What’s the relationship between division and square roots in students’ minds? Why did the kid write 15 / 15.
[Note: no idea how to categorize this in CCSS. Also, thanks to Timon for the submission.]
Categories
Month: June 2013
Last week I posted a short video from a tutoring session I had with a kid. We were solving equations, and he had some interesting ideas, and it was nice to have those ideas and his mental workings become explicit.
Here’s another chunk of that video:
Comment on whatever you like, but here are some prompts:
- Help me understand his thinking. How did he devise his test for whether his solution is correct?
- What does this say about what he thinks about 2/0?
Or jump in with whatever you like in the comments.
- What exactly is the shortcut?
- Why does this shortcut seem reasonable?
- We’d all agree, I think, that 2 x 6 = 26 is not a result of this kid not understanding what multiplication is. I’ve made that mistake before, and I bet that you have too. So, why is it a common mistake? What does this say about how a mind works while working on math?
[Any advice on how to tag this, CCSS-wise?]
Categories
Area and Perimeter
How would you help this student?
Comment on anything that you like, but here are some prompts:
- Do you like my questioning? (Because I didn’t. Notice that moment when I pause and try to unask my question?)
- Describe, as best you can, the way that this kid thinks about the Distributive Property.
- What would you say next, if you were me?
- Does this video have implications about the way that you’d teach this topic? (And, come on, don’t give me that “they need lots of practice stuff.” Of course they do. But what else?)
- Do you prefer having videos over images on this site? (Because I have about a half hour more footage from my work with this kid…)
Looking forward to a great bunch of comments here. Don’t let me down?
Update:
Here’s how I responded:
We’re looking at #4 here, guys: “Use a non-calculator shortcut to add up all the integers from 1 to 203.”
Are these differences significant? Which is most appropriate to introduce to students first? Do you introduce multiple techniques explicitly to your classes? What does this student work indicate about the way this class was taught?
Or, talk about whatever you like.
Categories
Odd Pairing
“Add up all of the numbers between 1 and 100.”
Easy, once you realize that (1, 100) make a pair whose sum is 101, (2, 99) make another such pair, etc.
“Add up all of the numbers between 1 and 101.”
Harder to make sense of, because there’s an odd number of integers that you’re summing, so they can’t be paired off evenly.
—
I’ve got (at least) pieces of student work that show (at least) 3 different ways of handling an odd number of integers, as in the problem above.
In the comments below, try to catch ’em all. I’ll update this post with the actual student work tomorrow.
—
Update: For pictures of student work on this, see the next day’s post.
Can you explain where each of the student’s responses came from? As in, how did he arrive at 8/24, 14/96, and what is either 24/72 or 14/72.
Where did 12/36 come from in part B?
I saw this one in class last week:
Probability of flipping 10 heads when flipping 10 coins: (1/2)^10
Probability of flipping 9 heads when flipping 10 coins: (1/2)^9