Methods for generating rational equations and some generalizations that can be used when writing classroom examples or test items are given. (MNS)

Suggests that algebra, geometry, and recent history can be combined in lessons pertaining to an ongoing, relevant controversy related to paper sizes. Early paper sizes, International Standards Organization (ISO) paper sizes, the "golden rectangle," and paper sizes in the United States are discussed. (JN)

Illustrated is how students can be directed to move from a geometric to an algebraic mode of thought and back again in linear algebra, thereby deepening their understanding. Rotations and line reflections in the plane are used as the example. (MNS)

An example is given of the discovery method of instruction applied in a remedial college algebra course. (DT)

This article investigates the transformations which result when all variables and constants in given functions are allowed to be complex numbers. (DT)

A method for changing repeating decimals to fractions is explained. (DT)

This book is designed to help teachers understand children's intuitive problem solving and computational processes and to figure out how to use that knowledge to enhance students' understanding of arithmetic. This book provides numerous examples of classroom dialogues that indicate how algebraic ideas emerge in children's thinking and what…

GED "Scoreboost" materials target exactly the skills one needs to pass the General Educational Development (GED) tests. This book focuses on the GED Mathematics test. To prepare for the test, the test taker needs to learn skills in number and operation sense, data and statistics, geometry and measurement, and algebra. To pass the test,…

We present two vignettes of classroom episodes that exemplify new activity structures for introducing core algebra ideas such as linear functions, slope as rate and parametric variation within a new educational technology environment that combines two kinds of classroom technology affordances, one based in dynamic representation and the other…

This paper presents the conceptualisation of infinity as a multi-faceted concept, discussing two examples. The first is from history and illustrates the work of Euler, when using infinity in an algebraic context. The second sketches an activity in a school context, namely students who approach the definite integral with symbolic-graphic…

This paper uses two terms, "algorithmic mathematics" and "dialectic mathematics," and attempts to synthesize the two aspects from a pedagogical viewpoint with illustrative examples gleaned from mathematical developments in Eastern and Western cultures throughout history. Some examples from teaching experiences in the classroom…

Symbols occupy a pivotal position between processes to be carried out and concepts to be thought about. They allow us both to do mathematical problems and to think about mathematical relationships. In this presentation, the discontinuities that occur in the learning path taken by different students, leading to a divergence between conceptual and…

The Purposeful Algebraic Activity Project is concerned with the development of algebraic activity in pupils in the early years of secondary schooling. Here we report on the different ways in which we have observed children articulating generalisations during semi-structured interviews which are being used to gain snap-shots of this development. We…

This study analyzed the criteria used in Harrison County, WV, to select students to participate in an accelerated mathematics program. The program's main component is an eighth grade Algebra I course that enables the students to complete five years of college preparatory mathematics, ending with calculus. The scores used as selection criteria,…

The recent call for "algebra for all" provided not only the impetus for teaching elementary students differently, but also for changing the way teachers are trained. University mathematics courses for pre-service teachers have undergone changes, and professional development sessions for in-service teachers have been created. The Mid-continent…