The goal of this study was to describe characteristic stages in the development of children's understanding of place value. Sixty children (15 in each grade, 2 through 5) at 5 elementary schools in Butte County, California, were individually administered 18 tasks designed to reveal their thinking about place value and part-whole relations. On six…

Examined were the effects of varying the number of practice problems in a programed unit on negative bases designed for high school students. A sample of 421 students from grades 9 through 12 was divided into three groups on the basis of amount of mathematics coursework completed. Students were given four pretests (numeration, arithmetic…

Developed by a committee of the National Council of Teachers of Mathematics, this publication is designed to help teachers provide interesting and worthwhile learning opportunities for slow learners in grades five through eight. It employs a variety of teaching strategies, many not commonly known or practiced, which are particularly helpful with…

This is Part 1 of the first course in a series which focuses on building fundamental mathematical structures. The arithmetic studied in elementary school along with modular arithmetic is examined and set notation and mappings of sets are presented. Mathematical group structures are introduced. Points and numbers are related both on a line and in a…

This booklet has been written for elementary school teachers as an introductory survey of the real number system. The topics which are developed include the number line, infinite decimals, density, rational numbers, repeating decimals, irrational numbers, approximation, and operations on the real numbers. (RS)

The third student text in this SMSG series of 14 covers the following topics from number theory: the division algorithm, divisibility, prime numbers, prime factorization, common divisors and common multiples, and properties of the whole number system. A second chapter discusses properties and operations with integers. For a special edition of this…

The early use of the distributive law can aid students in learning addition of fractions and provide rapid approaches to computation involving other operations. (SD)

Described is mathematics used by the ancient Babylonians and recorded on tablets which have been dated 3000-2000 B.C., and 700-500 B.C. (SD)

An instructional sequence in which number lines and beads are used to illustrate addition and subtraction of directed numbers is described. (SD)

In a thesis written for the Doctor of Arts in Mathematics, the connection between Euclid's algorithm and continued fractions is developed and extended to n dimensions. Applications to computer sciences are noted. (SD)

Examines the factors influencing the use of a plan by four- and five-year-old children to judge the relative number of two sets by one-to-one correspodence. Results suggest that most children have one-to-one plans in long-term memory by age four. (Author/RWB)

Describes various aids and activities to help in planning lessons that will encourage the development of sound place value knowledge. Also discusses various instructional strategies to help students avoid problems which may lead to an incomplete or faulty understanding of place value. (JN)

An explanation is given for the development of the Roman numeral system in terms of the smallest number of marks required to enumerate items. (RM)

Arithmetic reading can be made lighter if teacher explains vocabulary, selects simple text, and aids in improving reading skills. (DS)