Summer of Math Exposition

The video clearly expressed why associativity and commutativity are such important and essential concepts to understand. The actual proof part got a bit long, I think something like more color or even shapes being animated may have been additionally helpful. The handwriting was clear but also provided a personal touch that I appreciated. While novel might not be the word I would use to describe the subject I did appreciate and receive the importance and appreciation the speaker had for the topic which did make me care more. So big lead up to the Gauss’s proof was very interesting. Discovering what was happening felt exciting. Also, everyone loves a cat. I appreciated the steady pace.

A bit of a slow start, but then - CAT! Instant win. Please, more cats in math videos.

You have a warm, personal presentation/lecture style. I’m not sure whether to fall in love with it, or to have big reservations. On the one hand, it’s certainly great if that’s how you lecture in person, and for people watching a pre-recorded video it might be preferable for some people, but on the other hand it might put some off. However, you have a ready audience, so it works!

Taking the above as read; you prepared handwritten notes beforehand, which might be just a tad too hard for people to read, especially for whom English is not their first language. Consider typing them, maybe? This is a big accessibility issue. So, for example, “Associativity” would best be typed beforehand, whereas $a+(b+c)$ can be handwritten.

For some of the topics discussed, I do also have reservations about how this is pitched. On the one hand, you’re writing out “5 apples = 4+1 apples”, on the other hand you’re writing $-1 \in \mathbb{Z}$ within a couple of minutes of each other. The video was good overall, but I’m skeptical that this is calibrated quite correctly.

I thought perhaps some parts went on too long, such as Gauss’s arithmetic sum. Technically, the arithmetic sum to $n$ takes three operations, not two. Finally, I should advise you that the integers 6, 7 should not be pronounced in that order, or if so, a special voice should be used.

Please accept my score as a subjective opinion based on the above thoughts.

Cursive thick writing is so hard to read. I think the topics are not clearly proven. The cat is WAY too distracting. I don’t need a cat bum on YT. Jumping around from commutivity, but with negative numbers in between. Resizing and moving around page is distracting

The idea is interesting, as is the choice of a specific target audience. Perhaps what’s missing is a more engaging hook, and I feel that, given the topics covered, 30 minutes is too long.

The traditional lecture-style interface can still work: it gives the impression of being in a classroom, but it feels slightly at odds with the informal style of the graphics (somewhat messy handwritten text).

That was really nice! The only thing I see that could be improved is the writing, maybe? Your handwriting itself is fine, but it might be worth it to try a non-pressure sensitive pen and/or a smaller pen size in your note taking app.

I like the way you explain things! I think it would help to also write down some of the exposition in addition to the equations (or have a few words written in advance), to make the exposition easier to follow.

Great job on completing a 34 minute video for SoME. Normally, I don’t like to give such a professionally presented video like yours a score this low. But having watched it I think your audience might miss the point of the (a+b)+(c+d) exercise.

When you said Serge Lang had a high school level textbook, I immediately thought this must be an intro to formal math and proof writing but framed at a high school level. You also said “intro to proofs” at 0:08 so I assume that’s also your understanding.

When I imagine a middle school student who’s never seen proofs, and if I ask him to prove (a+b)+(c+d) = (a+d)+(b+c). I think it’s quite likely that he’ll do something like: peel off all the brackets so it becomes a+b+c+d, then shimmy the d two terms to the left.

The whole point of a formal proof is that you’re supposed to use commutativity and associativity formulas exactly as written. While this is what you implicitly did starting at 14:40, I don’t think you drove the point home hard enough. And if you don’t drive the point hard, the middle school student will not walk away with that lesson. The fact that (a+b)+(c+d) = (a+d)+(b+c) should be obvious enough to even to a middle school student that they may wonder what they’re learning.

The topics are a little all over the place, and the connections between them are somewhat vague. I liked the visual explanation of commutativity of addition, and the Gauss problem as well. But the associativity proof is quite tedious, and I’m not sure I follow what the integer partition example is for. Overall I’d say the presentation is nice, but the motivation for putting all these topics together needs some work.