Sep. 22nd, 2010

Math rant.

Sep. 22nd, 2010 01:54 pm
sarasvati: Greyscale picture of Kido Jou, studying at his desk (study)
Math Education: An Inconvenient Truth.

Some good points are made here, but it also makes a few assumptions that are blatantly unfair.

The person speaking clearly favours the traditional method of teaching, and that's fair. Personally, I find those ways to be the most effective too.

Because that was how I was taught them. It only makes sense that a person will be more familiar with the things they're taught than with the new concepts that come along afterward. The entire video seems to be targeted to parents who want to help kids with their math homework rather than how the kids themselves actually learn. ("Cluster? What's a cluster?") I'm sorry, but that shouldn't be the big concern here, that parents don't understand the methods a child is using to learn. And obviously these terms have to be expained to the children somehow, so how hard would it be for a parent to look it up and follow along from there?

Just as the new ways are not always best, it doesn't mean that the old ways are. There's room for improvement and change in just about everything.

She does make some points about kids not coming out of math class with a sufficient grasp of the material being taught, and I agree, sadly, that this is true. I think that there are more things at the root of this issue than a few teaching tools, however. She demonstrates using books that are being used in only a few schools, but it seems to me that educational standards are declining all over North America, and that includes schools that use a more traditional method of teaching. The fact that a lot of North American parents don't treat school as an educational experience but rather a government-sponsored babysitting service is a big problem. Lack of motivation of the students is another. Low attention spans caused by the sound-bite/social-media generation.

One thing I had issue with in this video was her demonstration of a question in one of the books, which asked a student to show two ways in which they solved 36/6. She says that a child who simply writes in the answer will not be given credit for their work. The answer is not good enough.

I wonder if she never went to school and took math tests where students did not get credit for questions that only gave the answer without showing their work. I know I did. The reason for that was because teachers couldn't trust students not to have cheated. It's one thing to memorize the answers to a test. That doesn't show you've learned enough to understand what you're answering. This bothered me sometimes because I often ended up knowing the right answer without knowing exactly how I knew it. In trying to muddle my way through the algorithm needed to show my work, I'd arrive at a different answer and it would be wrong. But it would have also been wrong to just put down the right answer, so I was often in a catch-22 situation.

Of course, I had some truly crappy math teachers in high school. In grade 11, the teacher loved to yell at the class that we should already know what she was trying to teach us because it was grade 10 math. According to her. I wish I'd had the guts to stand up and ask her why, then, was she teaching us grade 10 math at the end of the grade 11 year...

Anyway, personal gripes aside, when you get further down the mathematical road, people are asked to show their work, to show holw they solved the equation to prove that they didn't cheat somehow. Getting kids to start early on that, to show that they have a grasp of the concepts they're using, isn't too much to ask for.

I can see another benefit to asking students to show their work in two different ways. It may be time-consuming, but it helps to eliminate mistakes. If you get two different answers using two different algorithms, you know you've made a mistake somewhere. Get it wrong when you only have to show one algorithm, you may not know you got it wrong until much later.

It also allows for students learning better in different ways. The Trellis method the video scoffs at actually helps a friend of mine to not fail more than once. Not just failing a test, mind. Failing an essential class that would require her to repeat a whole year of school. Someone taught her the Trellis method and her grades picked up incredibly. It may not be the most efficient method known today, but for some people, it works. And if a person arrives at the right answer in the end (which is often what is wanted by the people who claim that basic math concepts should be taught by rote memorization), then where's the harm?

The Trellis method also nicely condenses longer equations into a neat box when a student is required to show their work. Oh noes!

I admit I have a problem with the teachers' guides saying that math isn't a big deal because it can all be done by a calculator anyway. That is, sadly, the way the winds are blowing, and honestly, a math textbook shouldn't be saying that it's okay to reach for a calculator every time you can't figure something out. There's a problem there that needs to be addressed, yes.

But to get annoyed because the book spends some pages teaching students how to use a calculator? My math books had those, at least sometimes. Partly so we could learn how to use them as a time-saving tool, and so we could learn how to use them properly in the first place if we ever needed them. But calculators were not allowed during tests, which meant that to pass the test in the first place we had to know what we were doing.

Maybe this rule has been relaxed somewhat in recent years. It's certainly possible. It wouldn't surprise me. I know that there are far too many cashiers who can't figure out correct change without their cash registers or a calculator to tell them, true, but let's look at the big picture here. Those people range in age groups from those who've just graduated high school to people about to enter retirement homes. And everything in between. Which means that there are still a lot of people taught the traditional methods who can't apply math to everyday life either. I don't hear traditional methods of teaching being blamed for why a middle-aged person can't subtract $9.57 from $20 and come out with the right answer.

Poor math skills across all age groups are why people who work at stores will often just give out the answers to skill-testing questions on contests, rather than let the customer muddle it out for themselves. So many people get it wrong, and those questions are designed to be fairly easy.

To me, this is the same problem that was encountered when "New Math" started hitting schools. I looked up some stuff on New Math. Some of it was needlessly complicated, by my way of thinking, but other bits, fascinatingly, were the very things that I learned in school myself. Take a look at this video parodying the way New Math taught subtraction. That's the way I learned it. But this was so revolutionary at the time that apparently a lot of people couldn't make heads nor tails of it. Particularly the parents, of course, who were taught things a different way and were resistant to change.

Multiplication, from what I saw of New Math, was taught involving concepts like getting 4 groups of 3 things per group in order to figure out 4x3. That's the way I learned it too. It's a good way to teach the concepts behind what's going on when you do more complicated equations later, and some people have an easier time grasping abstract concepts like numbers when they're presented in a visual and tactile way. I was also taught a bit of rote memorization for my times tables, but not very much, and the grouping method allowed me to see what I was working with. It made it come together in my mind so that I actually understood the question instead of just giving the right answer.

Remember the problem I meantioned earlier with sometimes knowing an answer but not knowing how I knew it? Especially in high school, which was where that problem really kicked up, we were taught the formula, made to apply it to problems, then moved on. No explanation of what the numbers in the formula meant. No real clue of what we were doing with them. It must have been assumed that we all either knew it in advance or that the meaning didn't matter. Likely the latter (given that once you passed the learning of basic concepts, no teacher I had ever really bothered to explain the subtleties of even the new concepts we dealt with), though that makes having to show the work even more annoying, because even solving the problem in steps didn't have to be understood so much as just written down in the correct way.

I personally don't see a problem with introducing a few new problem-solving skills to students. If their parents don't understand it, then perhaps they can learn it instead of complaining about it. It's commonly accepted that all children learn in different ways, and that to expect each child to have the exact same learning potential as every one of their peers just doesn't cut it. (At least, that's the philosophy here. Other places, not so much.) Where one child has a skill with words, another may have a skill with numbers. So where, I ask, is the harm in showing a few alternate paths to the same destination, so long as the children understand how they got there in the end.

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