Numerous studies indicate that performance in solving single step multiplicative word problems is influenced by both problem structure and the types of numbers involved in the problem. For example, including numbers less than one often increases the difficulty of a problem. What remains unclear is how problem structure and number type interact in…

Suggested are investigations for junior and senior high school students that may lead to discoveries and at the same time provide a variety of practice in computing with fractions. (JP)

This book emphasizes the importance of teaching mathematics in a meaningful way. It is designed for elementary school teachers who are interested in why and how certain mathematical concepts and skills work. Topics discussed include: numbers and numerals; sets and sentences; the teaching of addition, subtraction, multiplication and division in the…

To investigate the efficacy of a training procedure designed to facilitate the attainment of the mathematical concept of number conservation, 43 children from grades 1 and 2 were tested for their ability to conserve. Some of the pupils were found to be nonconservers; some, transitional conservers; and some, conservers. Pupils of the first two…

This study investigates effects of different instructional methods on positional numeration systems. It involved prospective elementary teachers and assessed (1) understanding, (2) performance, and (3) transference of numeration concepts. The effects were measured by the Test On Numeration Systems (TONS). During each of two semesters, three…

Analyzes the concept "growth" by investigating the logic core of the concept, using systems theory, and testing it employing free definitions. Determines the associative framework using free association tests. Shows that a shift takes place in the logic core and in the associative framework from a growth in terms of geometric dimension towards a…

A framework for organizing instruction on the basic facts is presented. Guidelines are given for blending work with concrete materials, thinking strategies, and drill into a meaningful program. (MN)

The use of counting sticks as a concrete manipulative material in the development of number understanding and the concept of place value is strongly urged. (JT)

In response to an earlier article advocating the elimination of fractions from the curriculum, the author argues for their retention. He points out examples of their use in music and physic, and discusses methods of presenting operations on fractions. (SD)

Ways to combine the strengths of teacher and computer are suggested. Multiplication concepts and an algorithm for multiplication are taught in the same lessons. The computer is used as an electronic chalkboard to teach at a semiconcrete level. The computer program is included. (MNS)

A modern adaptation of the historic lattice algorithm which can be used for multiplication and division is discussed. How it works is clearly illustrated. (MNS)

Establishing and maintaining the desirable kind of balance between meaning and computational competence is the subject of this reprint from a 1956 issue of the journal. Sources of the dilemma and suggestions for solution are discussed. (MNS)

Included in this section are brief articles on an algebraic puzzler, periodic decimal fractions with computers, and the arrow method of teaching logarithms. (MNS)

Questions about teaching rational numbers are discussed, dealing with when to teach the meaning of fractions and of decimals, when and how to teach computation with fractions and with decimals, and other issues. (MNS)