Each school year, children begin with their new supplies in hand, eagerly waiting to sharpen their pencils and get started. However, it is not long before the teacher overhears one student asking to borrow a pencil from another. Whereas some students delight in having a collection of pencils and crayons to use for their lessons, others manage just fine with only one or two writing utensils; and at least one student always seems to need to borrow a pencil.
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.
Proulx JÉrôme, Mary Beisiegel, Helena Miranda and Elaine Simmt
Highlighting multiple representations of systems of equations deepens student understanding.