This article describes a multisensory method for teaching students how to multiply and divide as well as add and subtract integers. The author uses sidewalk chalk and the underlying concept of integers to physically and mentally engage students in understanding the concepts of integers, making connections, and developing computational fluency.…

Many students in U.S. schools have trouble understanding fractions and Algebra II, the one difficultly occurring at the end of elementary school, the other in high school. One reason is that schools generally focus on one aspect of mathematics--calculation--and often fail to address the second aspect--interpretation. Also responsible is the…

The aim of this study is to describe and analyze students' levels of understanding of exponents within the context of procedural and conceptual learning via the conceptual change and prototypes' theory. The study was conducted with 202 secondary school students with the use of a questionnaire and semi-structured interviews. The results suggest…

In the typical first-year mathematics course--whether it be calculus or a general education quantitative proficiency course--we struggle to help students see the relevance of mathematics to their own lives. Particularly in a focused course such as calculus, there is a danger that students see mathematics as an isolated subject, with applications…

Effective teaching should focus on representational change, which is fundamental to learning and education, rather than conceptual change, which involves transformation of theories in science rather than the gradual building of knowledge that occurs in students. This article addresses the question about how to develop more efficient strategies for…

This paper reports the mathematical generalizations of two groups of algebra students, one which focused primarily on quantitative relationships, and one which focused primarily on number patterns disconnected from quantities. Results indicate that instruction encouraging a focus on number patterns supported generalizations about patterns,…

This paper explores the public awareness that there presently exists a crisis in mathematics education and a "dumbing down" of the curriculum, examines the nature of this crisis and argues that there has been a lowering of cultural, pedagogical and cognitive expectations with respect to most learners. The notion of cognitive development in…

The goal of this paper is to demonstrate the infrastructural nature of many modern conceptual technologies. The focus of this paper is on conceptual tools associated with elementary types of data modeling. We intend to show a variety of ways in which these conceptual tools not only express thinking, but also mold and shape thinking. And those ways…

From a rhetorical perspective, Mendel's work and its reception elicit two important questions: (a) why were Mendel's arguments so compelling to 20th century biologists? And (b) why where they so roundly ignored by his contemporaries? The focus of this article is to examine the latter question while commenting on the former by employing several…

The theme of the 38th meeting of the International Group for the Psychology of Mathematics Education (PME 38) and the 36th meeting of the North American Chapter of the Psychology of Mathematics Education (PME-NA 36) was "Mathematics Education at the Edge." Academically, the theme provides opportunities to highlight and examine…

How can teachers learn what they need to know? Every community of educators, regardless of field or specialization, can benefit from being well informed about current research findings. A considerable amount of mathematics education research exists to inform teachers and administrators about teaching and learning mathematics. Research can show…

This document plus diskette product provides nine interactive puzzles and games that both teach and provide practice with simple addition and subtraction concepts. The activities address these skills through carrying in addition and regrouping in subtraction. The activities address cognitive skills such as problem solving, planning, visual pattern…

This book contains 18 reproducible Math Storymats which can be a refreshing addition to any early elementary math program. Each storymat is accompanied by two separate read-aloud story selections that guide children in using plastic disk-shaped markers to interact with the mats in specific and open-ended ways. Together the mats and the…

A study examined 60 adult students' informal knowledge of percent and its relationship to their formal computational skills. The students studying in adult education programs were interviewed to ascertain the following: (1) their ideas of the meanings of three benchmark percentages--100, 50, and 25 percent--as they appear in advertising and media…

The National Assessment of Educational Progress (NAEP) is a congressionally mandated project of the U.S. Department of Education's National Center for Education Statistics. It assesses what students in the United States should know and be able to do in geography, reading, writing, mathematics, science, U.S. history, the arts, civics, and other…