Algebra, the easy way

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1. jsmith45Apr 2022
   Yeah, I must say I prefer the math teaching approach of:

   1. Explain some problem that is difficult to solve using other techniques. Ideally the problem should be interesting, even if potentially somewhat abstract.

   2. Propose a technique to solve it, without requiring full rigor, but that allows for intuitively feeling that the technique is probably valid.

   3. Show that the technique also works on other different problems.

   4. Show show some flaws (or limits of generality) of the technique. Propose fixes for the flaw, and/or better outline where the technique viable.

   5. Now either prove the technique's validity more rigorously (need not be a perfect proof, especially if a full proof requires far more complicated mathematics) or extend this technique to be able to solve more (but eventually coming back to proving the validity).

   This sort of approach is has been used in educational videos like some of threeblueonebrown's on youtube, and I've also seen this used as a faux historical development of algebra and high school calculus in "Algebra: the easy way", and "Calculus: the easy way", which did a great job of motivating the development of most of the ideas in those courses. I'm not familiar with similar texts for higher level mathematics (which would have a different tone, since they would be targeting adults, not teens/children), but surely some must exist, right?

   This is infinitely better than the all too common higher level math textbook approach of:

   1. Here is some unfamiliar theorem, that you might not even really understand, and certainly have no clue of the relevance.

   2. Now here is how to prove the theorem. (Which you might be able to follow, but you probably don't really care about right now).

   3. Now we finally explain what the theorem is, and hint at (but may fail to show why) it might be useful.

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2. JoshTriplettJul 2020
   As a child, I greatly enjoyed "Algebra the Easy Way", "Trigonometry the Easy Way", and "Calculus the Easy Way". They present each of the subjects not as already-invented concepts that you just have to learn, but as things being invented by a fictional kingdom as they need them. I greatly prefer that style over rote memorization; I can remember it better when I know how to recreate it. Even more importantly, it encourages the mindset that all of these things were invented, and that other things can be, too.

   (Note: the other books in the "Easy Way" series do not follow the same style, and are just ordinary textbooks.)

   Also, in a completely different direction, I haven't seen anyone mention Feynman yet, and that will definitely encourage a broader view of mathematics and science.

   Or, to go another angle, you might consider things like "Thinking, Fast and Slow".

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3. JoshTriplettMar 2015
   > Professor E McSquared's Calculus Primer: http://www.math.sjsu.edu/~swann/mcsqrd.html -- I actually was poking around my mom's copy when I was about seven or so, but didn't start understanding it until later. The comics made me interested in the content, and I think was a key factor in my growing up enjoying math rather than despising it.

   I had a similar experience with "Calculus the Easy Way", and its predecessors "Algebra the Easy Way" and "Trigonometry the Easy Way", all of which I'd highly recommend. They teach the topics as though being invented for the first time by a kingdom finding themselves in need of them.

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4. dnrJul 2021
   No relation to the link, but does anyone else remember these books?

   Algebra the Easy Way - https://www.goodreads.com/book/show/6781.Algebra_the_Easy_Wa...

   Trigonometry the Easy Way - https://www.goodreads.com/book/show/2077099.Trigonometry_the...

   Calculus the Easy Way - https://www.goodreads.com/book/show/3074478-calculus-the-eas...

   I read these in 5th grade or so and learned most of middle school and high school math just from those.

   They're written as a fantasy novel in which the characters discover the relevant math concepts as part of the story. I know, you're thinking that's a silly gimmick and it can't possibly be any good, but it was actually done quite well. At least until the later parts of Calculus where the situations have to get pretty contrived.

   Highly recommended, at least for precocious kids who like math and fantasy novels.

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