August 29, 2014

The Freebie Problem

I ran into my first real problem with Khan Academy the other night.
Both kids struggled a lot with the Rate Problems 2 section in Khan. These are problems that require multiple steps to solve, and a more complicated mental picture than the earlier word.
I really like these problems. They exercise our understanding of the relationships between rates and times and other factors. They compel us to think conceptually about the big picture instead of just crunching the numbers.
The kids might solve this by working out how long it takes 1 person to paint 3 walls, then how long it takes 1 person to paint 1 wall, then how long it takes 6 people to paint 1 wall, and finally how long it takes 6 people to paint 7 walls.
I urge the kids to make a chart, fill in what they know, and then figure out how they can fill in additional boxes on the chart until they have what they need.
Every now and then, however, Khan throws up a variant of the problem like this:
After Jessica carefully worked it out, I showed her how this one was actually easier. If the number of people and walls are the same in both cases, then the answer is also the same. 7 people take as long to paint 1 wall each as 1 person takes to paint 1 wall or as 11 people take to paint 1 wall each.
“It’s like a freebie,” I said. “You don’t even have to do the arithmetic.”
This Jessica remembered. As she continued to struggle through these exercises, every now and then she would proclaim, “A freebie!” and I would immediately hear the happy sound that Khan plays when you get one right. But she was otherwise struggling, and she didn't succeed in getting five in a row before we called it a night.

The next day she took a Mastery challenge. She aced it easily, and when the report came up at the end, it showed she had “Mastered” Rate Problems 2.
But she hadn’t come anywhere close to mastering it. She had just got lucky. The Mastery Challenge had served up a freebie.
Since I was watching, I promptly added more Rate Problems 2 exercises to her list and continued to work through these with her. Actually I first took her all the way back to the earlier Rate Problems topics. And eventually she really could do them all, and she knew it.

August 27, 2014

How We Started Reviewing with Khan

So far I’ve had the kids doing Khan in parallel. This is what that looks like.
They sit side-by-side, each at a laptop.
When there’s a video lesson that I think would benefit both, I make them both watch it. I actually launch the video on one computer so they can watch, then simultaneously launch it on the other with the sound off. That way both kids get “credit” for watching the video. I pause the videos occasionally to ask them to predict what’s coming, to reinforce a point, or to ask about a related topic. “Wait a minute,” I’ll say. “How is he doing 12 times 15 in his head?”
They do the exercises on a topic individually but simultaneously—each at a laptop. I monitor both from behind. Since Khan seems to serve exercises randomly, they’re working on similar, but different, problems. We have a strict rule that they can’t advance past a wrong answer ‘til Dad has a chance to ask about where it went wrong. I frequently ask them to narrate through problems even before getting them wrong, just to see their thought processes. I’m pretty adamant about letting them make mistakes, though. If I guide them to the right answer, then the “5 in a row” rule will fail to serve enough exercises.
Since the exercises keep coming until you get 5 consecutive problems right, it’s likely that one of them (generally Jessica) will finish before the other. I tell the one who finished first either to do Mastery Challenge quizzes or to repeat the exercise, getting another 5 in a row, if I think it needs further reinforcing. A couple of times I’ve let her call it a day while I’m still finishing up with Nathaniel.
I generally stop the lesson when I feel like they’ve had enough, after something between 30 and 75 minutes. Khan presents no more than a few Mastery Challenge quizzes, then introduces a 16-hour delay—we have to wait until tomorrow for the next Mastery Challenge. I usually stop when the kids have worked through exercises on one or more topics and no more Mastery Challenges are available to them.
As of August 1 they were both at about the 55% mark for pre-algebra. I hope they make it by Labor Day.

I Like 5 in a Row

I remember—too clearly!—what it felt like to open my math homework after coming home from school at 3:30. Or possibly from the school paper at 6:00. Or from the grocery store at 8:00. I was tired, math was the most tedious of all subjects, and there were so many exercises.
How many problems? 38? Turn the page. Heave a sigh. Whisper an expletive. 72! Pull the crushed spiral out of my backpack. Maybe we only have to do the odd-numbered ones tonight?... No such luck.
My son is the same way with math exercises. Filling out a worksheet holds no satisfaction for him. When he used to look at a page of math exercises, I saw my own dread in his face.
This is one area where Khan really shines. Last night I had the kids review both the distributive property and finding greatest common factors—areas in which they had missed problems on Khan’s Mastery quizzes. For each topic they watched a five minute video and did some exercises.
But Khan doesn’t make the kids do 38 or 72 exercises. It says Get 5 correct in a row.

That’s it. Just five problems. If you get them all right.
If you get four and flub the fifth, well, now you have to do five more. You could be stuck there all night, but you could be done in five or ten minutes. And that’s a powerful motivator.
Nathaniel, who has never, ever been careful about arithmetic, not since the first time he hastily filled in the space under 2 + 1 on a worksheet, never-once-careful Nathaniel, is being careful. When it comes to the last problem, I can see him sweating, checking his work.
Checking his work.
Checking work reinforces math principles wonderfully. When he’s confirming that solving 9 X (5 + 4) is the same if he works it out as 45 + 36 as if he works it out as 9 X 9, he’s really learning what the distributive property means. I can remember worksheets and tests where my teachers used to write Check your work! optimistically across the top. Khan doesn’t, but doesn’t have to. It’s enough to say Get 5 correct in a row.