Non-Examples

Last night I wrote about non-examples. Today I saw one I haven’t seen before.

We were reviewing 2-D geometry from awhile ago. Two areas of focus in 8th grade plane geometry are the Pythagorean Theorem and applying angle rules to triangles, and we did a number of problems along those lines as a class (they especially like Mathy McMatherson’s parallel line mazes). Then students practiced on their own. Wrapped up class with a short exit ticket, including this question:

Most students nailed it. And I watched in horror as one student wrote on her paper, with complete confidence:

48 + 50 = 98

180 – 98 = 82

82 degrees

I’m thinking she’s not quite there.Definitely a case of blindly following what the teacher does. Not sure how best to circle back on this one.

4 thoughts on “Non-Examples”

1. Teresa Ryan

I see this periodically also. Often from students who will tell me, “The angles in a triangle add up to 180”, and when I ask, “are you working with angles here?”, will tell me no. They cannot seem to make the leap however to why their solution is not making sense. I’m baffled.

1. dkane47 Post author

I’ve seen that as well. I’m curious what is going through students’ minds at that point, when they’ve been confronted with the fact that the solution they found is incorrect,they know that it’s incorrect, but they don’t know the way forward. Is it fear? Helplessness? Confusion?

2. banderson02

My first question to her would be to identify the 82* angle. Depending on how she answers that is how I would proceed on intervention. I’m not even sure I could say she’s blindly following the teacher since she is mashing two concepts together to create a faulty answer.

1. dkane47 Post author

I like that question. I wonder if, beyond blindly following a teacher, there is an element of associative memory at work. Student sees a triangle and latches onto everything that they know how to do with triangles, applying the first idea that comes solidly to mind. If that’s the case, pausing for a moment to contextualize may be the best way to have them reconsider their approach.