I wonder if the student would’ve made the same mistake with “scaling by 2.” In any event, this isn’t necessarily a nasty misconception to fix, but I’m always interested by the circumstances when addition and multiplication get tangled up.
— Lisa Bejarano (@lisabej_manitou) January 12, 2014
What interesting mistakes! Let’s make everything that’s puzzling about these explicit.
“6, 8 are equal, but 10 isn’t equal.”
“Yes, because all the sides are equal.”
This is mysterious to me, but what’s important is to not dismiss these students as hopelessly confused. Take the second mistake. What we’ve discovered is that you can know a lot and still think that a 6, 8, 10 triangle has all equal sides. That’s really cool!
As far as shedding light on these mistakes, I’m really having trouble coming up with anything that makes sense. I’d say that the top student is not saying that 6 and 8 are equal to each other, but then what is that student saying?
What other mistakes would you expect to see from this problem? How do you teach so as to help students avoid these pitfalls?
Thanks to Tina Cardone for the submission.
What’s the fastest way to help this student?
Thanks to Nico for the submission.
My sense is that this mistake isn’t as interesting as the rest, but it’s a pretty common one that I see in Trigonometry. The question is, what sort of activity would help this student out?