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…

This book presents motivational ways to teach key concepts and topics common to all secondary mathematics curricula. It is arranged by subject matter which includes algebra, geometry, trigonometry, probability, statistics, and miscellaneous topics. The objective to be attained by implementing the unit on each of these subjects is stated, and the…

As part of the Electrical Engineering program at the Univesity of Southern Maine, students are typically introduced to Two's Complement algebra and representation, a method to include negative numbers in the binary representation of integers that is widely used in microprocessors and related digital systems. The traditional, procedural method to…

This paper asserts that the key to algebra reform is to integrate algebraic reasoning across all grades and all topics, to "algebrafy" school mathematics. The distinction is made between algebra "the institution" and algebra "the web of knowledge and skill," which is also clarified. Finally, suggestions are made as to how the educational community…

This book contains a set of versatile enrichment exercises that cover a very broad range of mathematical topics and applications in pre-algebra from the Moebius strip to the googol. Several criteria have been used in developing the activities and selecting the topics that are included. All of them bear heavily and equally on concerns for…

This textbook furnishes abundant material for an intelligent review of the mathematics given in a large number of high schools, and it is the hope of the authors that other teachers may find the book useful in the hands of their pupils. The first-year review is intended to cover the work ordinarily done in the first-year mathematics course of the…

Discusses terminology used by teachers for the symbol "-x" which cause students to become confused. Suggested methods of avoiding this confusion are presented. (JP)

Grade nine students (n=116) were assigned to five different algebra word problem test versions: textbook, student, pictorial, textbook plus pictorial, and student plus pictorial versions. Analysis by IQ levels yielded results different from those obtained in previous studies. (JP)