1fast1 Supersonic January 6, 2013 Share January 6, 2013 Cliff Notes: Performance on a complex higher-level math test (PSAT) was positively correlated with activity in the part of the brain governing immediate fluent recall of very basic math (single-digit addition/subtraction). It was negatively correlated with the need to use "higher-order" thinking parts of the brain. Interpretation: The facile conclusion may be that this is not surprising: people who've practised math to the point that they basically just immediately recall (by recognition) all the basic stuff do better at math tests because of all the practice they've put in. But I think it has implications in the way young children are taught math in our schools. Singapore math used to be about "drill and kill", emphasising quick fluency in very basic mathematical skills. But now it's gotten sidetracked with all the "abstract-thinking", "model-drawing", "word-problem solving" claptrap. The problem is that the consequences of this pedagogical shift may only be apparent in a decade or so. Singapore used to be lauded as one of the countries with the very best technical subject (including math) education. People loved to use our textbooks (maybe they still do, but on the strength of past glory). Now, by changing our time-tested methods, are we risking our children's future? ↡ Advertisement Link to post Share on other sites More sharing options...
Sosaria Turbocharged January 6, 2013 Share January 6, 2013 It may be true, for all you know, because I notice that enrichment classes outside of school still emphasize a lot of "drill" method of repetition in basic mathematical operations like long division, etc. And some years after introduction of model drawing and word problem solving etc. etc., I don't think standards of maths have improved... instead I bet that many will say it declined, except maybe for elite schools - but then most of their students would be attending a lot of enrichment or tuition outside. Link to post Share on other sites More sharing options...
1fast1 Supersonic January 6, 2013 Author Share January 6, 2013 It may be true, for all you know, because I notice that enrichment classes outside of school still emphasize a lot of "drill" method of repetition in basic mathematical operations like long division, etc. And some years after introduction of model drawing and word problem solving etc. etc., I don't think standards of maths have improved... instead I bet that many will say it declined, except maybe for elite schools - but then most of their students would be attending a lot of enrichment or tuition outside. That's essentially what I'm saying. Why jump on the "new fangled" bandwagon? Why try to fix something that ain't broke? Link to post Share on other sites More sharing options...
Jman888 Moderator January 6, 2013 Share January 6, 2013 I think at lower primary, repetitive method can really still it into your brain and remember it forever! same goes to song lyric that we remember songs when we were younger, now I can't remember any recent song lyric after 1 day. Link to post Share on other sites More sharing options...
1fast1 Supersonic January 6, 2013 Author Share January 6, 2013 I think at lower primary, repetitive method can really still it into your brain and remember it forever! same goes to song lyric that we remember songs when we were younger, now I can't remember any recent song lyric after 1 day. Yes, it's very, very important to emphasise this sort of rote learning at a young age. So why are we trying to flood their hungry little brains with abstractions instead of concrete facts? Abstractions can wait till they're slightly older. Link to post Share on other sites More sharing options...
Ender Hypersonic January 6, 2013 Share January 6, 2013 (edited) But this guy use diagram to explain (a+b)2 , I can see the magic.. Last time we just take it it like that and memorize it as (a+b)2 = a2+2ab+b2 or do the tedious (a+b)(a+b)... Edited January 6, 2013 by Ender Link to post Share on other sites More sharing options...
1fast1 Supersonic January 6, 2013 Author Share January 6, 2013 But this guy use diagram to explain (a+b)2 , I can see the magic.. Last time we just take it it like that and memorize it as (a+b)2 = a2+2ab+b2 or do the tedious (a+b)(a+b)... The video didn't load for me. Is he using that a X b rectangle extended to an (a+b)x(a+b) square and adding up the areas of two squares and two rectangles? Because that's obvious to me, and I think it's trivial (in fact, I expect kids to be able to come up with stuff like that on their own, with the proper coaching). Let me ask you this: can you use the same method to justify (a+b)^3 without difficulty? How about (a+b)^4, and higher powers? In contrast, the binomial expansion (direct algebraic method) has great power and generalisability. Link to post Share on other sites More sharing options...
Ender Hypersonic January 6, 2013 Share January 6, 2013 (edited) The video didn't load for me. Is he using that a X b rectangle extended to an (a+b)x(a+b) square and adding up the areas of two squares and two rectangles? Because that's obvious to me, and I think it's trivial (in fact, I expect kids to be able to come up with stuff like that on their own, with the proper coaching). Let me ask you this: can you use the same method to justify (a+b)^3 without difficulty? How about (a+b)^4, and higher powers? In contrast, the binomial expansion (direct algebraic method) has great power and generalisability. I can only visualise 2D only.... 3D mind cannot compute the image.... Got to do the tedious (a+b).(a+b).(a+b) Edited January 6, 2013 by Ender Link to post Share on other sites More sharing options...
1fast1 Supersonic January 6, 2013 Author Share January 6, 2013 I can only visualise 2D only.... 3D mind cannot compute.... And that's sort of my point. Many people pride themselves on being "visual thinkers", until they realise just how limited their visualisation capabilities really are. The problem comes when authorities try to dictate a school curriculum that panders to the delusions of many about how "visual" they truly are. Link to post Share on other sites More sharing options...
Ender Hypersonic January 6, 2013 Share January 6, 2013 And that's sort of my point. Many people pride themselves on being "visual thinkers", until they realise just how limited their visualisation capabilities really are. The problem comes when authorities try to dictate a school curriculum that panders to the delusions of many about how "visual" they truly are. I see your point. images and diagrams tends to be alright for simpler stuff. Complex stuff, still got to do the tedious, and drilling. Link to post Share on other sites More sharing options...
Chrispie 5th Gear January 6, 2013 Share January 6, 2013 The video didn't load for me. Is he using that a X b rectangle extended to an (a+b)x(a+b) square and adding up the areas of two squares and two rectangles? Because that's obvious to me, and I think it's trivial (in fact, I expect kids to be able to come up with stuff like that on their own, with the proper coaching). Let me ask you this: can you use the same method to justify (a+b)^3 without difficulty? How about (a+b)^4, and higher powers? In contrast, the binomial expansion (direct algebraic method) has great power and generalisability. i wonder if he can explain diagrammatically (A-B)^2 ? for those who likes geeky stuff, check out numberphile or Vsauce on youtube.. very good channels to stimulate your brains. Link to post Share on other sites More sharing options...
Happily1986 5th Gear January 6, 2013 Share January 6, 2013 And that's sort of my point. Many people pride themselves on being "visual thinkers", until they realise just how limited their visualisation capabilities really are. The problem comes when authorities try to dictate a school curriculum that panders to the delusions of many about how "visual" they truly are. it is pretty much established (thus far or rather for the time being) in early childhood circles that cognitive capabilities related to abstract reasoning only really fire up in adolescence. Dogma set by Piaget. In my brief stint tutoring primary school kids, the little folks have much difficulties grasping algebra as opposed to the model method. Link to post Share on other sites More sharing options...
Lala81 Hypersonic January 7, 2013 Share January 7, 2013 model method was taught only in pri 5 or 6 last time right. Now earlier? I wasn't any good at math. But i remembered solving those difficult math question with the help of my sister/father with algebra. There was one question whereby only 2 of us solved the question and the teacher asked us to show on the board how we did it. I had to explain my solution at length but think some of my classmates still catch no ball. Lol then my friend wrote the model method on the classroom chalkboard, think they understood straight away. So there are merits to some use of the model method, at least within a limited scope. Link to post Share on other sites More sharing options...
Lala81 Hypersonic January 7, 2013 Share January 7, 2013 think we can't run away from simple mental sums. multiplication tables. In fact for someone lousy at math like me, it's the only thing i'm decent at. haha ↡ Advertisement Link to post Share on other sites More sharing options...
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