“U.S. Senator Jeff Bingaman recalled what his father, a chemistry professor, used to say about traditional lectures: the notes of the teacher go straight to the notes of the student without ever passing through the student’s mind.”
I stumbled on this in an article about a local charter school, and it relates directly to a situation I had yesterday. There’s a 10th grade girl in my geometry class who struggles in math. She told me this at the beginning of the year, and I tried to inspire her that this year could be different. She’s a really interesting girl who perks up at any mention of fractals or Fibonacci and turned in a really eloquent piece of writing for my first foray into making the students write in math class.
So she ends up pulling up to a B- last semester and was absolutely ecstatic. Then yesterday was the first test for this semester. A couple days ago I was having them work on a review of similar triangles while I went around and talked to each of them, and I started to become a little worried about her. Similar triangles usually involves dealing with fractions, and it became clear to me that her fraction skills were shaky at best.
So anyway, yesterday right before the test, she comes into my office and has this big confession to make. She says that she likes my class, but for some reason this whole unit on similar triangles has just not stuck with her. She says that she just feels like no matter how hard she tries to listen, she can’t focus on the lecture. When she can focus, she understands what I’m doing, but then she tunes out again and then when she’s looking at the homework problems, she has no idea what to do. She kept saying that she thought she knew the concepts but “couldn’t express it” the way that I showed, which basically meant she doesn’t solve proportions the way I do and was concerned about having to show her work. When I saw her working in class the other day, she actually knew what the answer was supposed to be but couldn’t explain why to her friend sitting next to her. She asked me “how to do it”, which I interpreted to mean how to set up the algebraic proportion and solve, and that’s where she was really lost.
I encouraged her to take the test and answer the questions “her way” to the best of her ability, not worrying if the “work” looked like what I showed in class. What I saw on her test was actually quite interesting. She was looking at the relationships between the sides in an addition sense – so that if one side increased by 10, she wanted the other side to increase by 10. She obviously missed the entire idea of increasing by a multiplicative factor, and I never managed to figure that out before the test.
So it makes me really wonder what to do now. I don’t feel right giving her a low test grade when I can finally just now see that she has a huge conceptual misunderstanding. Honestly, I’ve been questioning testing in general lately, but this really makes me wonder.
I know that when I give back tests, most students hardly look at it. The ones who scored poorly look embarrassed and are usually the ones that put it away the quickest. I kind of doubt most of them go home and pore over and read the comments and try to figure out how to improve.
I did a test corrections assignment earlier this year with mixed results. I’m still not sure it really shows them what to focus on; they just figure out how to fix that one problem in hopes of getting some points back. I mean after all, it’s hard for someone to look at their own paper and pick out their areas of weakness, but it’s fairly easy for me to do provided they show enough of their thought process in writing.
So I have this idea and I’m a little hesitant to do it because it would take longer.. but I was thinking of writing each student a short summary of their test that mentions the areas of deficiency, and giving them that before they ever see a red pen mark or a grade. Then, those that score below a certain threshold can meet with me to work on that deficiency and possibly earn back some credit.
I don’t know. It’s still playing in the “points game” which I am really starting to hate, but I’m not ready to go completely off the deep end with the anti-testing stuff yet. At least I feel like they’d have more of a chance of getting feedback before they shut off when they see a low grade.
Math for Humans 