29 Jul 2005 - 05:15

report from the summer doldrums

I am inspired by Christopher's having wrestled with a two-part story problem and won. He's right to feel manly; doing two-step story problems is the modern equivalent of hunting mastodons.

But we are in the doldrums, at our house.

I had an email the other day from someone who asked for suggestions as to how she could make math more interesting for her son, who is going to be a freshman in high school. Anyone have any ideas for motivating a child in high school?

It's a tougher age than elementary and middle school. What you can do at that age depends heavily on whether they're already behind, and have to make up material they struggled with unsuccessfully in an earlier grade.

I haven't dwelt at all on trying to make math more interesting. I have tried instead to make my son's experiences with math successful, positive ones, trusting that it would then become something he felt good about doing. If he has to tackle something hard, I first try to build him up with easy problems (for a lot more on how to use that trick, which I think will work very well with a kid of any age, see this post). If he gets a 100 on his work for the night, it's a big deal; it gets stickers and goes up on the fridge. He always gets rewards of some sort for doing his math (and getting released from duty is a huge reward all by itself).

Ben and I are ploughing through Prentice-Hall Mathematics Course 1 this summer. My basic message to him, when he objects to doing any sort of homework (which he does frequently), has been: Too Bad, we all have to work a little bit; here's your carrot if you buckle down and get it done, and here's your stick if you don't. I figure I'm just being his frontal lobes until the day (if it ever comes) when he can use his own. Rational arguments about his future in the global technological marketplace don't seem to make much of a dent, at least not yet (I'm sure he'll thank me profusely when he's older, though).

This summer, having finally broken free of Everyday Math, we've made some real progress at a good pace. He's learned a lot of math, and been successful.

But he's developed an allergy, lately, to intellectual work. He fights me insistently when I try to get him to do his homework, even before he knows what he'll have to do (his reaction when he gets his assignment is usually: "That's it? That's all I have to do?" Sheesh).

(As an aside, I've found that with Ben it's essential to tell him, at the beginning of a lesson, exactly which questions he'll be expected to do that day. This means I can't leave the lesson open-ended, but it's okay. He copes a lot better if he knows the bite he's expected to chew off.)

I'm beginning to think we just need a vacation. We'll be taking one in a couple of weeks (I'll be taking my computer, but no real work), to Seattle.

I have a plan: I want to go on a Whale Watch tour.

Back to main page.

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oh my god!!!!!!

I'm actually on my 'big' computer for once--I've been working on a teensy-weensy laptop for eons--and I logged on & burst out laughing at our first line....then scrolled down because I wanted to drop in an 'LOL' in the Comments box--and here's the whale!!!

Beautiful!

What a gift first thing in the morning!

-- CatherineJohnson - 29 Jul 2005

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If he gets a 100 on his work for the night, it's a big deal; it gets stickers and goes up on the fridge.

is there a reason why i couldn't have thought of this?

-- CatherineJohnson - 29 Jul 2005

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don't answer that

-- CatherineJohnson - 29 Jul 2005

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Rational arguments about his future in the global technological marketplace don't seem to make much of a dent, at least not yet (I'm sure he'll thank me profusely when he's older, though).

This post is going to be a ktm classic.

-- CatherineJohnson - 29 Jul 2005

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We are SERIOUSLY in the doldrums around here. Diagnosis watch for my niece, Boy Scout camp disaster for Christopher, no 'APE' in 'FAPE' for Andrew......and a huge, big pile of cr** on my desk and floor to wade through.

yuck.

We've gotten SO off-track with Saxon Math, although I have to say, on a positive note, that I've learned huge amounts of math from our whole KITCHEN TABLE MATH project. It's incredible; this 'blooki' actually is working, for me, exactly as I had hoped and imagined it would. (otoh, I've kept him on track with spelling, Fast Facts, & 1 bar model word problem a day. It's AMAZING how much he doesn't know about applying math to a problem! So I don't think I've radically dropped the ball. He's refusing to do more than 1 problem a day, though, and it's outrageous of me to let him get away with that. We're still in the 1st semester 3rd grade book, not even in the 3rd grade Challenging Word Problems book.)

More and more, I'm thinking that one of the fundamental secrets to learning maths is learning-it-more-than-one-way.....as both Liping Ma & the constructivists say.

Anne Dwyer had a wonderful story on her page about trying to help her daughter count money up by 10s starting with a number ending in 5.

Her daughter couldn't get it, and she tried all kinds of different ways to explain it, and finally when she said something like, 'Add 5 twice'--she got it!

That is happening to me constantly now.

Just some tiny shift in the way a concept is expressed or explained will suddenly give me that 'click.'

I've got to start bliki-ing about the smart constructivism I've been reading.....it makes perfect sense. All knowledge has to built on--constructed out of--the knowledge that is already there inside your brain.

I assume the reason why I can 'get it' from one good explanation and not get it from another good explanation is that one explanation connects better with my pre-existing knowledge.

The trouble is, I don't really know what my pre-existing knowledge is, and neither does the person trying to explain things to me.

Remember that line Cardinal Fang quoted?

"My job is to give you three different explanations. Your job is to understand one of them."

Cardinal Fang

Anyway, I've succumbed to the doldrums vis a vis teaching Christopher...but I've been (let's hope) galloping ahead myself, so I assume that's a Good Thing.

-- CatherineJohnson - 29 Jul 2005

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Remember that line Cardinal Fang quoted?

"My job is to give you three different explanations. Your job is to understand one of them."

I'm really starting to think that this is the main key to helping children learn math -- being able to hit a concept from as many angles as necessary.

-- CarolynJohnston - 29 Jul 2005

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I'm really starting to think that this is the main key to helping children learn math -- being able to hit a concept from as many angles as necessary.

We're channelling each other again. I've been planning to write a post about this for weeks.

If I had to identify one core idea, that's what it would be.

Hit a concept from as many angles as possible.

(I've started to think that the best math ducation would be a good curriculum & good teacher at school, AND a good but completely different curriculum & teacher outside of school. I'm serious.)

-- CatherineJohnson - 29 Jul 2005

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This is another lost in translation thing.

What you probably need to do is what Cardinal Fang's husband's teacher did, and what Steven Pinker says to do: teach each and every concept and problem 3 different ways.

BUT the 3 different ways have to be 3 different GOOD, EFFICIENT, AND ELEGANT WAYS.

The constructivists take this idea to mean EVERYONE COMES UP WITH A STRATEGY, AND EVERYONE'S STRATEGY IS GOOD.

-- CatherineJohnson - 29 Jul 2005

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Carolyn,

My comment will probably deserve to be ridiculed. That’s fine with me. Everyone should feel free to post comments making fun of me. That way, at least we will still have generated some of that FUN that you are finding so elusive right now.

Caveats:

• I will be conflating your desire to emerge from the doldrums with your friend’s desire to make math fun for her son.

• I don’t have a high schooler, so I’m sure I don’t know what he would consider fun.

• Many of my suggestions might work better with 4th-8th graders.

• Some of these probably require way more effort than they deliver in fun.

• These are not really instruction-oriented suggestions. They are more excuses to practice math in settings that might be fun. So, the underlying math may not represent any new learning for the student.

Suggestions:

• Go bowling. Ignore the automated system, and keep score manually. Then, work through the calculation for some counter-factual cases (“What would my score have been if I hadn’t missed that @#$! spare in the fourth frame?”). Try to figure which one roll would have boosted your score the most if it would have knocked down all the pins.

• Check the standings. Develop the formula for computing “magic numbers” for clinching the division in baseball. Just please don’t tell me how small the Cardinals’ magic number is to eliminate the Cubs.

• Follow the market. Each person picks five stocks to watch. Invest your pretend portfolio in them. Track their performance throughout the month of August. Figure out how to plot their daily performance on a graph, comparing their performance to the Dow, the NASDAQ, and the S&P 500. Trade into other stocks along the way.

• Try Mathmania. Look for interesting problems in the Mathmania booklets put out by Highlights publishing. These periodicals are probably aimed at 4th or 5th graders, but you can upscale some of the problems by trying to describe them using algebra.

• Look at MATHCOUNTS. The MATHCOUNTS web site (www.mathcounts.org). They’ve got a “problem of the week” archive (with solutions!) that you can browse through. These problems are often topically related to current events. They’re designed to interest kids, so maybe some of them will succeed with your kid. MATHCOUNTS is for math-oriented middle schoolers, so it will challenge most high school students, too.

• Graph the logical flow. Develop a flow chart—or pseudo-code, if you’re already into programming—describing scoring in tennis. Nest a loop for point scoring within a loop for set scoring. Sometimes deuce is an infinite loop.

• Play Jeopardy. Write up your own problems and arrange them in categories. This could be a lot of work, depending on how hard you make the problems. Don’t be too strict about answering in the form of a question.

• WARNING: High risk of failure. Plan a math rally around the yard or neighborhood. Students must solve clues in the form of math problems to find out, say, which envelope to open to get the next clue. Then they must determine which direction to walk to find the next clue. If you open the wrong envelope (or box, or whatever), you lose points, but it then tells you what would have been correct, so you can get back on the right track. If this turns out to be fun, that’s great. If, however, the kid thinks it’s bogus, then you’ve invested a lot of time to end up looking pretty foolish.

Okay. Have fun with these, or make fun of these.

-- DanK - 30 Jul 2005

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Go bowling. Ignore the automated system, and keep score manually.

No kidding!

I was shocked when I discovered, just this year, that nobody scores their own bowling any more!

-- CatherineJohnson - 30 Jul 2005