This is the final test for students in the twelfth-grade course Mathematics 30, offered in schools in Alberta, Canada. It contains 52 multiple-choice questions and five written-response problems, with two-and-one-half hours allowed for completion. Approved calculators may be used. Scoring is done by the provincial education department. (RH)

The theme of the sixth annual meeting of the North American Chapter of Psychology of Mathematics Education was "The Importance of Psychological Models for Research in Mathematics Learning." The conference proceedings contain papers organized around five major topics. In the first section, eight papers on the learning of arithmetic are…

This course is designed to review the arithmetic skills used by many Marines in the daily pursuance of their duties. It consists of six study units: (1) number systems and operations; (2) fractions and percents; (3) introduction to algebra; (4) units of measurement (considering both the metric and United States systems); (5) geometric forms; and…

Experiments by Russian educators on teaching algebra in elementary grades are summarized by the author. The algebra taught consisted of generalized solutions to concrete problems that are usually presented with fixed numerical values. (JP)

Problem solving approaches often find a path from the givens to the unknown or from the unknown to the givens. This study explores those approaches using written protocols of Navy subjects while solving for the numerical value of an unknown from several knowns and a system of equations. For a subset of the items, solutions require subjects to…

The English translations of the first six volumes of Studies on the Teaching and Learning of Mathematics in the Soviet Union are viewed in this document. The contents of each volume are briefly described: vol. 1, The Learning of Mathematical Concepts; vol. 2, The Structure of Mathematical Abilities; vol. 3, Problem Solving in Arithmetic and…

The material in this reprint, with minor editorial changes, is from the chapter "Doing the Impossible" in MONKEY BUSINESS by Irving Adler. This 25-page booklet contains brief accounts of historical attempts to prove impossible problems in mathematics. The mathematical recreations in this booklet of geometric constructions include the trisection…

Effects of strategy instructions on the problem-solving performance of junior high school algebra students was investigated in two experiments. In the first experiment, three groups of students were instructed to solve algebra problems using a backward, forward, or mixed directon of search. The pattern of solution times and errors indicated that…

Intended to be used in conjunction with a traditional curriculum, this book demonstrates the use of the computer, especially the on-line, interactive type of computer, to solve a variety of problems studied in secondary school mathematics. Each chapter presents several problems, and each problem introduces one or two concepts that must be…

A method is described for representing quadratic functions by three-dimensional wire models. This enables one to form a simple geometric concept of the location of imaginary zeros. (MNS)

Example of magic tricks that can be used as an integral part of various lessons in arithmetic and algebra are given. Their mathematical basis is also discussed. (MNS)

This paper discusses problems many tenth grade students have when asked to apply a familiar formula in an unfamiliar context: specifically factoring a compound expression. Some of their attempts at solution are presented and discussed in terms of structure sense. (Contains 1 table.) [For complete proceedings, see ED496848.]

This book offers ideas to enrich instruction and help teachers explore the intrinsic beauty of math. Through dozens of examples from arithmetic, algebra, geometry, and probability, the symmetries, patterns, processes, paradoxes, and surprises that have facilitated generations of great thinkers are revealed. Activities include: (1) The Beauty in…

Twelve linear algebra students were interviewed about the concept of a Solution of a System of Equations. The interviews were analyzed using APOS tools, in particular the ideas of Action, Process, Object and Schema, and Genetic Decomposition. The analysis of the interviews revealed several misconceptions of Solution. The analysis also revealed…

This 1998 yearbook aims to stimulate and answer questions that all educators of mathematics need to consider to adapt school mathematics for the 21st century. The papers included in this book cover a wide variety of topics, including student-invented algorithms, the assessment of such algorithms, algorithms from history and other cultures, ways…