-processing and the (neo)-Piagetian approaches, both well known in the United States, two other research paradigms can be distinguished: the action-oriented approach to…

This handbook, and the VITAL Mathematics Series videotapes, contain 12 lessons that model effective use of active learning strategies in elementary mathematics instruction. The lessons are designed for preservice and inservice teacher development programs through courses or individual study. The videotapes that are available separately demonstrate…

This report describes an investigation in England of some of the problems children experience with fractions. In particular, the restricted view that some children have of fractions is investigated. The methodology involved a large number of interviews with secondary school children (aged 12-14). The results of these interviews led to the design…

The Utah System Approach to Individual Learning (U-SAIL) Mathematics System was developed to make it possible for teachers to provide excellence in arithmetic instruction. It is based on the premise that in order to teach arithmetic well, teachers must accurately assess, teach directly, provide students with focused practice, corrective feedback,…

The purpose of this study was to determine the effects of two types of teacher inservice education programs upon fourth-grade students' achievement in solving mathematics story problems. Participating teachers attended two types of teacher inservice education programs; a traditional program, and a brief, narrowly focused special program (2.5 hours…

Gagne proposed in his learning hierarchy model that a final task could not be performed by an individual who does not have the subordinate skills, and that any superordinate task involved in the hierarchy of skill building could be performed by an individual provided suitable instructions were given, and provided the relevant subordinate knowledge…

The "General Mathematics" series contains six modules intended to help students become more competent with basic mathematics. This module on fractions is designed to build or increase students' level of understanding and to help them develop those skills necessary to successfully understand and use basic fraction skills that are necessary for many…

This booklet is a catalog of error patterns found in basic arithmetic and algebra courses. It is intended to be used as a resource by instructors and tutors teaching these concepts. The material is divided into major concept headings with subheadings. The error patterns are named and given a brief general description followed by a specific example…

Children appear to interpret the "equals" sign as an operator ("adds up to") not a relational ("the same as") symbol--e.g., viewing equations like 13 = 7 + 6 or 8 = 8 as senseless. This study, a natural experiment, examined the effects of long-term instruction emphasizing a relational definition of "equals."…

This document presents an overview of legislation and actions resulting in the passing of Public Law 94-142, the Education for All Handicapped Children Act, and presents information of use to school personnel in mainstreaming. The document's first section traces the history of the treatment of handicapped individuals by society since the…