The Power of Mathematical Visualization by James S. Tanton (The Great Courses)
The great physicist, Richard Feynman, used visualization extensively to understand problems. Temple Grandin, author of Thinking in Pictures, suggests we may be too hasty in trying to prevent and cure autism, since mild forms ot Autism Spectrum Disorder, at least, lead people to different and possibly important ways of thinking. But what about the rest of us, who are neither geniuses nor autistic (nor autistic geniuses)? Visualization is still a powerful and fascinating way to think about math, from basic arithmetic to esoteric and high-powered concepts.
Back when The Great Courses was called The Teaching Company, the course format was primarily a talking-head lecture, perfectly suited for audio-only listening in the car while commuting to work. Many of the courses still work well for that, but the company has grown and expanded considerably, not just in content but also in format. The Power of Mathematical Visualization includes plenty of diagrams, images, and physical demonstrations.
James Tanton is an engaging teacher. He does spent a bit too much time complaining about the unhelpful ways he was taught math in school, but I soon learned to forgive and ignore that. His enthusiasm for math is infectious. You can watch the introductory lecture on YouTube, if you want to check it out.
Here's a picture of the course contents. (Click for a larger image.)
I'd recommend this course to anyone, including all our grandchildren. Certainly the oldest three could get a lot out of most of the lectures. The six-year-olds, being especially interested in math, are also good candidates. Even the younger ones would benefit from at least being in the same room while others are watching. You never know what they are absorbing from their surroundings.
James Tanton has another series on The Great Courses Plus, called Geometry: An Interactive Journey to Mastery. Would I ever have picked that one out of their long list of topics that are at first glance much more interesting? Not likely. But we're watching it now, because Tanton is such a good presenter, and so far it's as intriguing as Visualization.