Illustrates the multiple strategies used by second graders to solve a problem with three addends and how their teacher tries to map their thinking into the system of mathematical notation. Describes the American Federation of Teachers' Thinking Mathematics program that the teacher uses. (MKR)

To determine how middle school students cope with the demands of arithmetic word problems, 140 eighth graders (67 males and 73 females) had to solve problems modeled after those of the National Assessment of Educational Progress. Extraneous information and extra steps reduce the accuracy of students' word problem solutions. (SLD)

Presented is a proof where special attention is accorded to rigor and detail in proving the lemma that relates ruler-and-compass constructions to arithmetical operations. The idea that some angles cannot be trisected by a ruler and compass is proved using three different cases. (KR)

Investigates the relative contribution of two main components often used in the instruction of arithmetic and word-problem solving to first-grade children and children with learning problems: external representation with manipulatives and formal mathematical representation with number sequences. Four computer-aided treatments were developed along…

This is the second of two papers that propose an expanded and enriched view of arithmetic problem solving by stressing the need to provide learning activities that include problems of varying structures. The first paper included a framework for the enhancement of text-based problems. This second paper proposes a scheme for the development of…

Computer operations involving complex numbers, essential in such applications as Fourier transforms or image processing, are normally performed in a "divide-and-conquer" approach dealing separately with real and imaginary parts. A number of proposals have treated complex numbers as a single unit but all have foundered on the problem of the…

The author recently read a research paper by Padberg (2002), in which the development of understanding associated with decimal fractions was studied. Padberg (2002) outlined the situation that existed in Germany, where students were introduced to decimal fractions in the sixth year of school. He claimed that it was assumed students would have a…

Usiskin takes another look at fractions, years after writing the article "The Future of Fractions" for "Arithmetic Teacher".

This booklet is a collection of 45 problems that have appeared in the Problem Department of the journal "School Science and Mathematics." The booklet is divided into four parts. The first part presents 20 cryptarithms, puzzles in which letters or symbols are substituted for the digits in an arithmetical calculation, that require knowledge of…

To determine how children cope with some of the demands imposed on them by arithmetic word problems, 200 sixth-graders were asked to solve prolems modeled after those used by the National Assessment of Educational Progress. A quantitative demand was imposed on the children by adding extraneous information to the problems, and a verbal demand was…

This study examined differential performances among groups (categories) of first grade children when solving eight different types of arithmetical word problems under two distinct experimental conditions. The categories of children were actually 4 ability groups: (1) low quantitative comparison scores and low IQ (Lorge-Thorndike IQ Test), (2) low…

The contemporary mathematics program set forth in this publication developed as a result of experimentation and evaluation in classroom situations. This is Part 2 of "Mathematics: 8th Year." Part 1, a separate bulletin, was published during the school year 1967-68. The materials in this bulletin are intended to serve as guidelines for…

Three diagnostic questions are presented and discussed to help locate a child's difficulty in problem solving. (JT)

The authors describe a series of magic tricks based on computation which they use in elementary and secondary school mathematics classes to motivate and challenge students. (SD)

Discusses procedures used throughout history to solve fractional and decimal divisor problems. Early rules and definitions, approaches in mathematics and methods books, "new math" approaches, research findings, and recent textbook procedures are included. Concludes by presenting nine recommendations for teaching the operation. (DH)