by smallpoxgirl » Tue 26 May 2009, 10:40:32
$this->bbcode_second_pass_quote('Schmuto', '3'). One kid's yearly math alotment seemed to be about 50% "estimation" exercises. Yet her actual math skills did not seem to be improving (that is, just add the numbers!!).
I'm kinda split on this one. I've seen some of the "new math" text books and they are the pinnacle of stupid. Clear example of the axiom that the enemy of "good" is "better". OTOH, I do feel like estimation is one of those skills that people woefully lack. If you walked up to people on the sidewalk and asked them for the square root of 17, I bet not more than 1% could give you any sort of reasonable answer. There are a lot of times in life when having an innate sense of numbers and having some idea whether a figure is "about right" or "way off" is a very useful skill. Often a good estimate is all that you really need. When I'm at the grocery store, I always have a running estimate going in my head, and it really helps with buying decisions. I don't need to know my running total down to the penny, but I'm usually within 20%. That's good enough to be very helpful. What I don't know is how you teach that. Most people approach math in a very mechanical way and just don't seem to "get it". They follow the instructions cook book style, but they don't ever have the "ahh ha" moment where everything makes sense. I think probably the way to do it is to teach them the actual precise math, and then force them to drill estimates.
There are also helpful tricks that I can see teaching.
Square root 17. Well 4 squared is 16. 5 squared is 25, so it's pretty close to 4, but a little higher. 4.1 is a reasonable guess. What's 4.1 squared? Well...I can't do long multiplication that well in my head, but I know that (x+y)^2=x^2 +2xy+y^2. So 4.1^2=(4+0.1)^2=4^2+2*4*0.1+0.1^2. So that's 16+2*0.4+0.1^2. 0.1^2 is so small I'd probably just disregard it. So 4.1 squared is about 16.8. By the same method 4.2 squared is about 17.6, so as our next iterative estimate, we might guess that the square root of 17 is about 4.13?