A weeklong unit in an eighth-grade classroom shows how instruction should extend beyond the four basic operations for better understanding of the realities and needs of today's world.
At a meeting of eleven middle school mathematics teachers who gather monthly to discuss various topics, this question arose: “Is 1 a prime number?” The response proved to be a little surprising. The answer can be either yes or no, depending on the particular set of images and metaphors for multiplication that are discussed.
The question of how to teach mathematics has become increasingly problematic in recent years as critics from diverse perspectives have offered wide-ranging, and often seemingly incommensurate, challenges to conventional conceptions of the teacher's task. This article represents an effort to “bring into dialogue” some of the varied commentaries on mathematics teaching, using an enactivist framework to interpret and to propose an alternative way of framing mathematics teaching. In this report, the manner in which the teacher listens is offered as a metaphoric lens through which to reinterpret practice, as a practical basis for teaching action, and as a means of addressing some of the critics' concerns. The report is developed around an extended collaborative research project with a middle school mathematics teacher.
Elaine Simmt and Brent Davis
Fractal geometry has become a topic of widespread interest in recent years as evidenced by brisk sales of books tracing the emergence of the field and the ever-increasing popularity of computer-generated images. As reflected in earlier issues of the Mathematics Teacher, the topic is also well represented in discussions among mathematics educators.
Brent Davis and Elaine Simmt
Complexity science may be described as the science of learning systems, where learning is understood in terms of the adaptive behaviors of phenomena that arise in the interactions of multiple agents. Through two examples of complex learning systems, we explore some of the possible contributions of complexity science to discussions of the teaching of mathematics. We focus on two matters in particular: the use of the vocabulary of complexity in the redescription of mathematical communities and the application of principles of complexity to the teaching of mathematics. Through the course of this writing, we attempt to highlight compatible and complementary discussions that are already represented in the mathematics education literature.
Tom Kieren, Brent Davis and Ralph Mason
Tanya and Ellen have made a “Fraction Flag” (fig. 1) by taking a half-sheet of paper and arranging smaller themselves how much of the whole sheet of paper is covered.