Workshop 1. Following Children's Ideas in Mathematics
An unprecedented long-term study conducted by Rutgers University followed the development of mathematical thinking in a randomly selected group of students for 12 years - from 1st grade through high school - with surprising results. In an overview of the study, we look at some of the conditions that made their math achievement possible. Go to this unit.
Workshop 2. Are You Convinced?
Proof making is one of the key ideas in mathematics. Looking at teachers and students grappling with the same probability problem, we see how two kinds of proof — proof by cases and proof by induction — naturally grow out of the need to justify and convince others. Go to this unit.
Workshop 3. Inventing Notations
We learn how to foster and appreciate students' notations for their richness and creativity, and we look at some of the possibilities that early work on problems that engage students in creating notation systems might open up for students as they move on toward algebra. Go to this unit.
Workshop 4. Thinking Like a Mathematician
What does a mathematician do? What does it mean to "think like a mathematician"? This program parallels what a mathematician does in real-life with the creative thinking of students. Go to this unit.
Workshop 5. Building on Useful Ideas
One of the strands of the Rutgers long-term study was to find out how useful ideas spread through a community of learners and evolve over time. Here, the focus is in on the teacher's role in fostering thoughtful mathematics. Go to this unit.
Workshop 6. Possibilities of Real-Life Problems
Students come up with a surprising array of strategies and representations to build their understanding of a real-life calculus problem — before they have ever taken calculus. Go to this unit.