A procedure is described that enables students to perform operations on fractions with a calculator, expressing the answer as a fraction. Patterns using paper-and-pencil procedures for each operation with fractions are presented. A microcomputer software program illustrates how the answer can be found using integer values of the numerators and…

Assessment data and other research findings on fractions are briefly reviewed. These indicate that students are able to add and subtract fractions but have substantial difficulty finding and using common denominators. Selected results for nine-year-olds from the first and second national assessments of mathematics are used to portray what students…

The major portion of the article establishes the basis for the stated rule - to divide by a fraction, turn it upside down and multiply. With this background, three justifications for the rule are given. Several possible errors in students' use of the rule are noted. (LS)

A discussion of early Egyptian hieroglyphic numeration and calculation is presented. (SD)

This speech was prepared for the National Conference on Metrication which was planned for April 1977 (but cancelled). In it the author observes that it is necessary to be clear about which of the several versions of the metric system is being adopted. He cites the relationship between the metric system and decimal numeration, and calls to task…

This study was conducted to address two questions: (1) are deficiencies in fraction skills due to current instructional programs, and, if yes, (2) should instruction on fractions be postponed until secondary school or should instruction at the elementary levels be revised? A battery of fraction tests consisting of 78 items was developed; tests…

This is part two of a two-part SMSG elementary school text for third-grade students. The development of mathematical ideas in the text is grounded in appropriate experiences with things from the physical world and the immediate environment. Chapter topics include: (1) addition and subtraction; (2) length and area; (3) multiplication; (4)…

The purpose of this study was two-fold: (1) to investigate the effects of a new approach for teaching decimals by comparing it with two other commonly used methods with respect to achievement and retention of computational ability in decimals, and (2) to determine those areas of the new approach which seemed to be in need of revision. The study…

Described are the advantages of using the metric system over the English system. The most common units of both systems are listed and compared. Pictures are used to exhibit use of the metric system in connection with giving prices or sizes of common items. Several examples provide computations of area, total weight of several objects, and volume;…

The purpose of this study was: (a) to develop a learning hierarchy for rational number subtraction using intraconcept analysis, and (b) to validate that hierarchy using the Walbesser technique and pattern analysis. Skills required to complete tasks within the hierarchy were operationally defined and ordered from both a mathematical and…

Provided is an introduction to the properties of continued fractions for the intellectually curious high school student. Among the topics included are (1) Expansion of Rational Numbers into Simple Continued Fractions, (2) Convergents, (3) Continued Fractions and Linear Diophantine Equations of the Type am + bn = c, (4) Continued Fractions and…

This is one of a series of units intended for both preservice and inservice elementary school teachers to satisfy a need for materials on "new mathematics" programs which (1) are readable on a self basis or with minimal instruction, (2) show the pedagogical objectives and uses of such mathematical structural ideas as the field axioms,…

Implications of the change to the metric system in our daily lives are discussed. Advantages of the metric system are presented, especially its decimal base and ease of calculation which are demonstrated by several worked examples. Some further sources of information are listed. A world map indicates the few remaining countries that have not yet…

The teacher's guide for the fifth unit of this SMSG series covers the two chapters on equations and inequalities and on decimals. The overall purpose for each of the chapters is described, the prerequisite knowledge needed by students is specified, the mathematical development of each chapter is detailed, behavioral objectives are stated, and a…