>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...
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...