A programing approach is described, using numerical methods to draw implicit functions, without solving the relationships explicitly. Several examples are discussed, with programs and printouts included. (MNS)

The need to incorporate deductive reasoning in the curriculum is noted. Guidelines for developing reasoning skills and activities to develop understanding of inductive and deductive processes are provided. (MNS)

Brief articles are included on creating in first-year algebra, making a Moebius hat, and graphing cubics. (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)

Reviews three programs produced by Edu-Ware Services: an introduction to spelling; an interactive guide to the essentials of the Basic language and computer operations in general; and the first of six volumes of tutorials, suitable for secondary/remedial-postsecondary mathematics, focusing on numbers versus numerals, line number, and sets/rules…

Described is a software program with two components. One is muMATH, a package of functions that can perform a wide variety of symbolic manipulations. It is surrounded by, and written in, the accompanying language, muSIMP. A problem is described with a muMATH solution; another example uses the muSIMP language. (MNS)

This paper analyses students' written work from an activity based on two well known games in the UK: Chinese Whispers and Consequences. Within this activity students were asked to translate formal algebraic equations into word statements and vice versa. Using the framework of affordances and constraints to offer an account for what the students'…

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.]

The broad goal of this report is to describe a form of knowing and a way of participating in mathematics learning that contribute to and further alternative views of transfer of learning. We selected an episode with an undergraduate student engaged in a number of different tasks involving a physical tool called "water wheel". The embodied…

Mathematical norms are important cultural knowledge of mathematical activities. This paper reports an analysis of mathematical norms in ten consecutive lessons taught by an eighth-grade Japanese teacher. The lessons were located in the unit of simultaneous linear equations. The videotapes of the lessons, their transcripts, and the interview data…

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…

The teaching and learning in algebra has been much debated. Traditionally early algebra has relied heavily on arithmetic. Recently our focus has changed to teaching algebraic thinking with arithmetic thinking. This paper explores the models that assist young students generalise the patterns of arithmetic compensation. A teaching experiment was…

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…

The purpose of this study was to determine the more appropriate strategy for improving eighth-grade portfolio entries. There was a comparison between two specific types of revising/correcting conferences, self-assessment and peer conferences. Most of the research concerning the writing process focuses on peer conferencing; however, it was…

This book contains an interactive calculator and worksheet program designed to teach the graphing of some of the functions that appear in high school mathematics courses. The graphs of linear, exponential, and logarithmic functions are explored as well as other functions. Activities focus on the graph that appears as a standard part of algebra…