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Sadly, in my experience, math is often taught theory first, followed by almost trivial or an insufficient number of examples, with more helpful examples left as

Sadly, in my experience, math is often taught theory first, followed by almost trivial or an insufficient number of examples, with more helpful examples left as exercises for the reader with no solution provided. Post-secondary math classes were actually amazing to cultivate the habit of persisting through long periods of feeling like a complete idiot. But I have to wonder what the same content would have been like had it been example-driven. It reminds me of learning a language through exposure to endless examples and internalizing rules without being explicitly taught them, versus deliberately memorizing the grammar rules of a foreign language and then applying the rules to specific examples.

dietr1ch 5y ago
I really like when they present examples and counterexamples to help you realize the subtleties of the definition. Often when presented with a definition it's easy to get fixed with examples that are too specific and then to conflate the definition with something a bit stronger.
cartoonworld 5y ago
>Sadly, in my experience, math is often taught theory first, followed by almost trivial or an insufficient number of examples, with more helpful examples left as exercises for the reader with no solution provided. Ugh. So much this. I've had so much difficulty grokking mathematical concepts and procedures in my life. In high school, I fell behind so hard. Algebra I was doable, and while learning Geometry I felt like I already knew everything about the subject. I never studied and the admins concluded that I must be cheating, given my performance in other courses. I concluded that in order to learn these things, I had to have "something to do with it". So to speak, some relatable examples to which I could apply the concepts in order to internalize the rules. This strikes me as the source of the never-ending choruses that are echoing still through so many study halls. ringing out, "WHEN ARE WE GOING TO NEED THIS???" If feels so good when the concepts click, it's like learning you had a superpower. Suddenly, the baroque, mysterious walls of lines instantly resolve into such crisp focus, it truly is an amazing epiphany, Ah-Ha! I feel like I could have really enjoyed the discipline, but I never achieved this feat in my educational career. I had problems that dramatically redirected the course of my life. This is probably why computers appealed to me so much, because of the direct cause-and-effect nature of interfacing with them. The Hacker Manifesto comes to mind, but I digress. I have Narcolepsy Type II and probably ADHD (as you may infer from my comment history) and let me tell you...
rightbyte 5y ago
I feel you ... going from high school to university math was a shock for me. Almost all proof and no handcraft. Going to lectures was a waste of time since I had no chance of understanding. I studied mechanical engineering, not a math program! How I actually learned the math was by examples and easy exercises, not understanding proofs.

dietr1ch 5y ago

I really like when they present examples and counterexamples to help you realize the subtleties of the definition. Often when presented with a definition it's easy to get fixed with examples that are too specific and then to conflate the definition with something a bit stronger.

cartoonworld 5y ago

>Sadly, in my experience, math is often taught theory first, followed by almost trivial or an insufficient number of examples, with more helpful examples left as exercises for the reader with no solution provided. Ugh. So much this. I've had so much difficulty grokking mathematical concepts and procedures in my life. In high school, I fell behind so hard. Algebra I was doable, and while learning Geometry I felt like I already knew everything about the subject. I never studied and the admins concluded that I must be cheating, given my performance in other courses. I concluded that in order to learn these things, I had to have "something to do with it". So to speak, some relatable examples to which I could apply the concepts in order to internalize the rules. This strikes me as the source of the never-ending choruses that are echoing still through so many study halls. ringing out, "WHEN ARE WE GOING TO NEED THIS???" If feels so good when the concepts click, it's like learning you had a superpower. Suddenly, the baroque, mysterious walls of lines instantly resolve into such crisp focus, it truly is an amazing epiphany, Ah-Ha! I feel like I could have really enjoyed the discipline, but I never achieved this feat in my educational career. I had problems that dramatically redirected the course of my life. This is probably why computers appealed to me so much, because of the direct cause-and-effect nature of interfacing with them. The Hacker Manifesto comes to mind, but I digress. I have Narcolepsy Type II and probably ADHD (as you may infer from my comment history) and let me tell you...

rightbyte 5y ago

I feel you ... going from high school to university math was a shock for me. Almost all proof and no handcraft. Going to lectures was a waste of time since I had no chance of understanding. I studied mechanical engineering, not a math program! How I actually learned the math was by examples and easy exercises, not understanding proofs.