Some statisticians have pointed out that the field of statistics essentially exists to study the variability seen in everyday life. Because variability is so foundational, the "Guidelines for Assessment and Instruction in Statistics Education" (GAISE 2007), published by the American Statistical Association (ASA), recommend that teachers…

The paper describes the importance of graphicacy as a key communication tool in our everyday lives. The need to better understand the development of graphicacy and its use in the school curriculum is emphasised. The need for a new research tool is explained and the development of a new taxonomy of graphicacy is described. The use of this tool…

While teaching a methods class for preservice secondary school mathematics teachers, Christopher E. Smith found that although all students could draw a reasonably close approximation of a circle, not all could provide an entirely accurate definition of a circle. A discussion with students led him to think about ways of reintroducing students to…

Mrs. Fisher's class was learning about arithmetic functions by pretending to operate real-world "function machines" (Reeves 2006). Functions are a unifying mathematics topic, and a great deal of emphasis is placed on understanding them in prekindergarten through grade 12 (Kilpatrick and Izsák 2008). In its Algebra Content Standard, the…

In our science for non-science majors course "21st Century Physics," we investigate modern "Hubble plots" (plots of velocity versus distance for deep space objects) in order to discuss the Big Bang, dark matter, and dark energy. There are two potential challenges that our students face when encountering these topics for the…

In this article, the authors explore the reasons why some mathematical functions are referred to as odd, and others as even. They start by recalling the definitions of both functions. Simply stated, the value of an even function is the same for a number and its opposite, whereas the value of an odd function changes for the opposite number when the…

An important concept in mathematics, yet one that is often elusive for students, is the concept of rate. For many real-life situations--those involving work, distance and speed, interest, and density--reasoning by using rate can be an efficient strategy for problem solving. Students struggle with the concept of rate, despite the many possible…

Creating charts and graphs is all about visual abstraction: the process of representing aspects of data with imagery that can be interpreted by the reader. Children may need help making the link between the "real" and the image. This abstraction can be achieved using symbols, size, colour and position. Where the representation is close to what…

Finding educational truths is an inherently multivariate problem. There are many factors affecting each student and their performances. Because of this, both measuring of skills and assessing students are always complex processes. This is a well-known problem, and a number of solutions have been proposed by specialists. One of its ramifications is…

An iPad® can be used to teach students to graph parabolas with ease and grasp vocabulary quickly. Parabolas come to life for students in this easily implemented activity described in this article. Teachers can use this tool in a fun and interactive way to not only address these graphing and vocabulary concepts but also introduce and explore…

Mobile device accelerometers are a simple and easy way for students to collect accurate and detailed data on an amusement park ride. The resulting data can be graphed to assist in the creation of force diagrams to help students explain their physical sensations while on the ride. This type of activity can help students overcome some of the…

How can the key concept of equivalent expressions be addressed so that students strengthen their representational fluency with symbols, graphs, and numbers? How can research inform the synergistic use of both paper-and-pencil analysis and computer algebra systems (CAS) in a classroom learning environment? These and other related questions have…

The article illustrates how statistical content and pedagogical reasoning were taught in tandem in an undergraduate course. A typical day in the course is described. It is also suggested that practising teachers can benefit from strategies used in the course. (Contains 1 table and 3 figures.)

The least squares method of fitting a line is not one that naturally occurs to students. We present three tasks to understand student views on how lines may be fit.

In mathematics, as in baseball, the conventional wisdom is to avoid errors at all costs. That advice might be on target in baseball, but in mathematics, avoiding errors is not always a good idea. Sometimes an analysis of errors provides much deeper insights into mathematical ideas. Certain types of errors, rather than something to be eschewed, can…