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You know, it's amazing to me sometimes to read comments about education.
Everybody is convinced that things were better when they grew up, and they use the most ridiculous ways to prove it. Inevitably, in some conversation about phonics, somebody who vaguely knows "phonics are better" but has no idea what that means will say that they know phonics are better because back in the 50s everybody learned from Dick and Jane and nobody of that age is illiterate today! And when talking about math, every single time, a dozen people will falsely proclaim that nobody was poor at math back when they or their grandparents grew up (whenever that was!) and that THEY certainly learned the traditional way - like everybody did up until ten years ago! (Some people never heard of New Math?)
Today I read one that made me roll my eyes. This kid was given two numbers - say 13 and 22 - and told to estimate the answer. She added the numbers, got 35, and was predictably marked wrong. This infuriated her father, as he commented, because "schools are just teaching kids what they'll never use instead of what they need to know!!"
I would've marked that one wrong too! She didn't do what was asked, which is round each number and THEN add. And I don't know about him, but I use estimation all the time. I certainly don't add up every single penny as I shop, I go to the nearest quarter. And I always find a reasonable range before adding (though if its only two numbers I do it without thinking) so that if I get a VERY wrong number I can tell before I check! But it's something about asking kids to estimate (never mind that, if my education was typical, most parents of my generation were formally taught to do that too) that seems to irritate people. People get irritated about lattice multiplication, but they get incensed about estimating and rounding. I just don't get it!
Today I read one that made me roll my eyes. This kid was given two numbers - say 13 and 22 - and told to estimate the answer. She added the numbers, got 35, and was predictably marked wrong. This infuriated her father, as he commented, because "schools are just teaching kids what they'll never use instead of what they need to know!!"
I would've marked that one wrong too! She didn't do what was asked, which is round each number and THEN add. And I don't know about him, but I use estimation all the time. I certainly don't add up every single penny as I shop, I go to the nearest quarter. And I always find a reasonable range before adding (though if its only two numbers I do it without thinking) so that if I get a VERY wrong number I can tell before I check! But it's something about asking kids to estimate (never mind that, if my education was typical, most parents of my generation were formally taught to do that too) that seems to irritate people. People get irritated about lattice multiplication, but they get incensed about estimating and rounding. I just don't get it!
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I suppose, in this example, she's being taught to round to the nearest ten so 10 and 20 making 30 which is also a valuable skill. One just needs to clearly state the parameters of the estimation (to the .05/.1/.25/.5/etc.). You're right - it's a valuable skill but people aren't often sure as to what standard they're rounding to when they see these problems in children's work. 13 and 22 may not seem like ideal candidates for estimation but they'd be happy if their kid learned that skill before they had to start working with seven-digit numbers or strange fractions!
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I actually found that an incredibly hard sum to estimate anyway because the numbers are so easy to add together. Estimation, as you say, is very valuable when you start working with bigger numbers - or, indeed, with numbers where you're adding over a ten. So 17 + 29 rather than 13+22. (Not that I expect small children to be learning it with 7 digit numbers.)
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By the same token, nobody who can add will ever estimate 13+22 as anything but 35, because 1+2=3 and 3+2=5, and it's totally stupid to be asked to pretend that one can't see that in a single glance. It's this kind of bullshit that teaches kids to hate math for life, because it makes no sense: why on earth would anybody 'estimate' a wrong answer when the right answer was staring them in the face? What kind of a crazy person would insist that they do so, and grade them down for not doing so?
Math is supposed to be logical. The MOST important thing about teaching math is conveying the idea that this is a sytem that makes sense, that is unvaryingly self-consistent, that is NOT based on somebody else's subjective, subject-to-change opinions. If one wants to shoot that idea right out of the saddle, I can think of no surer method than weasely trick questions where the right answer is wrong and the wrong answer is right. Sheesh, it's practically Orwellian: 2+2=5 if the
PartyTeacher says it does. One wonders what John Taylor Gatto would say.The 'New Math' started in the early 60's, and it crippled the math abilities of a great many of my generation. A lot of us can't even figure a tip, balance a checkbook or calculate how much paint a room will require. There are also plenty of functionally-illiterate products of the post-WWII public schools, and plenty more middle-aged adults who read on a middle-school level or less. 'Phonics' isn't magic, it's just a system for explaining what sounds the various letters make in different combinations - which can either be explained clearly and coherently, or can be presented in an incomprehensible arcane mish-mash by someone who doesn't really understand it herself, just like New Math.
Once children start to doubt either the good sense or the good faith of the adults teaching them, they become a lot harder to reach. So, what exactly is gained by telling a student that an obviously-correct answer is wrong? Is the goal of the exercise to teach her to lie for a grade, because the grade is what matters, not the accuracy of the answer? Then fine, 2+2=5, 2+3=0, whatever, because school is about learning to do what you're told to do. whether or not it makes any damn sense. And of course it's particularly important for girls to realize that they can't be good at math, or if they are good at it, it'll just get them in trouble. 13+22=20 if that's what it takes, and "yours not to reason why".
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As far as painting a room goes, my mother in high school (a prestigious high school, too!) was once asked just that, how many gallons of paint for a room, assume every inch is covered.
So she multiplied length by width by height, looked at the answer, realized she'd been filling the room with paint, and fixed it. Then she found out she was the only one to get it right! I related that to Ana just last week (we've been doing volume of a cube, and last unit was area), and to her credit she realized the mistake as soon as I described the problem.
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"This kid was given two numbers - say 13 and 22 - and told to estimate the answer. She added the numbers, got 35, and was predictably marked wrong."
The point - the only one I see as pertinent here - is that the student was ("predictably"?!?) marked wrong for getting a correct answer. It doesn't in fact matter whether the student added or she estimated, because - as
So, I ask again, what do you say the "right" answer should have been, and why? Are you seriously claiming that an approximate estimate is "more correct" than an accurate one, or are you claiming that in a math class, the only "right" answers are those found by following the teacher's directions, so parents should shut their pie-holes and stop complaining about their children being marked wrong for getting the mathematically-correct answer some other way?
Ha, yeah, if that is so, then "predictably" is right, all right, and some other things are also predictable as a result. As it happens, they have been predicted: John Holt totally nailed that whole trip half a century ago. and called it HOW CHILDREN FAIL (http://www.schoolofeducators.com/wp-content/uploads/2011/12/HOW-CHILDREN-FAIL-JOHN-HOLT.pdf). We've been watching his predictions coming true ever since, but a lot of people still don't want to hear it.
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Ambiguous wording always indicates a weasely trap. Assume "every inch" of what is covered? Important Science Fact: paint does not stick to air. Paint sticks to surfaces; it is not possible to cover anything BUT a surface with paint.
'To cover' does not mean the same thing as 'to fill' a container, either. When one covers the potatoes in the pot with water, it's the potatoes that are being covered - nobody "covers" an empty pot by filling it with water. Neither do real people buy paint for the purpose of filling a room to the ceiling with it. When people buy paint "for a room", they buy it to paint the walls, ceiling and/or floor.
Therefore, if the question was interpreted some weasely, sideways, out-of-normal-context way in order to deliberately make the right answer wrong, I call that a shuck. Apparently your mother got a wrong answer, realized her mistake, and would have corrected it - except that the rules were not only worded ambiguously, but interpreted in a bizarre, nonsensical way, so she was declared "right" instead. And every student who got the practical, real-world, normal-context answer was declared "wrong".
It's lovely if a student understands the difference between volume and surface area. Bonus points for knowing how to calculate them without looking it up. (On the other hand, a mind is a terrible thing to waste on remembering formulae; that's why we have reference books.) But what in Cthulhu's name is the point of asking students a jiggery-pokery question that muddles the difference between volume and area?
Suppose one were to go to 5000 different paint stores, randomly selected, and ask the store managers the question, identically worded, and with no other contextual clues? After all, those are the people who sell paint by the gallon every day to people who come in and ask them how much to buy; it's their profession to know this stuff. So how much cashy money would you be willing to bet that even one of those five thousand managers would come up with your mother's "right" answer?
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A practice paper I sat for my A-Level Human Biology (something like AP I think) had a diagram of the heart which (unintentionally) had circulation going in the wrong direction. I, and one other student, corrected the diagram and then answered according to reality. The rest of my class apparently didn't notice the error - or decided to just go along with it. They awarded the marks to the two of us who corrected it, for everyone else just struck off the question.
The paper will have been cobbled together from bits and pieces of old exam papers. I presume for actual exam from which it came, that they'll have struck off the question.
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You may be right - I've read the sentence over several times, and can't tell which is meant. It seems more plausible to me that some teacher would spring a deliberately-ambiguous trick question than that a whole classful of students would believe it takes thousands of gallons of paint to paint a single room. Thousands of gallons, sheesh! had none of them ever painted anything, or even ever seen anything being painted?
It really points up the truth of John Holt's How Children Fail, because in order to come up with such an answer, they must have totally disconnected 'math' from 'reality' in their minds: it didn't matter that the answer didn't make sense, because they didn't expect it to; didn't even look to see whether it did or not. Except Connie's mother, who apparently did expect her answer to make sense in the real world of real paint.
I hope your reading of the sentence is the correct one, because it would really bite if a child who got a wrong answer and then corrected it was told that the wrong answer was "right" after all. That kind of thing was all too common back in the 60's - trick questions were supposed to "make children think"; they'd even pull crap like putting contradictory instructions on the third page of a test so one always had to read the entire test before starting on it.
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