The First Graph

April 5, 2017

This picture was first published in 1638! It is from Galileo’s great work Two New Sciences, that he smuggled out of his home imprisonment in Florence, when he was 72 years old and effectively blind. Though famous for his telescope … Read more

Art Bardige

Tradition, Tradition

October 28, 2016

As part of the process of designing and developing new Labs, I visit math content sites all the time to help me think about the kinds of questions to ask and the way to explain or represent a concept. I … Read more

Art Bardige


October 26, 2016

“Today, it seems as if nearly everyone agrees that high school mathematics needs to change. For far too long high school mathematics has not worked for far too many students: too many students leave high school unprepared for college or … Read more

Art Bardige

Back- to-School – add 10%

September 8, 2016

It was forty years ago this September that I started my career as a high school mathematics teacher, a career that spanned 36+ continuous years. I continued some teaching and other classroom work over the last few years, but this … Read more

Peter Mili

What Algebra?

August 10, 2016

Each summer, as schools get ready for a new school year, the question returns, “Should we be teaching algebra to our children?” it seems to have been started by Andrew Hacker who has tried to argue and continues to argue … Read more

Art Bardige


July 20, 2016

The word seems so benign. Yet it has become the goto word in education. School superintendents, even the best and most advanced of them, use it all the time. “We want each of our students to reach mastery in each … Read more

Art Bardige

The End

July 18, 2016

Despite the many attempts to codify the creative process, it is as surprisingly individualistic as it is human. John Irving, author of iconic works like The Cider House Rules, describes his creative process as writing the conclusion before the beginning. … Read more

Art Bardige

Personalized Learning

July 7, 2016

These two words have caught the imagination of educators and parents. They were designed to be the frames for talking about the value of digital learning. They were to replace the bland “individualized learning.” They were meant to symbolize a … Read more

Art Bardige

Function Machines

June 29, 2016

I do not know who, when, or where this iconic mathematical representation was developed. It is, however, one of the most powerful and ubiquitous of all mathematical images, and I think the most important. It is taught to 2nd graders … Read more

Art Bardige

Stand and Deliver

June 20, 2016

It was an appropriate title for the movie about Jaime Escalante and it is an appropriate title for the role that teachers continue to play. We all too frequently see our role in both K-12 and in college as an … Read more

Art Bardige