In these two companion papers, a learning activity is introduced that teaches students how mathematics works through the visual aid of picture grids. The picture grids are composed of 60 different acrylic stained-glass window overlays. Each fractional part is represented by a different color: fifths are green, quarters are yellow, etc. The square…

The 16 units of this book are designed as textbook supplements to encourage students to think mathematically and as mathematicians. Each unit begins with an orientation session which raises general concerns that always occur within mathematical exploration. This is followed by a short, original text in which a mathematician creates a particular…

Sue Gehn teaches first grade at Cottage Grove Elementary School in Cottage Grove, just outside of Madison, Wisconsin. She achieves excellence in mathematics by applying the concepts of Cognitively Guided Instruction (CGI).The CGI approach is a philosophy founded on the notion that teachers must assess, and understand, the present knowledge that…

Car Builder is a scientific CD-ROM-based simulation program that lets students design, construct, modify, test, and compare their own cars. Students can design sedans, four-wheel-drive vehicles, vans, sport cars, and hot rods. They may select for aerodynamics, power, and racing ability, or economic and fuel efficiency. It is a program that teaches…

The theme of the fifth annual World's Largest Math Event (WLME 5) is "The Power of Nature." This theme encourages students to explore natural forces that affect humankind, including phenomena such as hurricanes, earthquakes, and snowstorms, and the mathematics that underlies their study. The 15 activities for WLMES have been grouped into five…

Applying and adapting a variety of appropriate heuristic strategies is one of the accepted standards of problem solving (NCTM, 2000). Thinking through a solution to a non-routine mathematical task, experts in problem solving call into play many sophisticated strategies (almost) without conscious efforts, while novices need to be taught how to do…

In this book, author Catherine Jones Kuhns introduces student- and teacher-friendly math activities designed to get students thinking like mathematicians and loving mathematics, while addressing content standards through grade 2. She also shows how to make math fun for students, get children actively engaged in learning, create a student-centered…

Mathematical norms are important cultural knowledge of mathematical activities. This paper reports an analysis of mathematical norms in ten consecutive lessons taught by an eighth-grade Japanese teacher. The lessons were located in the unit of simultaneous linear equations. The videotapes of the lessons, their transcripts, and the interview data…

This book offers ideas to enrich instruction and help teachers explore the intrinsic beauty of math. Through dozens of examples from arithmetic, algebra, geometry, and probability, the symmetries, patterns, processes, paradoxes, and surprises that have facilitated generations of great thinkers are revealed. Activities include: (1) The Beauty in…

This book contains a collection of division lessons that support curriculum and instruction. It is expected that 3rd and 4th grade students will establish a firm foundation of understanding and skills in division. The lessons address broader goals of division instruction and are aimed at supporting students' growth toward proficiency based on…

Arithmetic is the major focus of elementary mathematics instruction. This book offers lessons for developing children's numerical understanding and skills. The lessons help children learn to estimate, understand numerical relationships, develop number sense, compute mentally and with paper and pencil, and use arithmetic as a tool to solve…

The feature article of this newsletter issue describes a course designed for the professional development of math teachers that uses inquiry-based classroom learning and presents articles on inquiry-based science and mathematics teaching. Other articles include: (1) "An Inquiry-Based Mathematics Classroom" (Lesley Lee); (2)…

The materials and ideas in this document are intended to be used by teachers in schools in order to bring adults and children together to experience good mathematics. It features an evening of hands-on mathematics scheduled for one night a week for four weeks. Students and adults come together to share mathematics activities, solve problems, and…

The materials and ideas in this document are intended to be used by teachers in schools in order to bring adults and children together to experience good mathematics. It features an evening of hands-on mathematics scheduled for one night a week for four weeks. Students and adults come together to share mathematics activities, solve problems, and…

By studying and practicing metacognition, teachers and parents are instilling positive attitudes toward learning by teaching how-to-learn skills that prepare children for assessing their own thinking about learning as they become more and more developmentally prepared. This book stresses the strategies for thinking in mathematical terms without…