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…

The SCOPE Mathematics Achievement Test booklet for grade 4 presents 11 mathematical concepts with instructions for students to take the test with little or no teacher direction. Testing items are: writing number words to 100; giving the place value of any digit and using this to write in expanded form; finding a numeral between two given numerals…

This textbook aims to (1) train the pupil in that part of arithmetic used in everyday business which he can understand; (2) develop his skill in rapid calculation by short cuts and time tests; (3) show the necessity for checking, and develop the habit of checking; (4) develop the habit of thrift by planning budgets, keeping accounts, and becoming…

This document consists of two major sections. The first of these is actually three units that look at applications of arithmetic to business. Basic pre-algebra mathematics is an assumed prerequisite. These units are titled: 367-The Real Numbers; 368-Fractions and Their Uses: Ratio and Proportion; and 369-Exponents: Powers and Roots. Each module…

This study investigated a theoretical structure which attempts to explain the problem-solving strategies used by first-grade students who are successful in solving simple arithmetic story problems. The structure used describes the problem-solving procedure as consisting of a three-stage model building process: (1) comprehending the story, (2)…