I started this really interesting post about whether something students were doing on a test was a careless error or a bigger misconception. But then I realized that I was the one who made the mistake! I was glad to have started writing the post when I was only a third of the way through the tests so I didn't have to go back and re-mark all of them.
My question still holds though; when do you go from thinking "Why didn't they check their work? My students make so many careless mistakes." to thinking "Wow, they really didn't understand this." If a couple students make the same mistake is that a clue that they have a misconception or were they both careless? What if 10 students make the same mistake? On this same test quite a few students used 2π to calculate the period of a stretched tangent function (trig refresher: 2π is the period of sine and cosine, but π is the period of tangent). I'm still not sure if they just forgot in the moment with the pressure of taking a test, or if they don't know that tangent has a different period than sine and cosine. When does an error earn the label misconception?
If you're curious, here's what I was thinking:
And what the students were writing:
And the more precise way to write out the solution to the problem:
I think mine was a mistake because I realized it didn't make sense when I started thinking about it. Is that the difference between a mistake and a misconception?