3 ms·

I have strong opinions on how Calc should be introduced - visually. I think we don't cover basics like the distributive rule in school very well, and that it s

by jgord 2mo ago

I have strong opinions on how Calc should be introduced - visually. I think we don't cover basics like the distributive rule in school very well, and that it should be a much more nuts n bolts visual / measuring / counting experience. Ive attempted to outline how I think this stuff should be taught, by making a video tour of the concepts - from Counting, to Distributive rule / algebra, to Quadratics then the Derivative, here : https://www.youtube.com/playlist?list=PLEInJ-Z4qBKYxbK1Mm13grFyHRSl-0OdC https://www.youtube.com/playlist?list=PLEInJ-Z4qBKYxbK1Mm13g... All of these things are covered in some great books : W W Sawyer Vision in Elementary Mathematics Algebra by Gelfand Calculus by Thomas We have superb resources now like 3Blue1Brown, KhanAcademy and ArtOfProblemsolving.com / BeastAcademy .. so you _can_ get your kids a superb math education, even as many schools seemingly give up on teaching Algebra and Calculus.

imperio59 2mo ago
Honestly it's hard to beat how good 3Blue1Brown is at this... https://www.youtube.com/watch?v=WUvTyaaNkzM&list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr https://www.youtube.com/watch?v=WUvTyaaNkzM&list=PLZHQObOWTQ...
the-mitr 2mo ago
Of possible interest, presents basic notions of calculus as a dialogue Calculus Basic Concepts For High Schools by L. V. Tarasov https://archive.org/details/LevTarasovCalculusBasicConceptsForHighSchools/ https://archive.org/details/LevTarasovCalculusBasicConceptsF...
pelasaco 2mo ago
> so you _can_ get your kids a superb math education if their mother language is english. For my kids, mother language German, is much harder to consume such content. Both are doing well in math olympics and similar contests, but i still miss such evolving kind of content like 3Blue1Brown or Brilliant.com in German...
tgv 2mo ago
Missing are exercises, feedback and motivation. Without those, the content won't stick.
BobaFloutist 2mo ago
My experience was that the visuals were a cool distraction from familiarity with the rules/identities. People always want a shortcut to comfort, and they often want it to be that a thorough exploration of motivating examples, often with graphics, grants understanding and comfort before facility, but I've always found that a relatively cursory description of the motivating example is more than enough, and after that I just need well-organized reference materials, worked examples, and rote practice. It's frustrating, since it feels like an intelligent enough approach should be able to skip the rote practice, but it turns out that conceptual mastery requires mastery of execution, which requires familiarity, which requires practice. And I say this as someone with very strong intuition, who was always asking why I needed to practice if I already understood, who often grasped concepts immediately - turns out, I still needed practice to understand thoroughly.

by jgord 2mo ago

imperio59 2mo ago

Honestly it's hard to beat how good 3Blue1Brown is at this... https://www.youtube.com/watch?v=WUvTyaaNkzM&list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr https://www.youtube.com/watch?v=WUvTyaaNkzM&list=PLZHQObOWTQ...

the-mitr 2mo ago

Of possible interest, presents basic notions of calculus as a dialogue Calculus Basic Concepts For High Schools by L. V. Tarasov https://archive.org/details/LevTarasovCalculusBasicConceptsForHighSchools/ https://archive.org/details/LevTarasovCalculusBasicConceptsF...

pelasaco 2mo ago

> so you _can_ get your kids a superb math education if their mother language is english. For my kids, mother language German, is much harder to consume such content. Both are doing well in math olympics and similar contests, but i still miss such evolving kind of content like 3Blue1Brown or Brilliant.com in German...

tgv 2mo ago

Missing are exercises, feedback and motivation. Without those, the content won't stick.

BobaFloutist 2mo ago

My experience was that the visuals were a cool distraction from familiarity with the rules/identities. People always want a shortcut to comfort, and they often want it to be that a thorough exploration of motivating examples, often with graphics, grants understanding and comfort before facility, but I've always found that a relatively cursory description of the motivating example is more than enough, and after that I just need well-organized reference materials, worked examples, and rote practice. It's frustrating, since it feels like an intelligent enough approach should be able to skip the rote practice, but it turns out that conceptual mastery requires mastery of execution, which requires familiarity, which requires practice. And I say this as someone with very strong intuition, who was always asking why I needed to practice if I already understood, who often grasped concepts immediately - turns out, I still needed practice to understand thoroughly.