Testing, Testing!
Nov. 7th, 2019 04:26 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
stoutfellowToday I returned the second (and last) midterm to my Linear Algebra class. I wasn't pleased with the scores, and I guess quite a few students were even more displeased. I hate when this happens - I feel as though I've failed them somehow.
At any rate, I went over the problems for them. One of the problems had several different lines of attack, and I went over two of the most direct methods. One student - one who'd done well - raised his hand: "Could you do :this:?" It was a good idea, and I quickly described what he'd find if he took that route.
Finishing the review, I continued with the current material, involving coordinates with respect to a basis. I showed them a few examples, pointing out the geometric content and showing how this allowed a shift from abstract vector spaces to things that look very much like R^n. I got just to the verge of discussing the mechanics of change-of-basis when time ran out.
The student with the good idea came up to me then, and said, "I see what I did wrong. I stopped too soon; I should have gone and :done this and this: Then I'd wind up with :this:" I agreed, and pointed out that he was doing precisely what I'd been talking about moments before, and that the result was precisely change-of-basis - the subject of the next class session. "Yes, you're on the right track!"
As he walked away, he was laughing softly, in tones of joy.
I may not have connected with quite a few students, but this kid's got it.
At any rate, I went over the problems for them. One of the problems had several different lines of attack, and I went over two of the most direct methods. One student - one who'd done well - raised his hand: "Could you do :this:?" It was a good idea, and I quickly described what he'd find if he took that route.
Finishing the review, I continued with the current material, involving coordinates with respect to a basis. I showed them a few examples, pointing out the geometric content and showing how this allowed a shift from abstract vector spaces to things that look very much like R^n. I got just to the verge of discussing the mechanics of change-of-basis when time ran out.
The student with the good idea came up to me then, and said, "I see what I did wrong. I stopped too soon; I should have gone and :done this and this: Then I'd wind up with :this:" I agreed, and pointed out that he was doing precisely what I'd been talking about moments before, and that the result was precisely change-of-basis - the subject of the next class session. "Yes, you're on the right track!"
As he walked away, he was laughing softly, in tones of joy.
I may not have connected with quite a few students, but this kid's got it.
