Through an account of the history of exponential functions as presented in traditional calculus textbooks, I present my observations and remarks on the spiral development of the concept, and my concerns about the general presentations of the subject. In this article I emphasize how the different arrangements and sequencing of the subjects required…

Following an ATM working weekend funded by the Clothworkers Guild, the authors invited three neighbouring village primary schools to make a quilt as a collaborative venture. Using some ready-made quilts, resource books and boxes of ATM tiles (squares, hexagons, octagons, dodecagons) and a separate box containing plastic squares, triangles, two…

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…

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…

The purpose of this case study was to determine which mathematical instructional strategies met the learning challenges of a primary-age child identified with 22q11DS. This study investigated the processes by which a young child with 22q11DS acquires mathematical concepts within classroom and tutoring settings. It placed emphasis on building…

This research project investigates students' development of problem solving schemata while using strategies that facilitate the process of using solved examples to assist with a new problem (case reuse). Focus group learning interviews were used to explore students' perceptions and understanding of several problem solving strategies. Individual…

How do composing and decomposing numbers connect with the properties of addition? Focus on the ideas that you need to thoroughly understand in order to teach with confidence. The mathematical content of this book focuses on essential knowledge for teachers about numbers and number systems. It is organized around one big idea and supported by…

Using data collected in 125 seventh-grade and 56 eighth-grade Texas classrooms in the context of the "Scaling Up SimCalc" research project in 2005-07, we examined relationships between teachers' mathematics knowledge, teachers' classroom decision making, and student achievement outcomes on topics of rate, proportionality, and linear…