I finally tried my hand at a video explanation of a mathematical idea I like. This is part 1 in a short series on the Pythagorean Theorem. It starts where I’ve always felt the story should start: with the question of how to double the square.

What do you think? I’d love feedback, since I’m planning more. What works, what doesn’t?

Here’s the link if you prefer watching directly on youtube: http://www.youtube.com/watch?v=IG6aT3kFZf0.

That was a great video, Dan. (Good deep voice too :). I like your prompts to pause the video, too often instructional videos blurt out the answers before you know what just hit you. I can certainly use this with my students. This activity reminds me showing kids how to sketch segments of irrational lengths. Bravo! Look forward to your sequels.

Thanks! Number two is in the works, and should be appearing here soon.

Lovely.

I loved the playful nature of your video…in that the Pythagorean Theorem comes out of a fascinating and interesting investigation. I also loved (as was previously mentioned) the structure of the video with prompts to pause and attempt the question being posed. I am curious, however, about your intention for the video(s). This type of “instruction” seems contrary to the investigative and exploratory nature of many of your posts and, from what I can gather, your philosophy. Again, loved the initial investigation!

Bryan–I don’t have a simple answer to this question, because I’m trying to figure it out myself. (I should mention, too, that your recent blog post here, http://www.doingmathematics.com/2/post/2012/03/whats-the-difference1.html, is more food for thought.)

Basically, I’m wondering if there is any part of my teaching that can make the leap to video (or radio, or print) without losing too much. I am, in general, skeptical of too much reliance on screen-based teaching of any kind. At the same time that I have a grudging admiration for certain math-related computer games, for example, I don’t have the heart to use them in my own teaching or wholeheartedly recommend their use elsewhere. And that goes doubly for video.

At the same time, when I find myself repeating myself among classes or students, I have to wonder whether I’m approaching a presentation of a beautiful idea in mathematics that is worth sharing, and can make the leap to film without becoming denatured, so to speak.

In the end, I guess it’s an experiment. I think there’s a place for lectures in mathematics, if only as a place to showcase beautiful works of mathematical art. And I’ve found from personal experience that it doesn’t make sense to ask students to create art if they haven’t seen any. But could video be part of a larger curriculum? Maybe. Maybe not. I’ll just need to keep working, and thinking about it.

For now, I do feel a motivation to get more videos out there.

Thanks for your thoughts on this. As always, it will be fun to follow your work.

I thought this was extremely enlightening. It was a gentle entry into using these shapes to figure out problems that are often not so clearly understood. The stopping the video (giving time for pauses) was excellent–so that people could do that if they wanted to. Pace of the talk was good, and your voice was clear and a good speed. I also liked this as an example of direct teaching–which still poses challenging problems. And ending with the problems for next time– time to work on your own until the next video, is a nice touch!

I think videos are great for interested folks way far away–please keep them coming!

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Nice! I like it. I’m trying to think of ways to restructure my approach to teaching Formal Geometry in High School. My question is this: Is this discovery an appropriate activity for HS students who may have never been asked to think this way? I don;t want to be a nay sayer because i would love to present this to my high school students but I’m afraid of how long the students will stay engaged before they just say… WTF!

Those are awesome thoughts!

I’m going to think of to structure this so students stay engaged!

Steven–

My experience has been that giving students an activity that centers around an engaging question tends to bring out the best in them. It may be a little foreign to some, but I think it ends up being gratifying pretty quickly. You’ll notice further that someone used this activity in his class and the students really got into answering the questions at the end of the video.

If you do use it, let me know how it goes!

lovely video