The writing is messy, but to me it looks like 7/7 = 1.
No, it’s definitely “7=1” – you can see just above it, for example, “6, 6, 6 = 3”, or below it “10, 10 = 2”. The kid is working on a problem where the relevant information is how many instances there are and using the equals sign to mean “this is the answer.”
I think at least part of why this happens is that usually the only relational symbols kids get exposed to in a mathematical context are the equals sign and the less-than/greater than signs. They need to be introduced to more symbols so they can use something like an arrow or a colon or even the cardinality-of-a-set vertical bars in this situation.
Also, they need to be taught that equals sign means something like “these are different names for the same thing” or “this is a fair trade”.
This is kind of a tricky example. Over on the other blog, you say that the instruction that resulted in this was:”Then I asked them to organize all of the data any way that they saw fit.”
So yeah, they shouldn’t use the equal sign there, but I think the example here, in that context, is a great example of students trying to apply what they know in a situation that was intentionally open and creative. I don’t see this as being nearly as erroneous as the other math mistakes on the blog.
Thanks for the comment, Dave.
I don’t think that this is erroneous. I wouldn’t tell the student that she was wrong. I wouldn’t take off points or whatever. But I do think that this is an important mistake. Again, not one that’s problematic given the student’s grade level. The student wasn’t screwing up or anything. But there is a conceptual problem with the way that this girl sees equality.
(And it’s not just her. I had a whole classroom of students who were very, very willing to defend the idea that equals just means “the answer is” and that an equation is just a math question.)
4 replies on “7 = 1”
The writing is messy, but to me it looks like 7/7 = 1.
No, it’s definitely “7=1” – you can see just above it, for example, “6, 6, 6 = 3”, or below it “10, 10 = 2”. The kid is working on a problem where the relevant information is how many instances there are and using the equals sign to mean “this is the answer.”
I think at least part of why this happens is that usually the only relational symbols kids get exposed to in a mathematical context are the equals sign and the less-than/greater than signs. They need to be introduced to more symbols so they can use something like an arrow or a colon or even the cardinality-of-a-set vertical bars in this situation.
Also, they need to be taught that equals sign means something like “these are different names for the same thing” or “this is a fair trade”.
This is kind of a tricky example. Over on the other blog, you say that the instruction that resulted in this was:”Then I asked them to organize all of the data any way that they saw fit.”
So yeah, they shouldn’t use the equal sign there, but I think the example here, in that context, is a great example of students trying to apply what they know in a situation that was intentionally open and creative. I don’t see this as being nearly as erroneous as the other math mistakes on the blog.
Thanks for the comment, Dave.
I don’t think that this is erroneous. I wouldn’t tell the student that she was wrong. I wouldn’t take off points or whatever. But I do think that this is an important mistake. Again, not one that’s problematic given the student’s grade level. The student wasn’t screwing up or anything. But there is a conceptual problem with the way that this girl sees equality.
(And it’s not just her. I had a whole classroom of students who were very, very willing to defend the idea that equals just means “the answer is” and that an equation is just a math question.)