# I need education tips: If you struggled with math, what helped you get through the abstract and repetitive parts?

January 18, 2005 9:01 AM Subscribe

The math threads got me thinking; maybe someone can help my students? [+]

I teach math to violent repeat offenders in juvenile corrections, mostly sixteen- to eighteen-year-olds. I just returned an 8,000 USD Lego-based robotics curriculum because it doesn’t involve enough arithmetic. It needs to be replaced, and I want to have the most exciting math class ever.

I have to consider my students’ various learning difficulties/disabilities (they test as second through ninth graders in one class). On the other hand, I don’t have to deal with standardized testing, No Child Left Behinds, graduation standards, or any other restrictions on the format of the class. Right now, we’re getting by with freeware math games and individual tutoring.

So, if you struggled with math, what helped you get through the abstract and repetitive parts? Textbooks, experiential education, games, science experiments,

I teach math to violent repeat offenders in juvenile corrections, mostly sixteen- to eighteen-year-olds. I just returned an 8,000 USD Lego-based robotics curriculum because it doesn’t involve enough arithmetic. It needs to be replaced, and I want to have the most exciting math class ever.

I have to consider my students’ various learning difficulties/disabilities (they test as second through ninth graders in one class). On the other hand, I don’t have to deal with standardized testing, No Child Left Behinds, graduation standards, or any other restrictions on the format of the class. Right now, we’re getting by with freeware math games and individual tutoring.

So, if you struggled with math, what helped you get through the abstract and repetitive parts? Textbooks, experiential education, games, science experiments,

*Donald in Mathemagic Land*? What should I buy? What was just a gimmick?

Probably best not to encourage gambling in a place where some kids' lives may have been ruined by it.

Brainteasers and math games are awesome. So is pattern finding. One of my favorites: How many squares are on a checkerboard? 64? Nope. I mean TOTAL squares. so then the kids have to find the number of them and patterns emerge. It's fun to watch the lightbulbs go off.

Also, talk about Fibonnacci sequences in nature. Bring in flowers and have them count petals. Talk about the way that math isn't just something lame in books, it's all around you. The only reason people bothered putting it in books was to explain stuff they SAW. It's not an exercise to torture anyone, it's just a way to explain what's already there.

Email me for some interesting/fun ways to teach at the points where kids get stuck (universally, if a kid gets "stuck" irrevocably in math, it's on either arithmetic, fractions/decimals, or the introduction of variables. And I can tell you how to get past all of those but it'd take more space than is really possible here. All of them can be made fun, though).

Also, even if the kids have math levels from 2nd-9th grade, don't hesitate to incorporate algebra. I can give you ways to do this so that they won't even know what they're doing.

jeanettev (at) gmail (dot) com. I'd love to help you out.

posted by u.n. owen at 10:37 AM on January 18, 2005 [1 favorite]

Brainteasers and math games are awesome. So is pattern finding. One of my favorites: How many squares are on a checkerboard? 64? Nope. I mean TOTAL squares. so then the kids have to find the number of them and patterns emerge. It's fun to watch the lightbulbs go off.

Also, talk about Fibonnacci sequences in nature. Bring in flowers and have them count petals. Talk about the way that math isn't just something lame in books, it's all around you. The only reason people bothered putting it in books was to explain stuff they SAW. It's not an exercise to torture anyone, it's just a way to explain what's already there.

Email me for some interesting/fun ways to teach at the points where kids get stuck (universally, if a kid gets "stuck" irrevocably in math, it's on either arithmetic, fractions/decimals, or the introduction of variables. And I can tell you how to get past all of those but it'd take more space than is really possible here. All of them can be made fun, though).

Also, even if the kids have math levels from 2nd-9th grade, don't hesitate to incorporate algebra. I can give you ways to do this so that they won't even know what they're doing.

jeanettev (at) gmail (dot) com. I'd love to help you out.

posted by u.n. owen at 10:37 AM on January 18, 2005 [1 favorite]

Spatial understanding was my foundation of math understanding, trigonometry to differential equations. Rotation games? Drawing of the functions? Really basic knot theory, in hands?

posted by sled at 10:39 AM on January 18, 2005

posted by sled at 10:39 AM on January 18, 2005

How about...

-- computer programming, focusing on making games. You can use Flash, which is inexpensize (or free for 30 days) and program a game like asteroids, which needs trig to work.

-- how about a real-life simulation, in which the students set up a store and keep its accounts?

-- a stock market simulation. Does the hollywood stock exchange still exist?

-- focus on making pictures in math (i.e. fractals).

-- there have been some popular books that deal with "The Physics of Star Trek" or "The Physics of Lord of the Rings." It would be fun to grab some piece of pop culture -- something the kids like -- and work on the math related to it. I.e. work out Harry Potter's velocity on his brookstick.

-- all of the above (and more). The truth is, no two children will enjoy math in exactly the same way. So the more techniques you can throw in, the better.

posted by grumblebee at 10:44 AM on January 18, 2005

-- computer programming, focusing on making games. You can use Flash, which is inexpensize (or free for 30 days) and program a game like asteroids, which needs trig to work.

-- how about a real-life simulation, in which the students set up a store and keep its accounts?

-- a stock market simulation. Does the hollywood stock exchange still exist?

-- focus on making pictures in math (i.e. fractals).

-- there have been some popular books that deal with "The Physics of Star Trek" or "The Physics of Lord of the Rings." It would be fun to grab some piece of pop culture -- something the kids like -- and work on the math related to it. I.e. work out Harry Potter's velocity on his brookstick.

-- all of the above (and more). The truth is, no two children will enjoy math in exactly the same way. So the more techniques you can throw in, the better.

posted by grumblebee at 10:44 AM on January 18, 2005

I really enjoyed Donald in Mathmagic Land. In my experience teaching decimals and fractions and lots more math concepts becomes way easier if you frame it in terms of money. Half of one is .5 might seem weird and illogical to someone with a 2nd grade math proficiency, but talk about how half a buck is 50 cents and things start to make sense (cents?).

posted by bonheur at 10:46 AM on January 18, 2005

posted by bonheur at 10:46 AM on January 18, 2005

*Email me for some interesting/fun ways to teach at the points where kids get stuck (universally, if a kid gets "stuck" irrevocably in math, it's on either arithmetic, fractions/decimals, or the introduction of variables. And I can tell you how to get past all of those but it'd take more space than is really possible here. All of them can be made fun, though).*

I'd like to know your thoughts about this too, u. n. owen, both as a professional teacher and as someone who got stuck on many of these concepts as a kid. I wouldn't mind getting an email from you if you have the time (I'll email you if you want, so that you can reply), but I think it would be cool for you to post here. So what if it's a long post? It related to the question.

posted by grumblebee at 10:46 AM on January 18, 2005

*In my experience teaching decimals and fractions and lots more math concepts becomes way easier if you frame it in terms of money.*

When I was a kid, teachers often related math to money. Maybe I was an off kid (well, no maybe about it...), but I really didn't care about money that I didn't have. It would be great if you could give each child $1000 and then play all kinds of games in which they could lose or gain money, but I doubt that's in your budget.

But I think monopoly money would work just as well, as-long-as it leads to some real rewards in the end. Maybe there could be some special treats or priveleges or awards that the kids could "buy" after a period of time.

You could then set up classroom games, using the money.

I actually disagree that gambling would be a bad idea, as long as you REALLY teach the math behind casino gambling. If you study that math, you learn that it's foolish to risk money in a casino, because the odds are always against you. One of the reasons so many people have gambling problems, is because the don't get this.

posted by grumblebee at 10:51 AM on January 18, 2005

Ok. This is what I just gmailed, and then I'll put more about those particular sticking points in a moment.

I find that the biggest opposition to math learning in kids comes from the fact that they think math gets more advanced TO BE HARDER, when actually the opposite is true. Math is a process of learning shortcuts in order to simplify more difficult problems. Explaining that to kids is half the battle -- we're not teaching you variables to

make your life difficult. We're not showing you fractions to make you fail. We're showing them to you because once you know how to use them, things will be easier.

To introduce it practically (which should be done first), it's like learning a new shortcut to your house. The first time you use it maybe you'll get lost. The second time, you'll probably do better. Soon it'll be second nature and you'll wonder why you ever went the long way.

To introduce this idea mathematically, talk about counting versus adding - and how if you wanted to put together 2152 and 6745, it'd take forever to count it. Addition's hard to learn at first - but it sure beats counting. Ditto for multiplication. Adding a bunch of groups of 8 together takes a long time. Multiplying 12 by 8 is easy once you know how. And explain that ALL math is like that.

What I talked about with fibonnacci numbers really fascinates kids who think math comes only from textbooks and maybe 25% off clearance sales. To show them that math is part of the innermost fabric of nature is pretty neat.

If you're teaching geometry, be hands-on. Pi is 3.14..., right? For some kids, it's enough to tell them this. But don't be content with that because you'll lose an awwwwful lot of them. Cut out actual paper circles. Measure the diameter, then measure the circumference

with a string and a ruler. Use calculators to divide. When the kids figure out that no matter how big the circle is, the ratio's always the same, THAT's when you explain pi. Don't even bring up the word until then - it'll just be confusing.

Let them go through the same process that people did long ago to determine it. Then say, "hey, people back thousands of years ago realized this, too. And they thought it was so important that they gave that number a name." Then, by the time you've introduced the NAME for pi, they've already visualized the concept and have it more

solidly down than most kids ever will. They've also once again realized that math isn't something teachers made up - it's something that's an intricate part of our daily lives. :)

(more on the sticking points in a minute)

posted by u.n. owen at 10:57 AM on January 18, 2005 [2 favorites]

I find that the biggest opposition to math learning in kids comes from the fact that they think math gets more advanced TO BE HARDER, when actually the opposite is true. Math is a process of learning shortcuts in order to simplify more difficult problems. Explaining that to kids is half the battle -- we're not teaching you variables to

make your life difficult. We're not showing you fractions to make you fail. We're showing them to you because once you know how to use them, things will be easier.

To introduce it practically (which should be done first), it's like learning a new shortcut to your house. The first time you use it maybe you'll get lost. The second time, you'll probably do better. Soon it'll be second nature and you'll wonder why you ever went the long way.

To introduce this idea mathematically, talk about counting versus adding - and how if you wanted to put together 2152 and 6745, it'd take forever to count it. Addition's hard to learn at first - but it sure beats counting. Ditto for multiplication. Adding a bunch of groups of 8 together takes a long time. Multiplying 12 by 8 is easy once you know how. And explain that ALL math is like that.

What I talked about with fibonnacci numbers really fascinates kids who think math comes only from textbooks and maybe 25% off clearance sales. To show them that math is part of the innermost fabric of nature is pretty neat.

If you're teaching geometry, be hands-on. Pi is 3.14..., right? For some kids, it's enough to tell them this. But don't be content with that because you'll lose an awwwwful lot of them. Cut out actual paper circles. Measure the diameter, then measure the circumference

with a string and a ruler. Use calculators to divide. When the kids figure out that no matter how big the circle is, the ratio's always the same, THAT's when you explain pi. Don't even bring up the word until then - it'll just be confusing.

Let them go through the same process that people did long ago to determine it. Then say, "hey, people back thousands of years ago realized this, too. And they thought it was so important that they gave that number a name." Then, by the time you've introduced the NAME for pi, they've already visualized the concept and have it more

solidly down than most kids ever will. They've also once again realized that math isn't something teachers made up - it's something that's an intricate part of our daily lives. :)

(more on the sticking points in a minute)

posted by u.n. owen at 10:57 AM on January 18, 2005 [2 favorites]

Okay. So, the three main sticking points of math.

The first one's

When you start getting into multidigit numbers, use the little unit cube things that everyone sells. They're infinitely useful in teaching WHY we "borrow" when we subtract, it gives kids a way to see the numbers in a different way.

Also, to get kids thinking even more about arithmetic, get "Sideways Arithmetic from Wayside School." It's full of fun arithmetic games - some easy, some very difficult - for you to walk kids through. They will be able to get them if they put their heads together, and it's a great way to demonstrate mathematical REASONING.

The second issue is that of

Once they have a roadmap, the path seems more navigable. If you let them know WHY they're doing it, they won't be so frustrated in figuring it out.

Then, get cutting things up. The best way to show fractions is to start chopping things. And kids love that. There's a destructive element that's really fun for them there. Teach adding and subtracting fractions with 12-square paper that has 3 squares by 4 squares - this will teach them to add things like 1/3 plus 1/4 visually before you show them the mathematical representation. Once they understand WHY it works and that it in fact works, you can start to talk about least common multiples and keep referring back (more details on these, email me, this is something that I could talk about for days, because it's days' worth of lesson plans).

But watch this.

2 + ? = 5

You'd see that in any second grade textbook. And guess what it is?

The idea that a variable is just a question mark - or can, indeed, be any symbol at all - is an important one. Kids GET question marks, fundamentally. They understand what that problem means long before they understand what an

Once you've taught them that, you can begin to teach algebraic reasoning - why you add or subtract from both sides. Show that it WORKS, first. (i.e. 2 +

The fundamental issue in teaching a solid math background is teaching kids that it works and why it works. Once they know those basics, the mechanics come a lot easier with a lot less frustration.

posted by u.n. owen at 11:14 AM on January 18, 2005 [1 favorite]

The first one's

**arithmetic.**And actually, from a teaching standpoint, it's the hardest because kids learn it very differently. Flash cards are the best method for some kids, and should be incorporated into arithmetic learning for almost all kids so that they can get it down pat. if it takes a kid 30 seconds to figure out 6 * 8 or 5 + 9, it's going to take them a huge amount of time to do a sophisticated problem. So teaching basic ops for numbers under 10 is important to actually drill on, as much as it sucks. But do this in the "we're learning shortcuts so things will be easier" way, and it'll be a bit better.When you start getting into multidigit numbers, use the little unit cube things that everyone sells. They're infinitely useful in teaching WHY we "borrow" when we subtract, it gives kids a way to see the numbers in a different way.

Also, to get kids thinking even more about arithmetic, get "Sideways Arithmetic from Wayside School." It's full of fun arithmetic games - some easy, some very difficult - for you to walk kids through. They will be able to get them if they put their heads together, and it's a great way to demonstrate mathematical REASONING.

The second issue is that of

**fractions and decimals**. These are difficult for kids because they're often taught in totally different units. The way to explain the existence of these two forms of writing the EXACT SAME THING is to say conspiratorially - "sometimes, math can seem pretty dumb. well, this next part's gonna seem pretty dumb. You've probably seen decimals and fractions. But the thing is, mathematicians made two different ways of saying the same thing. We do that with words all the time. But why do we do it? We do it because maybe saying something in different words is useful at a different time. Well, it's the same way in math. Sometimes it's more useful to make things decimals. Other times, it's more useful to make things fractions."Once they have a roadmap, the path seems more navigable. If you let them know WHY they're doing it, they won't be so frustrated in figuring it out.

Then, get cutting things up. The best way to show fractions is to start chopping things. And kids love that. There's a destructive element that's really fun for them there. Teach adding and subtracting fractions with 12-square paper that has 3 squares by 4 squares - this will teach them to add things like 1/3 plus 1/4 visually before you show them the mathematical representation. Once they understand WHY it works and that it in fact works, you can start to talk about least common multiples and keep referring back (more details on these, email me, this is something that I could talk about for days, because it's days' worth of lesson plans).

**Algebra**may be the easiest of the three to teach. Stare in shock all you want, it is true. People say someone with a second grade math level can't do algebra. Bullshit. Call it algebra, and they can't do algebra.But watch this.

2 + ? = 5

You'd see that in any second grade textbook. And guess what it is?

The idea that a variable is just a question mark - or can, indeed, be any symbol at all - is an important one. Kids GET question marks, fundamentally. They understand what that problem means long before they understand what an

*x*is. Start kids out on question marks. When you can show them basic problems with question marks, and they get them consistently, tell them that mathematicians decided a long time ago to use letters instead of question marks, but they do just the same thing.Once you've taught them that, you can begin to teach algebraic reasoning - why you add or subtract from both sides. Show that it WORKS, first. (i.e. 2 +

*x*= 5. well, we know x is 3. Here's how our brains actually did that. In our heads, we just took 2 away from 5...)The fundamental issue in teaching a solid math background is teaching kids that it works and why it works. Once they know those basics, the mechanics come a lot easier with a lot less frustration.

posted by u.n. owen at 11:14 AM on January 18, 2005 [1 favorite]

Oh, and holy cow, don't talk down to them. Jesus, don't use software with disney characters. There's no easier way to piss off a kid that's behind in grade levels than treating them like a baby.

Part of the reason the methods I've outlined work is that you're teaching them as if they're young scientists/mathematicians just starting out on figuring out new things. The idea that they're FIGURING IT OUT FOR THEMSELVES is crucial, crucial, crucial. If Donald Duck could do it, they're going to feel stupid and clam up. You're not dealing with regular kids, you're dealing with older kids who've had a rough history and have failed so often that they have a lot of built-in defense mechanisms. Getting past those is the tricky part. If you can do that, the math is easy.

posted by u.n. owen at 11:18 AM on January 18, 2005

Part of the reason the methods I've outlined work is that you're teaching them as if they're young scientists/mathematicians just starting out on figuring out new things. The idea that they're FIGURING IT OUT FOR THEMSELVES is crucial, crucial, crucial. If Donald Duck could do it, they're going to feel stupid and clam up. You're not dealing with regular kids, you're dealing with older kids who've had a rough history and have failed so often that they have a lot of built-in defense mechanisms. Getting past those is the tricky part. If you can do that, the math is easy.

posted by u.n. owen at 11:18 AM on January 18, 2005

Things that held my attention in math class as a kid: 1. How other people see numbers differently (number systems that aren't base 10, Mayan calendar calculations, the invention of the zero), 2. how it applies to me, right now (I had a hard time giving a shit about abstract concepts, i.e., what u.n. owen said), 3. physical projects that required math (we designed skate ramps in one class), 4. rapid-fire mental math (hard as hell at first, but it gets easier fast and we got really competitive about it).

Oh, and I'm convinced that people can be divided into algebra-lovers (I think of algebra as the grammar of math and I love languages, so I think it appeals to the aural/oral learners more) or geometry-lovers (because it's spatial and appeals to the visual learners). But that's just me.

posted by cali at 11:26 AM on January 18, 2005 [1 favorite]

Oh, and I'm convinced that people can be divided into algebra-lovers (I think of algebra as the grammar of math and I love languages, so I think it appeals to the aural/oral learners more) or geometry-lovers (because it's spatial and appeals to the visual learners). But that's just me.

posted by cali at 11:26 AM on January 18, 2005 [1 favorite]

23skidoo, use bigger circles. ;-) Also good is cutting the circles out ahead of time, testing them yourself, and doing it in front of the class so everyone is using the same data points.

posted by u.n. owen at 11:31 AM on January 18, 2005

posted by u.n. owen at 11:31 AM on January 18, 2005

Thanks SO much, u.n. owen. That was all very valuable!

23skidoo, I disagree with you, with one exception. If you have to teach something, and you have a very short time-span to complete the teaching, you must make sure the students don't drift towards enticing (but wrong) answers. You won't have time to get them back. (I would argue that if you don't have enough time, the teaching won't work, anway, but that's for another, longer discussion).

I think your PI example would be really really valuable in a class. I would explore why they got all the different answers, and see if the class can approach the correct answer.

Too much teaching involves the teacher just lecturing, which generally doesn't help real learning. Too much teaching brushes real-world messiness under the rug. It must be dealt with, because it's part of reality.

posted by grumblebee at 11:34 AM on January 18, 2005

23skidoo, I disagree with you, with one exception. If you have to teach something, and you have a very short time-span to complete the teaching, you must make sure the students don't drift towards enticing (but wrong) answers. You won't have time to get them back. (I would argue that if you don't have enough time, the teaching won't work, anway, but that's for another, longer discussion).

I think your PI example would be really really valuable in a class. I would explore why they got all the different answers, and see if the class can approach the correct answer.

Too much teaching involves the teacher just lecturing, which generally doesn't help real learning. Too much teaching brushes real-world messiness under the rug. It must be dealt with, because it's part of reality.

posted by grumblebee at 11:34 AM on January 18, 2005

When I first learned algebra -- dumb as this seems -- I had a really hard time with variables because X, Q, Y, N and A made the math problem look more intimidating to me. All those free-floating letters made the problem on the board look like a scary equasion that I knew I could never understand.

When I learned computer programming, I was taught to use WORDS (as opposed to letters) as variables: number_of_apples = 17 as opposed to a = 17. I instantly got it.

I wish back in grade school, we had learned variables that way. I know it's not standard math, but I think I could have transitioned to the single letters if we'd just started with words for a week or so.

posted by grumblebee at 11:37 AM on January 18, 2005

When I learned computer programming, I was taught to use WORDS (as opposed to letters) as variables: number_of_apples = 17 as opposed to a = 17. I instantly got it.

I wish back in grade school, we had learned variables that way. I know it's not standard math, but I think I could have transitioned to the single letters if we'd just started with words for a week or so.

posted by grumblebee at 11:37 AM on January 18, 2005

Thanks UN Owen,

That's one of the best posts I've ever seen here. It inspired me to inspire my kid. I'll be sure to try the next tricky word-problem with a question-mark instead of an 'X'. Great.

posted by MotorNeuron at 11:42 AM on January 18, 2005

That's one of the best posts I've ever seen here. It inspired me to inspire my kid. I'll be sure to try the next tricky word-problem with a question-mark instead of an 'X'. Great.

posted by MotorNeuron at 11:42 AM on January 18, 2005

No problem. I'm contemplating writing a book that's basically "how to teach your child math when you're both hitting your heads on the wall in frustration."

posted by u.n. owen at 11:50 AM on January 18, 2005

posted by u.n. owen at 11:50 AM on January 18, 2005

Please please please don't force all the kids to do it u.n. owen's way. That can be great for kids who aren't abstractly inclined, but whenever they did that to us in math, I wanted to kill. I mean, I got it, and I felt like I was wasting my time playing stupid games. Just because kids may be behind doesn't mean they are automatically nonabstract thinkers.

I found that what helped me most when I got stuck was just having someone ask me to explain how I got to the point at which I was stuck. Halfway through the description, I always figured it out.

posted by dame at 11:50 AM on January 18, 2005

I found that what helped me most when I got stuck was just having someone ask me to explain how I got to the point at which I was stuck. Halfway through the description, I always figured it out.

posted by dame at 11:50 AM on January 18, 2005

Of course these things won't work for all kids.

But they'll work for most kids who are having severe difficulties. I'll guarantee you they've heard all kinds of abstract crap by the time they're in their teens, and if it didn't help them the first 10 times, it won't help the eleventh. You have to try radically different tactics when you're dealing with kids who are multiple grade levels behind. They need a kind of learning they obviously weren't getting - so give them something different.

posted by u.n. owen at 11:57 AM on January 18, 2005

But they'll work for most kids who are having severe difficulties. I'll guarantee you they've heard all kinds of abstract crap by the time they're in their teens, and if it didn't help them the first 10 times, it won't help the eleventh. You have to try radically different tactics when you're dealing with kids who are multiple grade levels behind. They need a kind of learning they obviously weren't getting - so give them something different.

posted by u.n. owen at 11:57 AM on January 18, 2005

I don't know where you went to school, but the stuff you're talking about is what they gave me all the way through elementary school. So it *is* possible that that's what didn't touch people. And being behind doesn't necessarily have to do with the material at school not reaching you--I know plenty of kids who were perfectly smart and perfectly ignored, with the latter being the problem.

That said, those a great ideas. I just would caution against applying them across the board, as you may unintentionally alienate other kids in the class. That's all.

posted by dame at 12:02 PM on January 18, 2005

That said, those a great ideas. I just would caution against applying them across the board, as you may unintentionally alienate other kids in the class. That's all.

posted by dame at 12:02 PM on January 18, 2005

Useful stuff you guys, especially u.n. owen, thanks.

posted by dash_slot- at 12:13 PM on January 18, 2005

posted by dash_slot- at 12:13 PM on January 18, 2005

Most people who struggle with math lack number sense. A great starting point for getting this is estimation. You can do this with concrete problems, like showing them a jar of pennies and have them estimate how many there are. My teacher used to do this with candy, and whoever came closest got the candy. These students may not care about candy, but perhaps you can figure out something they do care about.

There are a million problems like this, and they can be a jumping-off point for arithmetic and other math. For example, to estimate how many pennies in a cylindrical jar, first guess at the number visible on top, then multply by a guess of the number of layers of pennies. Or similar things.

You can also ask them to estimate heights of buildings, the weight of a collection of objects, amount of liquid. Etc.

Then puzzle/logic problems are also good, and can be a good way to learn algebra. I.e. I have a scale with ten pounds on one side and three on the other, how do I get it to balance.

Here is my pedagogical advice from teaching enrichment to 7th graders - don't lecture much. Give them problems, get them to generate suggestions as to how to start the problems, make it into a discussion. If they get stuck, either do a related example or give them process-related suggestions, rather than giving them the answer.

posted by mai at 12:52 PM on January 18, 2005

There are a million problems like this, and they can be a jumping-off point for arithmetic and other math. For example, to estimate how many pennies in a cylindrical jar, first guess at the number visible on top, then multply by a guess of the number of layers of pennies. Or similar things.

You can also ask them to estimate heights of buildings, the weight of a collection of objects, amount of liquid. Etc.

Then puzzle/logic problems are also good, and can be a good way to learn algebra. I.e. I have a scale with ten pounds on one side and three on the other, how do I get it to balance.

Here is my pedagogical advice from teaching enrichment to 7th graders - don't lecture much. Give them problems, get them to generate suggestions as to how to start the problems, make it into a discussion. If they get stuck, either do a related example or give them process-related suggestions, rather than giving them the answer.

posted by mai at 12:52 PM on January 18, 2005

Just in the inspiration department, something I think should be emphasized in a math curriculum is that math's important because if you don't get it, people can and will take advantage of you. Ignorance of math will cost you money. One discrete written example of this I can think of is in R.P. Feynman's

Feynman kept asking questions, and could readily determine it was a sucker's bet. If he didn't understand the math, he couldn't have.

Then again, I think all the classic confidence games should be part of a general curriculum so people know what to be on the lookout for. But probably not the best idea in your setting, glibhamdreck, where if any of your students ever tried using any of them, everyone would come down on you like a ton of bricks for having had the obvious bad sense to talk about them...

posted by Zed_Lopez at 1:44 PM on January 18, 2005 [1 favorite]

*Surely You're Joking, Mr. Feynman*when he encountered a professional gambler, who tried to entice him to place a bet.Feynman kept asking questions, and could readily determine it was a sucker's bet. If he didn't understand the math, he couldn't have.

Then again, I think all the classic confidence games should be part of a general curriculum so people know what to be on the lookout for. But probably not the best idea in your setting, glibhamdreck, where if any of your students ever tried using any of them, everyone would come down on you like a ton of bricks for having had the obvious bad sense to talk about them...

posted by Zed_Lopez at 1:44 PM on January 18, 2005 [1 favorite]

I definitely agree with dame. There is, of course, no ONE approach that works with all students. A good teacher uses many approaches.

However, when trying to decide whether a particular approach works or not, it's important to remember that there are many factors involved. You should NEVER write off a particular method because it didn't work for you. And I mean you should never write it off for YOU.

Games didn't work for you, dame. Was that because games are too concrete for you (or too disconnected with reality)? Was it the specific games used? Was it the way they were used? Was it the personality of the teacher who used them? You might have had 15 different teachers who all used games and they all failed. Still, you might not be able to reasonably deduce from this that games don't work for you. It's possible that all these teachers had the same sort of training and were using games in the same ways.

My point is that there's a lot of bunk spread around about teaching methods. Most of it is anecdotal and highly colored by individual childhood experiences. There's also a HUGE amount of dogma: all classes must have tests, all classes must have grades, etc. Very few of these assumptions are examined. They are just the way "things are done." It's SO hard to cut through the dogma and the prejudice and find teaching methods that REALLY work.

posted by grumblebee at 2:32 PM on January 18, 2005

However, when trying to decide whether a particular approach works or not, it's important to remember that there are many factors involved. You should NEVER write off a particular method because it didn't work for you. And I mean you should never write it off for YOU.

Games didn't work for you, dame. Was that because games are too concrete for you (or too disconnected with reality)? Was it the specific games used? Was it the way they were used? Was it the personality of the teacher who used them? You might have had 15 different teachers who all used games and they all failed. Still, you might not be able to reasonably deduce from this that games don't work for you. It's possible that all these teachers had the same sort of training and were using games in the same ways.

My point is that there's a lot of bunk spread around about teaching methods. Most of it is anecdotal and highly colored by individual childhood experiences. There's also a HUGE amount of dogma: all classes must have tests, all classes must have grades, etc. Very few of these assumptions are examined. They are just the way "things are done." It's SO hard to cut through the dogma and the prejudice and find teaching methods that REALLY work.

posted by grumblebee at 2:32 PM on January 18, 2005

Also, if one gets the feeling one is "just playing games" rather than learning, either you already know the concept backward and forward and should be allowed by the teacher to tutor other students who aren't as lucky, or you are just playing more-sophisticated-than-thou and refusing to go along with it to see the point. Sometimes those games can help show you a concept in a different way, if you let yourself be open to it.

posted by u.n. owen at 2:48 PM on January 18, 2005

posted by u.n. owen at 2:48 PM on January 18, 2005

I used to love watching Square One. If you can track down some episodes on video somewhere, that might be an idea.

My father taught high school math and used to tape the show to use with his classes. I'll see if he still has any of the videos lying around.

posted by sanitycheck at 3:36 PM on January 18, 2005

My father taught high school math and used to tape the show to use with his classes. I'll see if he still has any of the videos lying around.

posted by sanitycheck at 3:36 PM on January 18, 2005

*If not through anecdotal evidence, how can teaching methods that really work ever be found?*

Teaching isn't physics, but one can still do experiments and collect meaningful data. One needs to give a pretest, try a method, and then give a post-test. This should be done on a wide basis using many teachers and many students. It should be double-blind (the testers mustn't know which teaching methods were used). In my opinion, each student should also be given a questionaire/interview which asks questions to determine how much they enjoyed the particular learning experience. The goal is to find the most effective and enjoyable teaching/learning methods.

Of course, NO method will be universally effective. But we can generate some percentages and use them to learn generally effective methods. Good teacher will ALWAYS use multiple methods.

posted by grumblebee at 3:45 PM on January 18, 2005

Here's another Square One TV website, which mentions ten hour-long Mathnet specials. They're hard to find (I found a source for two; one was back-ordered and took months to get, the other was apparently not available and the vendor cancelled my order), but they sound really fun (and a good break from other things).

posted by WestCoaster at 4:34 PM on January 18, 2005

posted by WestCoaster at 4:34 PM on January 18, 2005

I would kill for a bittorrent of any Mathnet specials. I mean this.

posted by u.n. owen at 5:02 PM on January 18, 2005

posted by u.n. owen at 5:02 PM on January 18, 2005

Oh man. I also would love love love to have the Mathnet specials.

posted by redfoxtail at 5:27 PM on January 18, 2005

posted by redfoxtail at 5:27 PM on January 18, 2005

23skidoo, choosing items to test -- even in hard science -- often comes from anecdotal evidence, guesses and hunches. That's fine. You get an idea and then test it. It's the TESTING that must be rigorous and as bias-free as possible, not the original idea.

posted by grumblebee at 5:33 PM on January 18, 2005

posted by grumblebee at 5:33 PM on January 18, 2005

*When I learned computer programming, I was taught to use WORDS (as opposed to letters) as variables: number_of_apples = 17 as opposed to a = 17. I instantly got it.*

Somewhat irrelevant reminiscence: I began to learn to program, in BASIC and C, before I learned algebra. Consequently, when I got to algebra, it confused the fuck out of me that variables didn't

*vary*like I was used to. I kept thinking they weren't variables at all, they were

*constants*, dammit.

Yes, I realize that having written C before learning algebra is indicative of a misspent youth.

posted by IshmaelGraves at 5:37 PM on January 18, 2005

Have you considered teaching the history of mathematics alongside the practical? It was this, more than anything, that has made me determined to learn more. The school of Pythagoras, the origin of pi, the occult significance of 'magic squares'... maths has a long history, both illustrious and disreputable.

I switched off during maths as a kid because it was presented as a set of exercises to be drilled and formulas to be memorised by rote. When I asked the teacher 'what

posted by Ritchie at 8:24 PM on January 18, 2005 [1 favorite]

I switched off during maths as a kid because it was presented as a set of exercises to be drilled and formulas to be memorised by rote. When I asked the teacher 'what

*is*pi?', he couldn't give me a rational answer.posted by Ritchie at 8:24 PM on January 18, 2005 [1 favorite]

This is probably dead by now, but just to answer you grumblebee, the problem was a combination between the games being too concrete (oh, how I loathe those blocks--we have numbers so we don't need actual blocks) and feeling like I was being dicked around. The pi thing is a good example: The ratio was always going to be 3.14. I got that. I didn't need to spend an hour measuring circles to understand that; I just needed to be told. And when I was told, at the end, I felt played with. I felt like my time was being wasted.

(And don't even get me started on "helping the other kids." Students are not teachers and shouldn't be wasting their time in school helping others. They should be learning.)

posted by dame at 8:18 AM on January 19, 2005

(And don't even get me started on "helping the other kids." Students are not teachers and shouldn't be wasting their time in school helping others. They should be learning.)

posted by dame at 8:18 AM on January 19, 2005

dame, perhaps the best way to learn in school is to teach others. It shows that you have the concept not just learned by rote, but actually have mastery. It's the exact opposite of "wasting time."

Until you can teach it to someone else, you don't know it. Teaching other students is perhaps the best way to test real mastery of material. It sounds like you were pretty damned elitist in school, and it hasn't worn off yet. I won state math competitions and was miles ahead of everyone else, but that didn't mean that I demanded the teacher leave everyone in the dust in favor of teaching me multivariable calculus.

If you don't appreciate the process of discovery that goes into math, fine. But that process worked for a very long time and it still works today. It sounds like your time must've been awfully valuable in elementary school. What was the magic invention you were working on that made saving ten minutes more important than your classmates' understanding? I'm just wondering.

posted by u.n. owen at 11:14 AM on January 19, 2005

Until you can teach it to someone else, you don't know it. Teaching other students is perhaps the best way to test real mastery of material. It sounds like you were pretty damned elitist in school, and it hasn't worn off yet. I won state math competitions and was miles ahead of everyone else, but that didn't mean that I demanded the teacher leave everyone in the dust in favor of teaching me multivariable calculus.

If you don't appreciate the process of discovery that goes into math, fine. But that process worked for a very long time and it still works today. It sounds like your time must've been awfully valuable in elementary school. What was the magic invention you were working on that made saving ten minutes more important than your classmates' understanding? I'm just wondering.

posted by u.n. owen at 11:14 AM on January 19, 2005

u.n., I don't think it's fair to call dame elitist, although I agree with you that teaching someone else is OFTEN the best way to learn. I'm not elitist. But I'm shy. As a kid, I was painfully shy. Being forced to teach another kid never helped me learn, because I couldn't focus on the topic, I could only focus on the social aspect.

I was a smart kid, and I usually understood stuff way before most of the rest of the class. What I wanted to do at that point was to work on more challanging stuff by myself. Instead, I was either made to do busy-work or made to teach others. Neither ever helped me much.

I am aware that I'm not the norm. Maybe dame isn't either. Most people DO learn from teaching. But again, the danger in teaching is to rely on one method (or a small set of methods), even if they're generally effective. You can never assume that they will be effective with a specific student.

posted by grumblebee at 1:02 PM on January 19, 2005

I was a smart kid, and I usually understood stuff way before most of the rest of the class. What I wanted to do at that point was to work on more challanging stuff by myself. Instead, I was either made to do busy-work or made to teach others. Neither ever helped me much.

I am aware that I'm not the norm. Maybe dame isn't either. Most people DO learn from teaching. But again, the danger in teaching is to rely on one method (or a small set of methods), even if they're generally effective. You can never assume that they will be effective with a specific student.

posted by grumblebee at 1:02 PM on January 19, 2005

u.n. owen: Kids aren't in school to teach other kids; they are there to learn. I have actually turned out to be a pretty decent teacher (one-on-one) and spent all of high school tutoring other kids. However, I got paid for it and did it outside of my learning time, as is appropriate, since it was *work*.

Smart kids aren't free teachers, and holding them back is one of the most pernicious conventions in American education. In my case, making me teach other kids in elementary school just made them hate me. I was frustrated because I couldn't understand why they didn't get it, and they thought I was trying to be an authority. In the end, I wound up totally bored, entertained myself by acting out, and then got a reputation among my teachers as a troublemaker, which tends to make teachers treat you badly, thereby creating a vicious circle of mutual animosity.

And this is where it runs back into the topic at hand: some kids who wind up in trouble do so because they started off smart and bored. I was lucky: I ended up in a high school that was small and responsive enough to challenge me, and did really well. If I had been in a big public school, that might not have happened and I might be where the kids in question are.

Labelling kids who desire challenge elitist is (in my opinion of course) one of the grosser symptoms of American anti-intellectuality. I wasn't an elitist when I was six. I was a kid who really loved learning and was really frustrated by being dicked around. Like grumblebee, I just wanted to learn more. Instead, I got labelled a troublemaker who "asked too many questions" (as my second-grade teacher complained).

posted by dame at 2:09 PM on January 19, 2005

Smart kids aren't free teachers, and holding them back is one of the most pernicious conventions in American education. In my case, making me teach other kids in elementary school just made them hate me. I was frustrated because I couldn't understand why they didn't get it, and they thought I was trying to be an authority. In the end, I wound up totally bored, entertained myself by acting out, and then got a reputation among my teachers as a troublemaker, which tends to make teachers treat you badly, thereby creating a vicious circle of mutual animosity.

And this is where it runs back into the topic at hand: some kids who wind up in trouble do so because they started off smart and bored. I was lucky: I ended up in a high school that was small and responsive enough to challenge me, and did really well. If I had been in a big public school, that might not have happened and I might be where the kids in question are.

Labelling kids who desire challenge elitist is (in my opinion of course) one of the grosser symptoms of American anti-intellectuality. I wasn't an elitist when I was six. I was a kid who really loved learning and was really frustrated by being dicked around. Like grumblebee, I just wanted to learn more. Instead, I got labelled a troublemaker who "asked too many questions" (as my second-grade teacher complained).

posted by dame at 2:09 PM on January 19, 2005

Hey, I'm not saying gifted kids shouldn't be challenged. But communication skills are a nice thing to learn too. Believe me, as someone who was three grade levels ahead of her age for almost all of school and was STILL miles ahead of everyone else, I know what it's like to be bored. But if you're that smart, make your own new challenges. I did. everyone else I know with brains who wasn't just sitting around whining did.

Of course, I think much of that could just be resolved by letting kids jump grades to where they actually belong, or close to it. So what if we'd have a lot more 12 year olds graduating? I've seen 12 year olds graduate and do just fine.

posted by u.n. owen at 3:06 PM on January 19, 2005

Of course, I think much of that could just be resolved by letting kids jump grades to where they actually belong, or close to it. So what if we'd have a lot more 12 year olds graduating? I've seen 12 year olds graduate and do just fine.

posted by u.n. owen at 3:06 PM on January 19, 2005

*But if you're that smart, make your own new challenges. I did. everyone else I know with brains who wasn't just sitting around whining did.*

I did. Unfortunately, my teachers didn't appreciate them. And as someone who made it out of college before I could drink, I didn't need to graduate any earlier.

posted by dame at 4:12 PM on January 19, 2005

Smart kid pissing contest aside, u.n., my point was and remains just remember that not all kids learn the same way. There is nothing wrong with being smart *and* needing direction. Some kids with dig math games and some will find it unmitigated torture. But forcing--not giving the option, but forcing--a six-year-old to become a teacher is wrong.

posted by dame at 4:35 PM on January 19, 2005

posted by dame at 4:35 PM on January 19, 2005

This thread is closed to new comments.

posted by andrew cooke at 9:05 AM on January 18, 2005