Summer of Math Exposition

I was impressed by how integration by parts was explained visually using shapes. I think this video would be especially helpful for students who are learning calculus for the first time and find it difficult.

Very annoying intro. Confusing visuals especially when numbers bounce around and become unreadable. I also disliked every single analogy given in the video. Half-baked “intuitive” arguments give no understanding. The main method has visuals that are too stylized to have clear meaning. Some simpler diagram notation would have sufficed.

Good graphics, it does seem like this is just rehashing the way we learned this in school? It’s been awhile.

I am a computer teacher so the ‘chair and bush’ idea feels very close to the method of f finite differences use by Charles Babbage for the first computer.

In addition, the animations are fantastic and exactly match to the description. The animations are not just visual candy.

Last, I love the MarvelStudio after-trailer scene at the end that teases the next video.

This is certainly a novel way to present differentiation. You get full marks for originality. I would have gotten more out of the video if you had spent more time explaining your visual method. To be honest, I didn’t understand the rules. You assumed the viewer had some knowledge of calculus and functions such as exp and cos. Wouldn’t that imply that they were comfortable with differentiation? Perhaps you could have spent more time describing the benefits of your visual method.

Video was kind of hard to follow, the blurry lines did not help, I was confused about which ones were supposed to be straight and which ones were supposed to be curved, or what the method was supposed to be doing until you showed some examples. Neat technique though.

• I was a little confused about the initial chain rule explanation. Why is it that when $t \approx t_0$ we have $g^\prime (t_0)t + g(t_0) \approx g(t)$?
• I appreciate the creative distinctiveness of using the impressionist brushstrokes for lines, but when your goal is to differentiate between straight lines and curvy lines, it isn’t the best choice.
• Once you get to explaining what the method is, I think it makes sense and is a useful visual aid for students doing complicated derivatives.
• Although… you do say in the beginning of the video that understanding > memorization. Your method is nice, but it does substitute an understanding of why the chain/product rules are true, for rote memorization of some shapes that are used to keep track of the differentiation. There’s nothing wrong with that! But it does contradict your initial thesis a bit.
• The critical points example, while useful, doesn’t really have anything to do with differentiation. It feels tacked on at the end.

The beginning felt a little fast with the chain and quotient rule, but after that the explanation speed and visuals were great, I loved the intuitive and visual approach to differentiation.

This video does many things well: the narration is great, the visual/art style is great, offering a fresh perspective on a well-worn topic is great. I do think there is a big issue with this video, and I don’t want it to sound harsh, but it’s what I would want to hear if I was the creator. The stated motivation for the video was not accomplished in my mind. The motivation was that memorization isn’t the best way to learn math (agreed), but the approach offered is just a different, more artsy technique for memorizing than the standard one. You have found an approach that is sound and works great for you (and probably some others), but I’m imagining trying to tutor someone with this technique and I think most students would be very lost if it’s their first time with the material.

A few specific comments about the video:

1. The tofu animation is too fast, I’m dizzy. The tofu product rule doesn’t sense to me, it just seems like memorization again. Why do we divide by dt? Why does the second order term vanish?
2. The way functions are drawn in an artsy way is fun, but the color choice is odd, why do the function labels have different colors from the graphs at 2:40?
3. I don’t see how the final part of the video about critical points is related to the rest of the video. Is it because of how it decomposes functions and examines each piece individually? Someone learning this for the first time would probably be confused about why a monotonic function preserves critical points as well.

I hope this doesn’t discourage you from making more videos, what you’ve made here shows great potential for offering a new view about math on Youtube, which is very difficult to do, given how saturated it is.