Drill and Kill?
Sep. 21st, 2010 06:45 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
velvetpageThis morning's offering: a brief discussion of This article. Exciting, I know.
The article concludes that drilling for some knowledge, some of the time, in a way that isn't boring, is necessary to academic achievement. I agree. However, I'm going to go one step further and say exactly when material should be drilled, and a little bit of how and how much.
First, when: drill should only take place after the students thoroughly understand how a process works. Drilling is then useful to fix the specifics in their heads. For example, I will never drill multiplication for a kid who can't line up a rectangle made of blocks into an array that shows a given multiplication fact, or draw that same rectangle on graph paper, or group objects in a set number of groups with a set number of pieces to show how multiplication works. While they can probably learn the facts by rote even if they don't understand them, they won't know how or when to use them and they won't be able to manipulate them - for example, they will struggle with reversing the multiplication fact to get a division fact.
This is one of the biggest mistakes teachers make in math: if a student doesn't grasp a concept on the teacher's timetable, the teacher pushes ahead anyway, saying something like, "Just learn it." If they don't have the conceptual framework in place to learn it, then they won't, and years later some other teacher is going to discover they don't know this, and that they don't know any of the things that naturally flow from it, either. When a student truly doesn't get it, the best thing to do is put more and more things in place to help them see the connection you're trying to paint for them, until the light goes on. After they get it, THEN you drill them.
Second, how: for heaven's sake make it FUN. I don't care how you make it fun. Games between two or three students are a great way to do it. Flashy computer games to drill those facts are wonderful if you have access to computers in your classroom. Some kids like flash cards. Most kids like the feeling of being tested briefly on something they know, and getting a reward for it - a quick oral test of one multiplication table gets them a sticker on a chart and they're puffed up with pride. And there's nothing wrong with that. The two keys are that it doesn't feel like heavy work, and once they know a certain set of facts, they stop practising those facts. Giving students work to do that they already know is just as soul-killing as giving them work to do that is way above what they know.
Third, how much: it should be less than 20% of a math program. The bulk of math instruction should be problem-solving, analyzing strategies for problem-solving, and extending the problems. Drill fills in the gaps in this program. It does not replace it, ever, even for low-functioning students, because the studies show that teachers tend to underestimate the abilities of those who came to them with a label of "level 1" student already attached. So we give all students the opportunity to problem-solve, adjusting the numbers or number of steps in the problem rather than eliminating the problem itself, and follow up with drill for those students in about the same quantity as we do for those more able. I can guarantee that sometimes, those level 1 kids will surprise their teachers if they're given a chance to do so.
The article concludes that drilling for some knowledge, some of the time, in a way that isn't boring, is necessary to academic achievement. I agree. However, I'm going to go one step further and say exactly when material should be drilled, and a little bit of how and how much.
First, when: drill should only take place after the students thoroughly understand how a process works. Drilling is then useful to fix the specifics in their heads. For example, I will never drill multiplication for a kid who can't line up a rectangle made of blocks into an array that shows a given multiplication fact, or draw that same rectangle on graph paper, or group objects in a set number of groups with a set number of pieces to show how multiplication works. While they can probably learn the facts by rote even if they don't understand them, they won't know how or when to use them and they won't be able to manipulate them - for example, they will struggle with reversing the multiplication fact to get a division fact.
This is one of the biggest mistakes teachers make in math: if a student doesn't grasp a concept on the teacher's timetable, the teacher pushes ahead anyway, saying something like, "Just learn it." If they don't have the conceptual framework in place to learn it, then they won't, and years later some other teacher is going to discover they don't know this, and that they don't know any of the things that naturally flow from it, either. When a student truly doesn't get it, the best thing to do is put more and more things in place to help them see the connection you're trying to paint for them, until the light goes on. After they get it, THEN you drill them.
Second, how: for heaven's sake make it FUN. I don't care how you make it fun. Games between two or three students are a great way to do it. Flashy computer games to drill those facts are wonderful if you have access to computers in your classroom. Some kids like flash cards. Most kids like the feeling of being tested briefly on something they know, and getting a reward for it - a quick oral test of one multiplication table gets them a sticker on a chart and they're puffed up with pride. And there's nothing wrong with that. The two keys are that it doesn't feel like heavy work, and once they know a certain set of facts, they stop practising those facts. Giving students work to do that they already know is just as soul-killing as giving them work to do that is way above what they know.
Third, how much: it should be less than 20% of a math program. The bulk of math instruction should be problem-solving, analyzing strategies for problem-solving, and extending the problems. Drill fills in the gaps in this program. It does not replace it, ever, even for low-functioning students, because the studies show that teachers tend to underestimate the abilities of those who came to them with a label of "level 1" student already attached. So we give all students the opportunity to problem-solve, adjusting the numbers or number of steps in the problem rather than eliminating the problem itself, and follow up with drill for those students in about the same quantity as we do for those more able. I can guarantee that sometimes, those level 1 kids will surprise their teachers if they're given a chance to do so.
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(no subject)
Date: 2010-09-21 12:15 pm (UTC)Tatiana has 20 words a week this year and the words are mostly words that have to actually think about. This week's words include boisterous, wilderness, illuminate, access, idle, brilliant, earnestly and so on. Spelling has always been her weakest subject area. Trying to get these words learned has been an exercise in frustration for both of us. First week she got an 85, second week she got 100. Not sure what she got last week. The words are also their vocabulary words.
(no subject)
Date: 2010-09-21 10:49 pm (UTC)One, however, is global: spelling lists don't work. The vast majority of students will still get those words wrong when they use them in context, if the spelling list was the first place they came across those words. Students learn to spell correctly by using words in context and remembering them in context. So the key is almost always contextual; the learning style will help pin down which type of contextual learning will work best for her. For example, I'm a strong oral learner and I like to syllabify, so for me to spell something correctly, I will break it down into syllables or sometimes individual letter sounds and pronounce it out loud as I write it; for years I couldn't spell "beautiful" without saying to myself, "Bee-ah-oo-tiful" every time I wrote it. (That ended after I acquired French well enough to have the sound "O" associated in my brain with the letters "eau." When that happened, I switched to mentally pronouncing it "bO-tiful.") That technique might not work for her, though, if her learning style is very visual or if she doesn't like lists of concepts as a way of organizing information.
(no subject)
Date: 2010-09-21 11:02 pm (UTC)What we did last week was I made post-it notes of the words and put a few in the places she is most often so she had to see them and could practice them. Then we spelled them aloud when we were driving in the car. Then everyday I gave her the words and she wrote them out and the ones she misspelled she wrote 5 or 10 times each. They are her vocab words too so she is using them in context in class and is tested on the meaning as well.
She strongly prefers math and science. She is extremely advanced in reading. But spelling drives her crazy - she likes her rules to stay consistent. She wants phonics to make sense and for there to not be so many exceptions to everything. She was about 4 I think the first time she argued with me about the word have. There's that pesky silent E at the end and she insisted that it should either be pronounced HAY-VE or spelled h-a-v. Then she wanted to learn to spell in a different language that makes more sense. I suspect she'd be very good with Russian.
I chunk words when I learn them. When we were doing permanent last week both chris and I kept telling her there's a man in the middle because she wanted it to be permenent. She doesn't seem to do that. It drive me crazy to listen to her spell out loud because the way she breaks words up makes no sense to me.
(no subject)
Date: 2010-09-21 11:22 pm (UTC)I'll look some stuff up and get back to you.
(no subject)
Date: 2010-09-21 10:53 pm (UTC)The contextual for me is based in the morpheme more often than not; that is, if I can connect the word to a word family, I can figure out how to spell it (and a few dozen related words besides.) That's why "bO-tiful" works for me; I'm connecting it to its French origin. When I can't do that, the next best method for me is auditory or oral, which is where I start pronouncing things in my head according to how they sound. I put the two together when spelling words like "definite," which to me becomes "de-finite", as in finite mathematics. I don't mistake the second i for an a that way.
(no subject)
Date: 2010-09-21 11:08 pm (UTC)I tried doing word families with her early on but she didn't like that as a concept so much either.
I've never been able to pin point her learning style (or mine really) but I think that they are different and that that is why we butt heads so much.
(no subject)
Date: 2010-09-21 10:08 pm (UTC)Although, at the high school level about the only things we DO drill are the quadratic formula, the Pythagorean theorem, what conjugates are, the trig double-angle identities, and the product, chain and quotient rules for derivatives. So about one thing per year from grades 8-11, and three formulas in grade 12.