The number [pie] [approximately] 3.14159 is defined to be the ratio C/d of the circumference C to the diameter d of any given circle. In this article, the author looks at some surprising and unexpected places where [pie] occurs, and then thinks about some ways of remembering all those digits in the expansion of [pie].

In line with current efforts to understand the piece-by-piece structure and articulation of children's mathematical concepts, this case study compares the reversibility schemes of two eighth-grade students. The aim of the study was to identify the mechanism through which students reverse their thought processes in a multiplicative situation. Data…

This paper examines a Special Issue of "Educational Studies in Mathematics" comprising research reports centred on Peircian semiotics in mathematics education, written by some of the major authors in the area. The paper is targeted at inspecting how subjectivity is understood, or implied, in those reports. It seeks to delineate how the conceptions…

This article discusses key ideas and concepts involved in understanding fractions and offers a range of hints to the classroom teacher on how to support students to develop a connected understanding of this important topic. (Contains 8 figures.)

In this information age, the capacity to perceive structure in data, model that structure, and make decisions regarding its implications is rapidly becoming the most important of the quantitative literacy skills. We build on Kaputa's belief in a Science of Need to motivate and direct the development of tasks and tools for engaging students in…

How do students think about algebra? Here we consider a theoretical framework which builds from natural human functioning in terms of embodiment--perceiving the world, acting on it and reflecting on the effect of the actions--to shift to the use of symbolism to solve linear equations. In the main, the students involved in this study do not…

This article explores the question, "When should you mail in your entries to a sweepstakes in order to have the best chance of winning?"

In the context of discrete Fourier transforms the idea of aliasing as due to approximation errors in the integral defining Fourier coefficients is introduced and explained. This has the positive pedagogical effect of getting to the heart of sampling and the discrete Fourier transform without having to delve into effective, but otherwise long and…

This article describes how roulette can be used to teach basic concepts of probability. Various bets are used to illustrate the computation of expected value. A betting system shows variations in patterns that often appear in random events.

It is well known that simple examples are really encouraging in the understanding of rearrangements of infinite series. In this paper a similar role is played by simple examples in the case of infinite products. Iterated products of double products seem to have a similar spirit of rearrangements of products, although they are not the same.…

For many students, mathematics is anything but coherent, and textbooks often do not make connections among concepts. Mathematics teachers must teach more than what is in the text in order to help students see and understand the big picture. Doing so will also help students recognize the concept and apply it in contexts outside of mathematics. The…

This article expresses concern for the sloppy language that is often used by the media to describe numerical comparisons and suggests guidelines for how such comparisons should be described such that the meanings are unambiguous.

Teachers want and need students to excel in the classroom. Cooperative learning is one method recognized to address this. Numerous researchers have shown that cooperative learning leads to improved skills in teamwork and communication in other fields (Johnson and Johnson, 2007; Slavin, 1995). Cooperative learning used in this study showed that the…

This importance of mathematical skills cannot be denied. Particularly for students with learning disabilities that may not earn a college diploma, math skills applicable to jobs they may take are necessary to learn in high school (Patton, Cronin, Bassett, and Kopel 1997). Unfortunately, students that reach high school and have not yet mastered…

Current research has focused on early numeracy in the preschool setting, but few studies have addressed the relationship between elementary school children's understanding of mathematical concepts and parent-child interactions during math play or work. As a result, the researcher sought to understand the extent to which math concepts were…