Observes the application of probability theory to a game between two players. Shows how basic techniques such as tree diagrams can be used to demonstrate optimum strategies, how the art of bluffing can be quantified, and how this might be applied to a game of poker. (Author/ASK)

Presents seven mini-lessons on chaos theory and fractal geometry for use in a high school setting. Examples include the Sierpinski Triangle and Julia Sets. (MM)

One problem that students have with mathematics is that they often view the topic as a series of unrelated ideas. Sometimes they are aware that they have to know one concept to move to the next, but what is done in geometry is not necessarily related to anything in algebra. This failure to recognize mathematical connections limits students'…

The idea of a graphing portfolio and its implementation in two levels of traditional university calculus courses is described. The activity of graphing helps students to gain a broader and deeper understanding of the connection between a function and its graph.

This paper explores what happens when students engage with mathematical tasks that make no attempt to be connected with students' everyday life experiences. The investigation draws on the work of educators who call for a broader view of what might count as real and relevant contexts for studying mathematics. It investigates students' experiences…

Based on survey responses from 230 students enrolled in a summer gifted program at a university, this study gives a description of gifted students? participation in extracurricular activities in and outside of school. Findings show that gifted students were more involved in competitions, clubs, or other extracurricular activities in mathematics…

Teachers of mathematics face a particular tension, which the authors call the "planning paradox". If teachers plan from objectives, the tasks they set are likely to be unrewarding for the pupils and mathematically impoverished. Planning from tasks may increase pupils' engagement but their activity is likely to be unfocused and learning difficult…

This column describes suggestions for daily activities in a calendar format. This month's theme is math and more. Among other things, this column features several web sites for mathematics activities.

Teaching K-8 is published eight times during the school year. Every issue of Teaching K-8 staff visits every school for there cover story, complete with pictures to provide a window into the life of school. Every issue has a curriculum focus with 3-5 features, written by classroom teachers, with detail lessons and best practice for using…

From time to time, the International Commission on Mathematical Instruction (ICMI) mounts studies to investigate in depth and detail particular fields of interest in mathematics education. This paper is the Discussion Document of the forthcoming ICMI Study 16, "Challenging Mathematics in and beyond the Classroom."

This paper shows how inequalities can be utilized in reducing dimensionality of problems associated with the partition of unit fractions into the sums of two, three, and four like fractions. The need for such a reduction in this context stems from using a spreadsheet as a modelling tool. Activities described in this paper are grounded in standards…

The students of a Mathematical Modeling and Problem Solving class investigate and explore the mathematics involved in fitting a box spring mattress up a stairwell by solving various optimization problems and by using The Geometer's Sketchpad. The results show that a very small fraction of the class was actually able to solve the problem without…

This article proposes four strategies for posing mathematics problems that raise the cognitive demands of the tasks given to students. Each strategy is illustrated with three common middle school mathematics examples: finding the greatest common factor, finding area or perimeter, and finding the equation of a line. Posing these types of problems…

The title may appear daunting, but the exercises, which can be presented to students from middle school to graduate school, are not. The exercises center on creating fractal images in the xy-plane with free. easy-to-use software and questions appropriate to the level of the student.

This report summarizes findings on strategies chosen by students (n=38) when solving algebra problems related to various functions with the freedom to use a TI-83 graphing calculator, influences on student problem-solving strategy choices, student ability to approach algebra problems with use of multiple representations, and student beliefs on how…