Monday, January 22, 2007

Solving the world's problems

I've had problem-solving on the brain today. This afternoon I participated in a telephone conference with two professionals who will be involved in Bud's developmental assessment next month. They asked a lot of questions to try to get a sense of who Bud is, and they asked me about his problem-solving skills. We talked about him teaching himself to tie a knot, and about his creative problem-solving when improvising characters for his pretend play.

I also told them about Bud's struggle with this week's school homework. The exercise involved a grid with the numbers 1 - 100. I was instructed to choose two numbers and say, for example, "I'm thinking of a number between 10 and 20." Bud would guess a number and if it wasn't my number I would instruct him that my number was "higher" or "lower" until he guessed it correctly.

Bud was baffled by the activity.

I started small: "I'm thinking of a number between 7 and 9." Bud's first guess was 15. His second guess was 9. I tried to show him visually, pointing to 7 and sliding my finger to the right as I said "hiiiiiigher than 7," then pointing to 9 and sliding my finger to the left as I said "looooooower than 9." Both times I left my finger on the number 8.

Bud guessed 5.

I tried to reframe the problem, using different terms - more than/less than, bigger than/smaller than - but it wasn't happening. We moved on to spelling words, and Bud was much more successful.

After I recounted the homework experience to the clinic professionals, I found myself thinking about it and wondering what problem was at its core. Was Bud having trouble responding to questions under pressure? Or was it the conceptualizing of the question that he found challenging?

So tonight I tried another problem-solving experiment. Earlier in the day, I'd purchased a toy harmonica for him (he's been wanting one because Curious George plays one in a favorite episode.) I entered the room with the toy behind my back and said, "I bought something for you today."

"What?" Bud asked.

"See if you can guess," I said. "It's something you use your mouth for."

"Twizzlers," he said, almost immediately.

"That's a good guess," I said, "But it's not Twizzlers."

"Cookies?" he asked.

"Nope," I said. "It's not something you eat."

"It's what?" he asked. "Snacks."

"It's something you use your mouth for, but you don't eat it."

Bud thought for a second, then guessed, "Juice?" (Clever boy! You drink juice; you don't eat it.)

"Good guess, Bud! But this is something you don't eat, you use your mouth for, and you blow."

"Balloons!" he guessed.

"Great guess!" I said. "But it's something you don't eat, you use your mouth and blow and make music."

Bud thought again, then smiled and said, "Harmonica!"

He was delighted to learn that he was correct, and immediately set about trying to figure out how to play Twinkle, Twinkle Little Star, which I taught him to play on the glockenspiel, and he taught himself to play on the xylophone, keyboard, and toy clarinet.

So, I think it's the concept of the homework that is baffling to Bud. Quite frankly, he probably inherited his aptitude for math problems from his mom.

The problem-solving, on the other hand... the problem-solving is not a problem.


Ms. Clark said...

If you asked what amount of apples is more than 7 apples and less than 9 apples could he get it? I bet he could.

This is not right, my word verification is "bratt"... I think it's talking about me, though...

kristina said...

However many questions it takes to get to the answer (the solution?), each step is a small triumph. I think.

Teal said...

What about the difference between using a number line and a graph? Do you think one is easier for Bud to grasp?

Estee Klar-Wolfond said...

I'm very interested in this post. I'm also trying to teach Adam numerical concepts. Camille, I haven't tried that more than 7, less than 9. Hmmm....

Swechcha said...

My first time at your page. Started reading, finished off all the links that are readily available on your page and I know I'm not going any place until I make substantial inroads into the archives.

In the understatement of the year, I must tell you, I love your site.

MOM-NOS said...

And, Swechcha, I love your comment! Thanks so much. And welcome!

ms. clark, I have a hunch that if I talked about apples, he'd struggle, but if I had two groups of apples he'd definitely be able to count them and tell me which one had more. It's the conceptualizing that seems to be difficult for him.

Teal, he struggled with homework that involved a graph as well. It depicted how many marbles someone pulled out of a jar, and I could see him looking at the stripes on the page and thinking "How are you getting marbles out of that?"

KathyIggy said...

Even though the number grid is visual, Megan ALWAYS had problems with these kind of math questions (I think it was the "between" that baffled her). What I ended up doing is making a larger number grid and then put some of her "My little ponies" (her long-standing obsession) on the grid with numbers taped on them, explaining the number was between "Pinkie Pie" and "Minty" for example. I have taught so many concepts with the ponies over the years, I've also used the idea of the houses on our street to teach place value.
Maybe if you somehow tie Bud's favorite characters or something really concrete into it, it might help. Though the grid is visual, the numbers are still abstract. But if you attach the numbers to a concrete object, it may help. Megan is 11 now and in 5th grade, but I remember these Kdg and 1st grade problems well.

Mommyof3 said...

Mom-nos, I am back again with a small contribution. It is similar to the ponies suggestion and it worked for us. Two characters, not small or really large characters but a comfortable size are glued to two different popsicle sticks facing each other. (We used dragons colored by son). One is for the left hand and it faces the one in the right hand. You have your number line (ours is laminated so it is thick...he likes that)and it is flat in front of him. Then you introduce the whole concept of all that lies between by playing the squishing game. The two characters start at selected points, let's say 2 and 7. They are facing each other and the numbers the child focuses on are what is in between...3,4,5,6 This was a good visual. Sqishing involves sliding the popsicle-stick characters closer and closer and settling on exposing only one number, any number that is between is fine to simply get used to the concept. We have since used our dragons to move up or back spaces for fun and then to help with assignments like minus 2, etc... I do not know if this is adaptable for Bud or not. But it may help in some way. mommyof3

MOM-NOS said...

KathyIggy and mommyof3, those are both EXCELLENT suggestions! They present ways to make the activity more concrete, while still working on the skill of conceptualizing. I think I'll print them out to show Bud's teacher as well! Thanks!

Natalia said...

i think i learned those concepts on cuisiniere rods (sp?).
do you think he would like those?

MOM-NOS said...

Natalia, I've never heard of them, but my friend Teal e-mailed me the same suggestion earlier today. Sounds like I need to look into them!

Ricky said...

I was thinking of something similar to that squish method mentioned earlier.. but not as exciting due to the lack of toys ;)

Have the numbers written out vertically on the page from 1 to 10 (put ten at the top). Then, have two blank pieces of paper ready.. one at the bottom of the number page, one at the top.

So, you start with all the numbers visible, and imagine the number you are thinking of is 6.

So, if Bud starts with a guess of 9, you say "Nope, it's lower than 9", and use the top blank sheet to cover the numbers 9 and 10. If the next guess is 5.. you say "no, it is higher than 5", and use the lower sheet to cover the numbers 1,2,3,4,5. "So, if it higher than 5 and less than 9, we are left with the numbers 6,7 and 8."

This way, you hide the numbers that aren't valid choices anymore, and by only showing the ones still relevant to the problem, hopefully Bud will focus on the options that are left. With time, Bud will hopefully be able to do this exclusion in his head without needing the paper.

MOM-NOS said...

Ricky, that's a great idea. It makes the exercise visual, while still keeping it abstract. It's the abstractions of math that are most difficult for Bud. Show him two cookies and two cookies and he'll tell you there are four. Ask him what 2 plus 2 is, and he struggles.