The kid’s handwriting is hard to read, so I want to point you towards 9 times 13, near the top of this page.
I think that this is a great example of a mistake that you can feel fairly good about. Your thoughts, on any of his work?
Category: Grade 4
7 = 1, huh?
Check out my post over at the other blog for what I did about this. Comment here or there, whichever you prefer.
I don’t have a picture for this, but every single one of my 4th Graders thought that “average” meant “the most common thing.”
(a) Where do they get this idea from?
(b) Is it a big deal misconception?
(c) How do you create a need for something besides “most common”?
(I think I have my own answers for (a) and (c), but I’m more curious to know what you guys all think.)
The kid also answered the “How do you know?” question:
“Because 5 is half of 10, and 50 is the same number as 5, just with a 0, and 10 is the same number as 100 just with another 0.”
What does this mistake say about the way kids see numbers and multiplicative relationships?
I’m inclined to say that this is a classic working memory mistake. You’ve got a resources-heavy calculation being done in the student’s head, and you’ve got this 3 floating around in the problem, and it ends up in the ones place.
Agree? Disagree? Thoughts?
Any idea what’s going on here? In case fuzziness is an issue, the question is “What is the biggest multiplication that you know without thinking very much about it?”
Also, I anticipate getting some flack for the wording of this question being potentially confusing. I don’t disagree, necessarily, but I want to offer a partial defense of the question. First, I had been reading the TERC curriculum and they make a point of not saying “multiplication facts,” instead always saying “multiplication combinations.” I haven’t wrapped my head around what makes sense to me, so I punted on the question, figuring that I’d be there to help kids figure out what it meant. And I did, and everybody else offered answers that made sense. Most importantly, the question served it’s purpose: some kids wrote “8 x 8” while others wrote “1,000,000,000,000,000,000 x 10.”
Explanations? What lessons are there about the way kids think in this work?
- 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?]
I’d love to hear anything that you’re thinking about this in the comments.
I wonder: should we be giving kids explicit guides for these sorts of algorithms at all? Algorithms ought to be patterns in thought. Does a mistake like this begin to make a case against these sort of printed aids?
Thanks to Professor Triangleman for the submission.
From the submitter: “I came across these answers to sig fig questions when marking a pre-algebra numeracy test last night. I’ve attached two answers, one is a very common mistake where students just can’t believe that they are asked to round up that much. The second… well I don’t have any idea what the student was thinking, so I thought your readers might be able to help.”
Readers?