Six one-hour video programs and user guide
and Surprises in Mind, a one-hour public television documentary

Research shows that children formulate extraordinarily interesting and complex mathematical ideas, even at a very young age. The Private Universe Project in Mathematics demonstrates and honors the power and sophistication of these ideas, and explores how mathematics teaching can be structured to resonate with children's sophisticated thinking. This workshop offers the rare opportunity to follow the mathematical development of one group of students through grades 2-12, and to observe teachers in the process of redefining what mathematics is for themselves and for their students.

Produced by:
Smithsonian Institution Astrophysical Observatory
in partnership with the Robert B. Davis Insitute for Learning at Rutgers University and the Annenberg Foundation (2000)

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.

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.

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.

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.

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.

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.

Surprises in Mind
A video documentary on learning mathematics for K-8 teachers, administrators, and the general public, which uncovers a surprise: Mathematical creativity - expressed in art, architecture, and music and valued by industry - is built into the brain and can flourish under the right conditions. Summarizing the 12-year study following students from first grade through high school, it demonstrates the brain's surprising natural abilities for learning math. In the documentary, these results are corroborated by new research from leading cognitive psychologists. Discover ways to unlock this natural human gift for mathematics in classrooms, workplaces, and homes.

Additional video: Extended algebra classroom segment from Workshop 4
Math teacher, Janet Walter in Provo, Utah encourages her students to "think like mathematicians" in this extended sequence of classroom footage, an excerpt from a roughcut of the Workshop 4 program. This segment shows Dr. Walter with a number of different math classes, where students of all levels and abilities engage in back-and-forth argument and peer mentoring. Includes reflections from students describing how this approach has changed their learning. Producer/videographer: Alex Griswold. Running time: approx. 45 minutes.