Summer of Math Exposition

This is a perfect topic for a mathematical animation since it’s all about deriving identities in a visual (animated) way. I enjoyed these and think they could be legitimately useful for teaching algebra in middle school or early high school.

Just the entire visual nature of it provides a perspective that isn’t usually given to students learning these concepts for the first time.

This was definitely one of the better videos I’ve watched. Everything is simple and explained, I’ve learned something new, it’s visually clean and mathematically memorable. There’s nothing I would add or subtract. This video is perfect as it is.

The only reason I’m not giving a full score is because I’ve not been wowed enough. But I’m still pretty amazed.

Cool, I think this would be very useful for a certain type of algebra II student who does better with pictures. I thought many of the early examples, particularly the quadratic formula were well motivated, but a lot of the later examples were not clearly motivated. I did think the last example and shapes of equivalent area was clever. Overall this is a very useful video and I can see it really helping a certain type of person.

I’ve seen the other videos too and i think they’re literally perfect! The animations and explanations are so beautiful and easy to understand. This deserves to win!

You make a nice point that area models continue to be useful in algebra, outside of mere arithmetic.

I think it would be nice to note the pros and cons of traditional algebra with symbols versus algebra with area models, in terms of explanatory value, memorability, ease of use, suggestions of possible methods, etc.

It’s really accessible and follows the same principle throughout! Shows a lot of unique identities derivations that I haven’t seen before

Cute little video. Probably most enjoyable for younger highschoolers struggling with all these formulas. I appreciated the connections to the inequalities. The usefulness of some of the later identities is debatable.

Neat presentation, clear message, topic. is relevant for many students.

You should mention that the geometric approach breaks (or needs more attention) with negative numbers, while the algebraic manipulation can be done with no such concerns.

The visuals are very good, and the use of animation helps a lot to illustrate the argument. Also, I think this could be used “out of the box” in a classroom setting or at least as homework viewing. To that end, it’s clear that you were successful in what you were trying to do. The motivation could be stronger: as it stands it’s mostly “you already have to knows these equations, here’s a different way to memorize them” (framing as “not memorizing” is probably fine for the audience, but I find it a bit disingenuous— you still have to remember the pictures!)

It’s always dangerous to do 3D graphics but I thought that your cube example was very tastefully done. The opacity made it reasonably clear where the prisms were, and the rotation and color coding does a lot to clear up confusion that the viewer might still have. If I had to complain: for the intended audience I feel it was a little fast to take in the details, but the graphic itself is excellent.

I find myself fascinated by the last example in this video and I am grasping to explain why. The exposition is about as clear as one could hope for, and just like the rest of the video, the animations are deployed to great effect. However, I think that after 10 examples in 11 minutes(!), a little fatigue has set in, and so the seemingly much greater complexity of that last one will probably be intimidating. Since I have seen a lot of talks and explainers, I could tell that you were trying to say “hey, don’t worry, this is bonus material”. But I actually think that the medium of explainer videos simply doesn’t have language to express this in the way you intended, a limitation that I’d never considered before.

(To elaborate slightly: I think that because of the general culture around mathematics, “not finishing the video” for pretty much any reason will be interpreted by the viewer as “failure”. Because the example, on its face, looks so similar to the others, it’s hard to meaningfully convey that it’s okay to feel challenged by this one. So they’ll feel forced to either accept “inadequacy” or to blame you for their not understanding, even though you weren’t intending that choice.)