Discourse analysis usually focuses on oral discourse, what people say within a classroom setting. The goal of this study was to show that methodologies that would normally be used in English/language arts classes could also be used in mathematics classes. In this case study, the basic methods of discourse analysis are used to examine adolescents'…

"Two and Two Make Zero" considers children's acquisition of numerical concepts from a wide range of perspectives including topics that are often overlooked, most notably: the principal properties of the counting numbers in and of themselves; the role that numerical symbols play in number acquisition; the underlying conceptual structure of number…

In many ways, algebra can be as challenging for teachers as it is for students. With so much emphasis placed on procedural knowledge and the manipulations of variables and symbols, it can be easy to lose sight of the key ideas that underlie algebraic thinking and the relevance algebra has to the real world. In the The Xs and Whys of Algebra: Key…

This book examines the five key elements (meaningful use of symbols, mindful manipulation, reasoned solving, connection algebra with geometry, and linking expressions and functions) identified in "Focus in High School Mathematics: Reasoning and Sense Making" in more detail and elaborates on the associated reasoning habits. This volume is one of a…

This book is for people with an interest in algebra whether as a learner, or as a teacher, or perhaps as both. It is concerned with the "big ideas" of algebra and what it is to understand the process of thinking algebraically. The book has been structured according to a number of pedagogic principles that are exposed and discussed along the way,…

In this paper, Piaget's theory is analyzed using Locke's philosophy. The first part, "Mental Experiences," describes the author's view (with a tentative interpretation of Piaget's position) of reflection, abstraction, re-presentation, and the use of symbols. The second part, "Piaget's Theory of Abstraction," has four sections:…

A glyph--short for hieroglyphic--is a form of picture writing that conveys information. This book uses 10 glyphs to teach math concepts that are linked to the new NCTM Standards. There are four key parts to each glyph: (1) a legend (or survey questions); (2) directions for the teacher that tell students what to draw, color, or write based on…

Practical examples from everyday life, spanning personal financial matters to traveling and even cooking conversions are the lessons offered in this useful guide. The vast majority of older students and adults who come to America come from countries that use the metric system. Learning a new system for measuring, telling time, and so forth is…

Algebra is no longer just for college-bound students. After a widespread push by the National Council of Teachers of Mathematics (NCTM) and teachers across the country, algebra is now a required part of most curricula. However, students' standardized test scores are not at the level they should be. NCTM's seventieth yearbook takes a look at the…

Research Ideas for the Classroom is a three-volume series of research interpretations for early childhood, middle grades, and high school mathematics classrooms. Each volume looks at research from the perspective of the learner, the content, and the teacher, and chapters are co-authored by a researcher and a teacher. Chapter titles in the high…