1. A lot of math teaching is terrible, full of teaching formulas and abstract concepts, instead of the why's and how those abstract concepts relate to real life. A former girlfriend of mine was amazed when I taught her to treat math as something conceptual, rather than memory-based -- that she almost never needed to memorize formulas, that if she understood their meaning, she could usually just derive them on the spot. Her grades suddenly skyrocketed. No teacher had ever explained that to her.
2. Math is hard because it is exact. Fuzzy thinking is tolerated, even encouraged, in literature, political science, etc., so people can slide by with a lot less talent. Math doesn't let you do that. So, it's "harder", and can take a lot more time to learn.
3. Concepts in math build upon each other much more rigorously than in many other disciplines. You can understand the basic concepts of postmodern literary criticism in just a few minutes, without even knowing about medieval criticism. But you can't understand the basic concepts of differential equations without a massive background in mathematical concepts up to that point.
So basically, in math there's a ton of stuff (similar to other disciplines) but it's all insanely exact (unlike many other disciplines) and most of the little bits depend on having a solid understanding of all the bits that come before it (unlike many other disciplines).
uhm… I don't think you can have math without abstract concepts. Some counting on fingers yes, math—no.
And operating abstract concepts is hard. And there are no tricks, cheat-codes, *cademies to help with that.
That's why math is hard. That's why programming is hard too.
"A lot of math teaching is terrible, full of teaching formulas and abstract concepts, instead of the why's and how those abstract concepts relate to real life."
Well, I think your terrible description shows how the situation is more like "teaching math is hard".
One thing about math is that once you get it seems easy and so it's easy to assume the teach who failed to teach you before this was doing it wrong. The problem is different students fall off the wagon at different points. Too much abstraction? Too little abstract? Not enough "real world applications", too many "real world applications" (the horrid "word problems" etc).
I'll give you that one-to-one teaching is especially useful since there are so many ways to misunderstand maths.
I should apologize for saying "terrible". That was mean-spirited. The description seems a little foggy but it is hard to explain. I'd say math is full of teachers facing multiple pressures that results in them seeming terrible. They aren't terrible in scheme of things either.
1. A lot of math teaching is terrible, full of teaching formulas and abstract concepts, instead of the why's and how those abstract concepts relate to real life. A former girlfriend of mine was amazed when I taught her to treat math as something conceptual, rather than memory-based -- that she almost never needed to memorize formulas, that if she understood their meaning, she could usually just derive them on the spot. Her grades suddenly skyrocketed. No teacher had ever explained that to her.
2. Math is hard because it is exact. Fuzzy thinking is tolerated, even encouraged, in literature, political science, etc., so people can slide by with a lot less talent. Math doesn't let you do that. So, it's "harder", and can take a lot more time to learn.
3. Concepts in math build upon each other much more rigorously than in many other disciplines. You can understand the basic concepts of postmodern literary criticism in just a few minutes, without even knowing about medieval criticism. But you can't understand the basic concepts of differential equations without a massive background in mathematical concepts up to that point.
So basically, in math there's a ton of stuff (similar to other disciplines) but it's all insanely exact (unlike many other disciplines) and most of the little bits depend on having a solid understanding of all the bits that come before it (unlike many other disciplines).