Considered is a conceptual analog of buggy algorithms and rule-based mathematical development. The investigations consider whether children's efforts to make conceptual sense of new mathematics instruction in terms of their available knowledge may sometimes lead them to make systematic errors. In particular, the possibility is explored that…

The ideas and techniques involved in learning about fractions were investigated with students in grades 1-12, in the first 3 years of colleges, in community college mathematics courses, and in graduate school. Also included were some high school mathematics teachers, some mathematicians, and some retired persons. Part I provides the rationale and…

Eight sixth-grade students received individualized instruction on the addition and subtraction of fractions in a one-to-one setting for 6 weeks. Instruction was specifically designed to build upon the student's prior knowledge of fractions. It was determined that all students possessed a rich store of prior knowledge about parts of wholes in real…

Four papers are presented which view research in mathematics education from different perspectives. The titles are: (1) Review of Recent Research Related to the Concepts of Fractions and of Ratio; (2) Some Trends in Research and the Acquisition and Use of Space and Geometry Concepts; (3) A Portrayal of Traditional Teachers of Mathematics in…

This document lists references on the teaching of fractions, with many of the entries annotated. They are alphabetized by the author by categories: Activity and Game; Addition and Subtraction; Teaching Aids; Application; Assessment; Curriculum; Decimal; Common Fraction; Division; Equivalence of Fractions; Errors; Fraction Concept; Multiplication;…

This collection of reprints from the IDEAS section of the "Arithmetic Teacher," has been selected from those activities appropriate for students in grades 4 through 8. The selections have been reprinted just as they originally appeared in the journal. The ideas are grouped under the headings computation, fractions, problem solving, geometry, and…

Presented are student performance objectives, a student progress chart, and assignment sheets with objective and diagnostic measures for the stated performance objectives in College Algebra II. Topics covered include: differencing and complements; real numbers; factoring; fractions; linear equations; exponents and radicals; complex numbers,…

This is one in a series of manuals for teachers using SMSG high school supplementary materials. The pamphlet includes commentaries on the sections of the student's booklet, answers to the exercises, and sample test questions. Topics covered include factors and primes, perfect numbers, divisibility, expanded notation, repeating decimals, number…

This is part two of a two-part SMSG elementary school text for sixth-grade students. The content is aimed at the development of some of the fundamental concepts of mathematics such as number, numeration, the operations of arithmetic, and intuitive geometry. Chapter topics include division of rational numbers, volume, organizing and describing…

This is a supplementary manual for teachers using SMSG junior high school text materials. A chapter-by-chapter commentary on the text is given as well as answers to all the exercises. Chapter topics include: (1) sets; (2) projective geometry; (3) repeating decimals; (4) tests for divisibility; (5) finite differences; and (6) prime numbers. (MP)

This text is one of the sequence of textbooks produced for low achievers in the seventh and eighth grades by the School Mathematics Study Group (SMSG). There are eight texts in the sequence, of which this is the fifth. This set of volumes differs from the regular editions of SMSG junior high school texts in that very little reading is required.…

The workbook is intended to help the vocational high school student understand and gain competence in working with fractions. The exercises provide practice in reducing and changing fractions, multiplying, dividing, finding a least common denominator and equivalent fractions, adding and subtracting. The types of fractions are also defined. Quizzes…

THis is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this volume concern use of decimals and are related to the…

The sixteen chapters of this book provide the core material for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functional-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…

This booklet is one of the ten in the series "Experiences in Mathematical Discovery", produced by the General Mathematics Writing Project of the NCTM. Each is designed for use by students of ninth-grade general mathematics. The discussion and problems are designed to guide the student through an understanding of: 1) fractions, 2) equivalent…