Sunday, September 09, 2012

Hey, it's not just me

A link to my old post on third grade math is eluding me, mainly because I apparently don't remember what I titled it. (Wait!  Here it is.  Thanks, honey.) Anyway...Seems like I'm not the only one who is frustrated with common teaching methods.

One of my Facebook friends has a third grader and posted something to the effect of he is being asked to estimate the answers of things they don't know how to do yet.  She gave this example

"You have white bread or wheat bread. Ham, turkey or roast beef. How many different one-meat sandwich combinations are possible?"
 Now, this is actually a stupidly easy question.  The way you solve things like this, of course is to multiply the number of each choice you have.  So, you have two choices of bread and three choices of filling and all you have to do is write out 2 x 3 = 6.  Easy peasy.  It's even a sort of problem said child is going to encounter repeatedly throughout the course of school.

So what's the problem?

Well, for starters: her child hasn't been taught multiplication yet.  (I'm pretty sure Bobbie was taught that in third grade, but it came later in the school year.)

In this case, it's not a big deal.  As someone else said, you can make three different sandwiches with white bread and three different sandwiches with wheat bread, so this problem can be solved by 3 + 3.  My problem with that, of course, is that it's going to confuse things in the long run and make it harder.  Because eventually little Johnny is going to have a word problem like "Jane has 17 shirts, 6 pairs of pants, and three belts.  How many outfits can she make?"  You teach kids the correct (which in this case I'm fairly certain just means most efficient) way to do the problem quoted above, and they'll look at this one and know exactly what to do: 17 x 6 x 3 =  306.  If they've learned how to limp through it with addition, they're going to be sitting there looking at their paper getting a headache and starting to hate math because it's hard.

Nevermind that a lot of math isn't hard if you've been taught well.

That's one problem.  Here's the second problem: Didja catch that little word I used up there?  Estimate?  Yeah.  They're not interested in teaching this kid how to actually solve the problem, they're interested in him figuring out a half-assed way to get kinda sorta the answer.


Math is very specific.  That's the beauty of it.  There is no benefit to teaching a child to estimate the answer of 2 x 3.  NONE.  All this sort of shit does is make it harder for kids and teachers both.  It's harder for both for the same reason: when it does come time to learn multiplication, the teacher is going to have to go back and tell them "Forget all that stuff you learned earlier about estimation".  And the kids, who have internalized the estimate and the harder way to figure out the problem, are going to have a very hard time forgetting what they were taught and learning how to do it correctly.

And yet, this nonsense persists and persists across state lines.  (I'm in TX.  Friend is in the Midwest.)  As I told her, every teacher I have ever met, in person or online loves this nonsense.  Honestly, I forget the justifications, because they are stupid and I try not to let stupid ideas take up too much space in my head.  If I recall correctly, it had to do with learning to make estimates on the fly when you don't really need to know the actual answer, and/or estimating your answer first as a way to check and see if your actual answer is correct based upon how closely it jibes with your estimate.

Of course, this benefits no one in the long run.  It makes math harder (again: 2 x 3, people!), or at least increases the perception that math is difficult.  This means that kids aren't going to take any more math classes than they have to in high school, it means that more money is going to be spent on remedial courses in college as the math professors (who'd probably happily kick elementary teachers in the head for this shit) have to erase years of bad practices, and it means that the STEM fields are going to continue to suffer a lack of qualified, interested students.

{As a side note to this, my now-fifth-grade daughter brought home a worksheet the other day and showed Erik and I a multiple choice problem.  She had worked it out and it seemed that none of the answers were correct.  I double-checked her work twice, and reached the same conclusion.  So we ran it by Erik, who was able to tell at a glance that she was right.  Her teacher's explanation?  She'd just downloaded the worksheet from the Internet and hadn't bothered going over it.  So much for thinking NEISD might have higher standards.}


peter said...

I estimate that one could make several sandwiches in that instance. Am I correct?

Mattexian said...

But-but-but... she found it on the Internet, it has to be right! {shakes head} I wonder *how* the kids today learn anything in school, by what I hear about the current teaching methods. Sometimes I'm amazed that *I* turned out as well as I did, until I look at one of those exit exams for 8th Grade from 1900, and there's stuff on one of those that I hadn't heard of even in college!

rick said...

Math is, mostly, being taught by people who were, and are, bad at math.
Estimation is an incredibly useful skill. It will help you when you don't have the actual data and need to make a reasonable guess. It will help you when you punch 352x451 into your calculator. (because if it spits out 15,840 or 15,785 you need to know to punch it in again)
Estimation will help you out on those tedious multiple choice questions because you will be able to eliminate three answers that are the wrong order of magnitude or are negative when they should be positive.
But you can't teach someone to use estimation for these things if you don't know how to do it yourself. If all you know is that estimation is an important skill, or worse, that estimation is part of the curriculum then you won't be able to teach it because you don't really know what it is useful for.

Albatross said...

I think, with those choices, really just one sandwich is possible. A very big club sandwich.

With cheese.