Comments on: When Is Video Valuable?

By: John Baglio

John Baglio — Mon, 19 Dec 2011 12:08:39 +0000

Oops. Sorry. I didn’t see the previous post by @another Eric.

By: John Baglio

John Baglio — Mon, 19 Dec 2011 12:07:33 +0000

Hi Dan, this is purely a video technique question. How did you create the animated circle and spinner for this post? I love your videos and would like to do some similar things for my science class. Also, how did you overlay the the graphs for the Graphing Stories piece? They are fantastic! I use them in my physical scence class when we talk about motion.
Thanks, John

By: gasstationwithoutpumps

gasstationwithoutpumps — Thu, 01 Dec 2011 05:00:20 +0000

I’m a little bothered by Brian’s explanation of expected value. I’m afraid many students will expect to have two spins come out to exactly $300, rather than $200 1/4 of the time, $300 1/4 of the time, and $400 1/4 of the time. Going up to 8 spins gets a binomial distribution that will be very difficult for most students to handle. To use Brian’s approach, you would have to have already established the additivity of expected value, but I thought that his was intended as a first lesson on expected value, not a review at the end of a unit.

By: Brian Cormier

Brian Cormier — Tue, 29 Nov 2011 18:15:05 +0000

I love this video, and I think starting with a simple spinner with 2 equally-likely outcomes is a great way to start. I’d probably start with the $100s split evenly and ask students if they’d pay $50 to spin the spinner and receive the prize landed upon. Yes. Then $75. Yes. Then $100. (They may say “Why bother?”) Then $125. No. Discuss why. We expect the outcome to be $100.

Then do the 50-50 $100/$200 split. Would you pay $100? Yes. The least you get is $100, anything else is gravy. Would you pay $200? No. The most you could get is $200, anything else is a loss. What would you pay? Here’s where I’d talk about how the probability ties in to “expectation”. If we expect $100 to hit one out of two times, and we expect $200 to hit one out of two times, what do we expect to happen if we spin twice? $100 + 200 = $300. If we expect $300 for 2 spins, what do we expect for 4 spins? $600. 8 spins? $1200. For each scenario, how much for 1 spin? $150.

Continue with varying areas of the circle.

By: Bruce

Bruce — Tue, 29 Nov 2011 16:54:03 +0000

Great stuff, Dan! My colleague Richard said “This about sums up why animation is such a fantastic tool for a math ‘textbook.’ ” We like your stuff – keep it up!

Oh – I did have one particular thought about this video – I found myself thinking the animation would’ve flowed better with the initial posing of the problem, had it run in the opposite direction, from half to full… Perhaps it’s just how my brain prefers it, but I do find that when teaching with video (we use it a lot), little things matter – though this one could purely be my own pref. (I’d like to know if others found the same thing).

Anyway, thanks again for the challenging, sharpening thoughts, as always!

By: Testing expected values using Geogebra | gealgerobophysiculus

Testing expected values using Geogebra | gealgerobophysiculus — Tue, 29 Nov 2011 09:40:34 +0000

[…] expected values using Geogebra I was intrigued last night looking at Dan Meyer’s blog post about the power of video to clearly define a problem in a way that a static image does not. I loved […]

By: Dan Meyer

Dan Meyer — Tue, 29 Nov 2011 04:09:14 +0000

Adobe AfterEffects.

By: a different eric

a different eric — Tue, 29 Nov 2011 02:17:08 +0000

@ dan…
What program do you use to create videos like this?

By: Jim Hardy

Jim Hardy — Mon, 28 Nov 2011 19:26:34 +0000

I love this concept… and I’d love it even more if at the end there was a wondering asking the student to choose a new value instead of the Â£200 (let’s say Â£1,000) and ask them to draw the slice. [great assessment/box ticking for the teacher]

Sure there’s a coder out there who could program the slice growing/shrinking depending on amount, and then allowing the teacher to input multiple variables (Â£100, Â£200 and Â£300, etc). That would be cool.

This is real similar to your 25% amounts of a square, then seeing one of the diagonals slide down the vertical. Both could be presented so utterly boring in a text book, but in these visual ways are so very captivating!

By: Christopher Danielson

Christopher Danielson — Mon, 28 Nov 2011 19:20:52 +0000

Dan:

I think you’ve put video in too small a box.

Or maybe I have too narrowly construed the term video when you mean to point to dynamic representation. GeoGebra on a Smart Board is actually a really nice alternative here-you and the students are looking at the same image-the same one you're pointing at. You drag that point around the circle, stop when students are loudly cheering for their favorite, etc. To follow up on your "goes without saying"...do you show the video if I narrate it? I'm still guessing no. I just don't feel that it's video you're pointing to with this example. No, this example (for me) is quite different from the escalator problem, or Coke v. Sprite, or etc.