One of the great pleasures of being a mathematics teacher lies in experiencing that very special buzz in the classroom that occurs when every single student is thoroughly engrossed in the task the teacher has set them. The teacher knows that in those precious moments genuine learning is taking place, however noisy and chaotic it may appear to an…

The fundamental theorem of calculus, in its simplified complexity, connects differential and integral calculus. The power of the theorem comes not merely from recognizing it as a mathematical fact but from using it as a systematic tool. As a high school calculus teacher, the author developed and taught lessons on this fundamental theorem that were…

How can statistics clearly be mathematical and yet distinct from mathematics? The answer lies in the reality that statistics is both an art and a science, and both aspects are important for teaching and learning statistics. Statistics is a mathematical science in that it applies mathematical theories and techniques. Mathematics provides the…

This article presents an example of how middle school teachers can lay a foundation for calculus. Although many middle school activities connect directly to calculus concepts, the authors have decided to look in depth at only one: the concept of change. They will show how teachers can lead their students to see and appreciate the calculus…

The U.S. school mathematics curriculum changed slowly during the last century, and only in the past few decades have there been serious efforts to establish it nationally rather than having it be, at least in principle, locally determined. Waves of change have periodically swept the curricular ocean, but on the seabed, in the classrooms where…

This paper presents some internet aesthetic texts collected over a period of two years through chain message communications with colleagues located in different parts of the world. The aesthetic texts are grouped into four themes of mathematical magic, values, beauty, and prediction. Mathematical magic aesthetics show fascinating things that can…

This article is based on a study that compared the FET (further education and training) phase mathematics literacy curriculum and mathematics curriculum. The study looked into how the conceptualization of a mathematical literacy curriculum enhanced the acquisition of mathematical concepts among the learners. In order to carry out this comparison…

A recent report by the Mathematics Advisory Panel referred to algebra as a "gateway" to later achievement (National Mathematics Advisory Panel, 2008). To address the problem of low academic performance in algebra, an increasing number of states and districts have started to implement a policy of requiring algebra for all students in…

This study investigates the role of digital cognitive technologies in supporting students' mathematical thinking while engaging with instructional tasks. Specifically, the study sought to better understand how the use of technology is related to the cognitive demand of tasks. Data were collected in four secondary mathematics classrooms via…

This paper presents our initial work to develop trajectories of preservice teachers' knowledge of teaching algebra for equity. We have developed two overlapping hypothetical learning trajectories (HLTs) for teachers' learning to engage and motivate diverse students to solve algebra problems. These HLTs are being used to guide the development of…

Students in the 21st century are exposed daily to a staggering amount of numerically infused media. In this era of abundant numeric data, students must be able to engage in sound statistical reasoning when making life decisions after exposure to varied information. The context of nutrition can be used to engage upper elementary and middle school…

In this article, I describe a classroom investigation in which a group of prospective secondary mathematics teachers discovered theorems related to the power of a point using "The Geometer's Sketchpad" (GSP). The power of a point is defines as follows: Let "P" be a fixed point coplanar with a circle. If line "PA" is a secant line that intersects…

The concept of "function" spans elementary school through high school. When introducing the topic to elementary school and middle school students, the authors ask them to work with a variety of examples and representations of functions, since a formal definition of a function is rather abstract. They give the most accessible geometric functions…

Piecewise linear functions and story graphs are concepts usually associated with algebra, but in the authors' classroom, they found success teaching this topic in a distinctly geometrical manner. The focus of the approach was less on learning geometric concepts and more on using spatial and kinetic reasoning. It not only supports the learning of…

In this article we report the influence of contextual factors on mathematics and science teachers' reasoning in risk-based decision-making. We examine previous research that presents judgments of risk as being subjectively influenced by contextual factors and other research that explores the role of context in mathematical problem-solving. Our own…