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With that kind of thinking you might like the site/book at betterexplained.com.

allegory 12y ago
Yes I do indeed like that site and have purchased the ebook already! I have actually self-taught my oldest two their entire mathematical knowledge outside of school (bar that, physics and software engineering, I know little else) and they've done wonderfully compared to their peers because they understand the meaning and not just the method. That's the real tragedy of the education system here.
- pinkyand 12y ago
  That sounds great. Did you teach them mostly what's on better explained? Also I wonder how would math studies look if we teach people the intuition, a bit of the formalism and lot of how to use numeric and symbolic tools - instead endless rote learning.
  - allegory 12y ago
    No. I actually went through the book "Mathematics, from the birth of Numbers" by Jan Gullberg (and Mathemtics for the practical man) and extracted material and wrote my own course. This was all done before betterexplained was brought to my attention. This was trialled against my children and a couple of colleagues who were interested. I've retrospectively applied some of the ideas on betterexplained to this rather than apply it directly as it's not really suitable for people so young and without some foundation. You can't just pick up that book and apply it without some formal knowledge. I've been meaning to write the whole thing up as it's about 150 pages of hand written material at the moment. Time rarely allows for such things. One of the key things I concentrate on is not teaching arithmetic but the relationships between values and the basic rules such as the commutative, distributive and associative laws (which whilst are important in arithmetic aren't understood thoroughly without abstract concepts first). The values themselves are only of consequence once you've worked out the relations. Basically it starts with algebra.

Yes I do indeed like that site and have purchased the ebook already! I have actually self-taught my oldest two their entire mathematical knowledge outside of school (bar that, physics and software engineering, I know little else) and they've done wonderfully compared to their peers because they understand the meaning and not just the method. That's the real tragedy of the education system here.

pinkyand 12y ago
That sounds great. Did you teach them mostly what's on better explained? Also I wonder how would math studies look if we teach people the intuition, a bit of the formalism and lot of how to use numeric and symbolic tools - instead endless rote learning.
- allegory 12y ago
  No. I actually went through the book "Mathematics, from the birth of Numbers" by Jan Gullberg (and Mathemtics for the practical man) and extracted material and wrote my own course. This was all done before betterexplained was brought to my attention. This was trialled against my children and a couple of colleagues who were interested. I've retrospectively applied some of the ideas on betterexplained to this rather than apply it directly as it's not really suitable for people so young and without some foundation. You can't just pick up that book and apply it without some formal knowledge. I've been meaning to write the whole thing up as it's about 150 pages of hand written material at the moment. Time rarely allows for such things. One of the key things I concentrate on is not teaching arithmetic but the relationships between values and the basic rules such as the commutative, distributive and associative laws (which whilst are important in arithmetic aren't understood thoroughly without abstract concepts first). The values themselves are only of consequence once you've worked out the relations. Basically it starts with algebra.