Mathematical games provide wonderful opportunities to engage students in meaningful and rich mathematical investigations. This article describes three mathematical games suitable to be played by different groups of students, from young elementary school students, learning the basics of arithmetic and geometry, to older students making their first…

Digital photos and digital movies offer an excellent way of bringing real world situations into the mathematics classroom. The technologies surveyed here are feasible for everyday classroom use and inexpensive. Examples are drawn from the teaching of Cartesian coordinates, linear functions, ratio and Pythagoras' theorem using still images, and…

If the goal is to promote mathematical thinking and help children become flexible problem solvers, then it is important to show students multiple representations of a problem. Because it is important to help students develop both counting-based and collections-based conceptions of number, teachers should be showing students both number line…

This article presents a brief biography of Johann Carl Friedrich Gauss. Gauss was born on April 30, 1777, in the German city of Braunschweig (Brunswick). He was the only child of Gebhard Dietrich Gauss and Dorothea Benze. Neither of Gauss's parents had much education, his father could read and write, but earned his living doing menial jobs such as…

This article contains a small selection of mathematical fiction chosen with the teaching of mathematics in secondary school in mind. However, an attempt is made to classify the works and provide a few ideas about how these items may be used by mathematics teachers, sometimes, but not necessarily, in collaboration with science and humanities…

Pattern recognition is a critical component of success in mathematics. Students at all levels should be provided with opportunities to investigate and uncover patterns throughout their mathematical careers. Further, they should be allowed to explore situations in which pattern recognition plays a vital role in the construction of important…

The Internet, an exciting and radically different medium infiltrating pop culture, business, and education, is also a powerful educational tool with teaching and learning potential for mathematics. Web-based instructional tools allow students and teachers to actively and interactively participate in the learning process (Lynch, Moyer, Frye & Suh,…

Trinity College is a low-fee independent school in Gawler, South Australia. The college has an enrolment of 3500 students of varied socioeconomic mix, drawn from the northern suburbs of Adelaide. Trinity has recently been restructured into four R-10 schools and one senior school for Years 11-13. The schools share a common mathematics curriculum.…

This article discusses prime numbers, defined as integers greater than 1 that are divisible only by only themselves and the number 1. A positive integer greater than 1 that is not a prime is called composite. The number 1 itself is considered neither prime nor composite. As the name suggests, prime numbers are one of the most basic but important…

Teachers are expected today to assess student understanding as an integral part of instruction, using a combination of various assessment methods and tools, among which are observing students solve problems in class and listening to their mathematical discussions. The aim of our study is to explore what it might mean for a teacher to hear students…

There are two basic guiding referents in the present investigation: the teaching and learning of school-level geometry (basic concepts of Euclidian geometry and measure) and the analysis of the conceptions of prospective primary teachers in Spain. The work assumes that such conceptions appear and develop during school years, and that consequently,…

We report on how two middle-grade teachers supported their students' mathematical reasoning within the context of a novel modeling task in data analysis. We examine how the task features supported the development of teachers' knowledge as their students engaged with the task. Analyses of the teachers' practices suggest that the task features…

It is over 25 years since Wood, Bruner and Ross (1976, "Journal of Child Psychology and Psychiatry," 17, 89-100) introduced the idea of "scaffolding" to represent the way children's learning can be supported. Despite problems, this metaphor has enduring attraction in the way it emphasises the intent to support a sound foundation with increasing…

The principal objective of this study was to gain insight into preservice elementary teachers understanding of the mean. Specifically, the research focused on identifying preservice teacher conceptions of the role and function of the mean as a statistical measure. Multiple data sources and data collection methods were utilized in an effort to…

This article discusses theoretical assumptions either explicitly stated or implied in research on teachers' beliefs. Such research often assumes teachers can easily articulate their beliefs and that there is a one-to-one correspondence between what teachers state and what researchers think those statements mean. Research conducted under this…