Approximate math
Posted by aogThursday, 14 September 2006 at 11:26 TrackBack Ping URL

Elsewhere in educational news I read that basics are back for math. I suppose we’ll see how long this fad lasts, and if there is any interest by the educrats to check up on its efficacy in educating students (as opposed to generated educrat jobs).

One place that I have dealt with personally recently (and therefore of immense importance) is that of estimating.
The 1989 standards tried to promote understanding of math concepts by downplaying “right answers” in favor of estimation.
For example, an elementary-school student tackling the problem 4,783 divided by 13 should instead divide 4,800 by 12 to arrive at “about 400,” the 1989 report said. The council said this approach would enable children using calculators to “decide whether the correct keys were pressed and whether the calculator result is reasonable.”
Clearly the emphasis in math should be about obtaining the correct answer. However, I have some sympathy for this view because estimating is a very powerful skill that should be taught as well. It should, however, be taught as ancillary to pencil and paper (or purely mental) arithmetic as well. It would help produce citizens would be somewhat less susceptible to the kind of propadanda that floats around these days. So much of it doesn’t survive this kind of quick and easy “order of magnitude” check. Expecting people to do problems like 4783 / 13 in their heads, or whip out a calculator, in unrealistic. I think it’s somewhat more realistic to expect that, having been taught how to do rough estimates in their heads, they might do that and realize “wow, that can’t be right”.

P.S. I was also attracted to this because it fits in to the discussion of evolution, which can only do the equivalent of rough estimates and if you expect precise answers, you’re using the wrong tool. But even rough estimates have a lot of uses.

Comments — Formatting by Textile
cjm Thursday, 14 September 2006 at 14:00

if you want to check your answer, do the inverse calculation (with it) and see if you get the original numbers.

Annoying Old Guy Thursday, 14 September 2006 at 14:52

Estimates are about 80% of the accuracy at 20% of the effort. If it’s important, I do the full back calculation check but if it’s, say, homework or just fact checking some report…

cjm Thursday, 14 September 2006 at 18:24

sure, estimating is of course a valuable skill and worth learning to do well. on re-reading the original post i think i misread it slightly. i am always telling #1 son to check his answers for reasonablness, and to back-calculate when in doubt :)

my criticism of the way the local schools here, teach math, is that they don’t stay in a given area long enough to really master it. as i am sure you know, the way to learn math, is to do problems— lots and lots and lots of problems. easily rectified by having them do more work at home, than is assigned, but it still takes time for it all to percolate down.

Annoying Old Guy Thursday, 14 September 2006 at 19:11

Yes, if your estimate isn’t compatible with your exact result, it’s time to do things like back calculate to see where the problem is. The very concept of verification is something that seems very lacking to me in modern society.

It’s interesting that the report brings up the Singapore cirriculum. It’s very heavy on the drills for precisely the reason you mention and not so oddly the Singaporean children learn math better. I know several parents (including us) who have purchased the workbooks used in Singapore for our own children. They’re remarkably cheap.

Peter Burnet Friday, 15 September 2006 at 03:49

But at what age to you start teaching estimating seriously? It seems to me that those in the “back to basics” brigade generally have a keener sense of what young children do and do not respond to. And they don’t respond well to abstracts introduced too early.

My wife teaches grade four and two years ago the school introduced one of those new math curriculums educational gurus like to inflict on kids to justify their existence. It was all about estimating and what “relates” to what, etc. Disaster. The kids were demoralized, parents couldn’t help because they had no idea what was going on, natural math students were confused and everybody was horribly bored. Fortunately it’s a private school and they were able to chuck it all fairly quickly and get back to right and wrong answers.

Look at poor cjm. He was obviously introduced to free verse far too early and is now condemned to go through life unable to capitalize.

Annoying Old Guy Friday, 15 September 2006 at 08:53

Boy One is in fourth grade this year and he’s learning estimation. I would start shortly after starting multiple digit multiplication, because it’s not useful until you have your basic multiplication tables memorized. I would agree to eschew abstraction, but estimation can be easily taught as part of getting the real, exact, concrete answer.

cjm Friday, 15 September 2006 at 15:15

two reasons for the lack of capitals:

1. it slows down my typing

2. it hurts my fingers to shift

3. it’s 31337

guess that’s 3 reasons :)

erp Thursday, 27 May 2010 at 09:21

Estimating was never taught when I was in school (40-50’s), nor when my kids went (70-80’s), but I can’t remember not estimating things, and not only calculations, but sizes and ratios. Will half a gallon of milk fit in that pitcher, will the new refrigerator fit in that space in the kitchen, etc. Measuring is for sissies.

One of my fondest memories as a parent was when my youngest came home from school to tell me that he doesn’t know why he should have to remember that 2 × 9 = 18, when all he has to do is multply by 10 and subtract 2. I hugged him and said something about an acorn …

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