Mindblown: a blog about philosophy.

Today’s talk at NCTM San Diego… enliven the introduction to e by telling its true story. It’s one more enteresting than compound interest. We’ll examine average rates of change, series, Pascal’s triangle, limits, probability, and even euler’s method, with multiple representations in Precalculus.  I will be adding more of what I said out loud in the workshop to this post in…

Below is a page I wrote 15 years ago for the Exploring Calculus with the Geometer Sketchpad Summer Institute.  Was thinking about it before going to Exeter in June.  In thinking about starting calculus again next year, I am reflecting on the many tools available for illustrating calculus (and math) today; the question remains, I…

Attached are slides from my featured talk at the Anja S. Greer Conference on Mathematics and Technology at the Exeter School.  My goal is to create pages that will let readers choose their own adventure through the talk.  For now, check out the models of CYOA stories in the attached pdf, or at Patterns in…

My session with Cheryl Kaplun at NCTM San Francisco. 32, Pantozzi:Kaplun, Take a Walk on the Random Side Lesson Plan

Some years ago, in 1996 to be precise, I read this article: Davis, G. E. (1996) What is the difference between remembering someone post a letter and remembering the square root of 2? It was in the Proceedings of the 20th Conference for the International Group for the Psychology of Math Education. I’ve been thinking…

Here’s a short summary of the Random Walk activity: A student takes a random walk on a number line determined by flips of a fair coin: one step forward with a flip of a heads, and one step back with a flip of tails. After students propose questions about an individual’s random walk, the whole class,…

Eight years ago my colleagues and I were looking to create a series of lessons about probability that would build upon each other across middle and high school. We wanted to create an engaging activity that would inspire students to ask lots of questions about probability, and be one that students would remember years later. Being…

“Do you see what I mean?” When we talk about understanding, we often use words associated with vision and sight. Yet there is so much to the concept of “understanding” that does not fit the conventional definition of something that is literally “visible.” In my first year of teaching, 23 years ago, I asked my students to make…