ANFP:
Extraversion (52%) ---- Introversion (48%)
Sensing (26%) ---- iNtuition (74%)
Thinking (16%) ---- Feeling (84%)
Judging (5%) ---- Perceiving (95%)
9w1 so/sx/sp
There's so much I could say about this topic, but all I can really say is that Math education in the U.S. is in a downward spiral and I don't see an easy way to turn it around. (Heh, I'm usually not this pessimistic, but in this case it's really bad.)
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What you're observing is the academic discipline of "Education" on a desperate search for relevance.
The basic techniques of teaching elementary math have been known for centuries and are proven to work, generally speaking. This messing about with technique is foolishness, but it serves to justify doctoral dissertations and sell textbooks.
Kumon North America
Highly recommend (well, if it's the same as 15-20 years ago )
I should absolutely start an online version of this for parents.
I saw the flaws in the lattice method and random adding of multiples, but I actually thought that one of the methods they showed for long division made a lot of sense, because I've always struggled to do it the regular way. (In fact, I just use a calculator if I'm asked to divide a number by anything other than 2 or 4.)
I do think that math should be taught as an algorithm whenever possible, however. Algorithms are the easiest things to understand, because they do the same thing to the numbers, in the same order, every time.
Kumon methods had been a childhood nightmare for me to tell you the truth. I've been forced through that for a while and I absolutely hated it. I understand the concept that repeat practice helps to re-enforce learning... but endless repetition for the sake of repetition is dreadful from the student's point of view. If I understood the concept, I don't need additional practice. I ended up refusing to do all of the exercises... at that point my parents saw the need to switch to something else.
I can see that the Kumon method can help some kids though... but it's just not for everyone. At the end of the day... education needs to be tailored based on the child. There's not insufficient resources to do that effectively. =/
Oh yeah, I remember excessive practice. In Grade 3 we did two digits times two digits, then three digits times two digits. At the end of the three digits times three digits I put together a problem with six digits times five digits, solved it, then underneith I wrote: "I get this now, can we please move on?!"
Dreams are best served manifest and tangible.
INFP, 6w7, IEI
I accept no responsibility, what so ever, for the fact that I exist; I do, however, accept full responsibility for what I do while I exist.
I hate hearing this. You really do need to do the problems. Over and over and over again. Concepts are the smallest part of math - it is only by doing that we gain an in depth ability to do the math. Even now I'm realising how true that is - I'm working through annuity problems for my financial math stuff - I learnt this a decade ago. I learnt it again when I was taking my CSC (securities courses). And yet, when I started doing it now, I realised that I barely knew it. They taught it but I never used it. Now I have reams of excerzies - I do every practise excersize - and I've saved up a huge amount of problems for my test review. But it isn't just about marks - I've been able to start making use of them - I've solved problems that took me much longer before... not because I didn't know the math but because I didn't have the practical experience in doing it. The difference is astounding - this is true at every single level of (practical) math.
What I hated the most was how slow school moved relative to Kumon - when I gained expertise, I moved up... in school, I got held back by the rest of the class (meaning I can relate to runvardh).
I fought and struggled with my parents for years and years when suddenly I realised I'd gone from the bottom to the top of the class... beyond the class - to this day I can do math in my head that people don't believe is possible. It isn't unique to me either - I still know a couple of people who were in it as children. The "doing" is true for anyone - in elementry school all the way to university. Doing is what makes you good at something.
In hindsight, I wish my parents had done this with languages - it might of helped me out with my weakest point. Hard to do, I suppose... and I wasn't exactly the type to sit down and put up with it either.
Hm, I never really saw the need for those after-school programs. TBH I never even did the work the school wanted us to do, let alone anything extra, and I was always at the top of my class for math and spelling/reading. Maybe it would work for kids who struggle with it though.
Actually, even if you struggle I think it'd be better to teach kids yourself rather than relying on a special tutoring program. I still remember my dad teaching me how to do math problems that were several years ahead of the ones I was doing in class. In fact if I remember correctly, I always knew how to do problems before I was taught how in class, other than long division. I think that's a more effective way to teach kids.
I do agree that you need to practice until you completely get something though...it's more of an issue with complicated things though, since the simpler things you'll be practising in the course of doing more complicated things, usually. I always hated repetition that went beyond the point of knowing something inside and out though.