Betty Duffy

Tuesday, September 14, 2010

Mathematically Challenged

I’ve been thinking about third-grade Math. I might as well come out of the closet and admit that I’m home-schooling one of my kids this year, the one who came home from school one day last year with 25 unfinished ditto sheets that he was supposed to have completed that day. I thought that was a little much for a kid with a few manual dexterity issues, so this year, we have done not a single worksheet. Not one. What we have done is try to memorize things, beginning with Math facts.

I don’t know what kind of brains both the child and I have, being that we are both completely incapable of remembering that 7+8=15. I used to get good grades in Calculus once upon a time, but I have always done addition facts on my fingers, and so does the boy. He has memorized three very long poems, however. I read him a stanza, and he doesn’t need to hear it twice before he’s got it in his head. He’s quite amazing that way. But knowing by heart the various sums of the numbers between one and ten are just not within our reach.

I was thinking about this whole concept recently in my sleep, because that seems to be the only time my brain is functioning lately. Indeed the current hour is some time in the middle of the night, and I had to get out my bed to write this, because I won’t remember it tomorrow. I was thinking about how words are relational. How they connote images and concepts that relate to one another in graphic ways, and by graphic I mean that I could draw several horizontal lines indicating the plot points of a novel and show how when the tension rises within one character, it might drop in another. Relational.

I was just having this dream, and in my REMs I could see a staff of music, and could hear the music written on it at the same time. I have never in my life written a piece of music, though this has happened to me before that I think I’m writing music in my sleep and when I wake up, I cannot remember the notes I saw on the staff. I wake up thinking I must have some subconscious genius inside writing music, but hell if the genius doesn’t dissipate as soon as I’m conscious.

Anyway, I do remember this: There was a cello line, these lower grumblings in eighths and sixteenths that cut off when the treble piano line interrupted. And the treble was actually two separate themes, a duet that moved up the scale with a crescendo, climaxed, then shifted back to that bass line on the cello.

Maybe you followed that, maybe you didn’t. But I was trying to think of pieces that sound similar, maybe something I’ve played in the past. It sounded so familiar. What was it? And then I realized, that the piece resembled nothing so much as the short story I’d read right before I feel asleep. It was John Cheever, “The Jewels of the Cabots.” It began with a sort of neurotic and comical male narrator, who then told a story about a woman he once dated and her mother. The end of the story went back to the male narrator, and I can see now that the music in my dream was some sort of echo of the voices in that story.

If I can graph the plot of a story on a musical staff, writing music being an inherently mathematical endeavor, there has to be a better way to see the graphic relationships between single digit numbers. When those numbers keep showing up, without rhyme or reason on the other side of a shuffled deck of flash cards, however, those relationships completely defy me.

Also, it seems like I used to know a way to graph patterns like this one:

His cheek fur grows in a whirlpool. I wonder if it will do that when he has whiskers. (And by cheek fur, I really do mean the cheek on his face. I just realized that this picture could be mistaken for the other kind of cheek.)


Karen LH said...

I don't know if this would be at all helpful, but sometimes when I have to add numbers like that in my head, I find myself doing it in steps like this:

8 is 2 short of 10
2 taken from 7 is 5
5 added to 10 is 15

(And for some reason, when I do this, I see the process in pictures.) It's slower, but there's less to remember, and it might get him past the hump until he starts remembering the addition tables directly.

Melanie B said...

Like Karen, I somehow worked out a way of visualizing numbers as patterns that helps me with addition and subtraction.

It's like I see seven as the pattern of five dots on a domino with two more dots on top. Nine is a group of five dots and a group of four dots. It's easier for me to rearrange the numbers in my head when I think of them as visual units of five or ten minus or plus a few.

I wonder it would help him if you used some sort of manipulative like dominoes or cuisinaire rods or Montessori bead bars.

Entropy said...

We have this problem too.

Have you drawn a "rainbow"? Take the number 15 and write it at the top of the page, then draw 0 and 15 towards the bottom of the page a good distance from one another, draw a rainbow line connecting them. Next to the 0 write a 1 and behind the 15 write a 14 etc connecting with rainbow lines and ending with 7+8 in the center. Maybe seeing it like that will help. (Plus (ha!), he can color it after)

In addition (I just can't help myself), check out you tube for math tricks. There's lots of great visual techniques on there.

Congrats on the homeschooling. Hope you love it!

Jordana said...

I have one child who has a lot of trouble learning her math facts. We have a book of silly stories called Addition the Fun Way that helps some. Also, I bought her Teaching Textbooks math, which she does on the computer, and it is the first time she's ever enjoyed math. It makes me so happy to see her finally not avoiding math or complaining about it.

Jus said...

WE have had huge amounts of success using "visual" math programs - two examples are "right start math" and Math-U-see". It has madea HUGE difference for my eldest who simply can not relates to random facts without a conceptual context.

antonina31 said...

First, I want to commend you for your bravery in pulling your son from school and your love for him evident by knowing him so well. Then, I want to second the recommendation for the Math U See program. Each number 1-10 has its own color bar, so it might help to associate the colors with the numbers, like pink + yellow = tan. May your year be filled with wonder!

Melissa Wiley said...

Math U See is full of helpful tricks for memorizing math facts. Like "9 always wants to be 10" and you imagine the hole in the 9 is a vacuum tube sucking one away from the other number, which makes the 9 turn into 10, and the other number is one less. 9 + 8 = (make sucking noise) 10 + 7 = 17.

And 8 has two vacuum tubes, so sucks two away from the other number.

7 + 8 are "neighbors" --since they come one right after the other when you count. You add neighbors by doubling the smaller neighbor and adding one. So if you've got doubles down pat, the neighbors become easier.

I am fairly blown away by your dream image of the story's plot as melody lines on a music staff. Gorgeous.

Sally Thomas said...

8+7= hard. I do something like the "neighbors" thing, too. I ask what 10+7 would be, for instance, and then we count back from there.

Number lines are also massively useful and don't require that much dexterity. We rely on them heavily until we've practiced facts to the point of memorization.

My 6-year-old and I have also been having fun playing with the Math Cats site ( The story problems are fun (and written by kids, so there are some goofy trick questions), and we do them either mentally, or on the whiteboard together -- today I drew six horses, then two going away, then four coming along, then we wrote it as a "number sentence." I'm thinking we'll write some "math stories" soon.

Tari said...

A friend of mine mentioned today that he was using a story-based math program for his daughter learning her times tables. It's this:

You might be able to make up something similar with addition, or there may be a similar resource. My friend's daughter is stubborn to the nth degree, and this is (finally) working with her.

BettyDuffy said...

Thank you everyone for the resources and links!!

I'm going to spend some time looking into these. At the last minute, once I was convinced I was going to do this (homeschool him), I went with the curriculum they had been using at school, which is Saxon. I let him dictate the answers to me, but that of course puts everything in our heads, which I'm not sure is the right solution for working with manual dexterity issues. I've been thinking some manipulatives might be in order, and I've heard good things about MathUSee from people in real life too.

dylan said...

Math. I used to get fairly good grades in math, but now, at a whisker over forty, I find I have to double-check my subtraction with a calculator. Or, lacking a calculator, I have to add the difference to the subtrahend (?) to see if I get the original number back. This is especially true of numbers such as 904.32 minus 587.69 -- where most of the digits being subtracted are larger than what they're being subtracted from.

Addition, multiplication, division pose no problem with pen and paper. But with subtraction, I choke.

Kate said...

Thank you so much for bringing up the subject of difficulty with math! My 7YO daughter and I are really struggling, and I am so grateful for the resource recommendations!

Suburbanbanshee said...

There used to be these contraptions that had a matrix of numbers, all hidden under little trapdoors. You would pull out one numbered stick on the left and another numbered stick on the top, and the little trapdoor would slide away from the number they made. I think this was mostly for multiplication tables, but there may have been addition ones also.

It was great, because you could run through all the iterations, up and down and around, as often as you wanted (or until your mother got sick of the noise of you pulling open little trapdoors with the sticks).