One Should Separate Related Topics!

This is part of a multifaceted strategy to teach heterogeneous classes. Read about it in this article: Reaching the Full Range.In a previous post, I discussed the benefits of "lagging homework".  These included extending student exposure to new ideas, which benefits everyone: stronger students get the forward motion they want and need, and students who… Continue reading One Should Separate Related Topics!

All of high school math in one year?

In my previous post, I responded to Michael Thayer's comments about my Mathematics Overview. In this post I will respond to Mike's proposal for a one-year course to replace all of high school math.Mike and I largely agree about the failings and shortcomings of traditional curriculum and pedagogy, but I don't agree with his solution.… Continue reading All of high school math in one year?

More on the Mathematics Overview

 In his Hyperbolic Guitars blog, Michael Thayer writes:I've been mulling over the one-year course idea some more. And what to my wondering eyes did appear (thank you, @tieandjeans) but this really spectacularly well-thought-out and well-organized course outline created by Henri Picciotto. It's got everything, really, that I'd love to see in the course I'd proposed, and it… Continue reading More on the Mathematics Overview

The third dimension!

This is another post about sessions I attended last weekend at the Asilomar Northern California CMC conference. (To read the whole set, start here.)Kevin Rees presented two variations on a classic volume optimization problem. In the traditional problem, you start with a square piece of cardboard, cut off congruent squares at the four corners, and… Continue reading The third dimension!

Kinesthetic Radians

(Previous kinesthetic posts: Pascal's Triangle, Graphing, Distance.)If radians are introduced strictly with a formula, the meaning of the word is difficult to grasp for many students. Some years ago, I learned two tricks from a colleague, which I'll share here:- Tell students that "radian" is short for "radius angle".- A one-minute kinesthetic activity: ask students… Continue reading Kinesthetic Radians