I just asked my honors students to submit their second portfolio write-ups. Only two emailed them in and I left the rest at school on Friday — February break yeah! — so I thought I’d get into those.
Of course, the ones that emailed in are some of my hardest-working students. One of them has had over a 100 average in my class pretty much all year even though I give extra credit about twice a quarter. The girl is unstoppable and obviously I recruited her for the programming club. Still, I think there are some useful bits to notice in the two pieces of work. They have the same main problematic area as most, which is that the students assume that other people will know what they’re talking about without fully explaining it.
Here are links to their full things, with names removed:
I didn’t give much instruction for this assignment. I simply asked students to take their work for any question they had encountered in class and explain how they had gotten from the question to the answer.
Interestingly, both students chose questions about switching between quadratic forms. One was quite a bit more difficult than the other, as not only did Jane make a more difficult switch, but she did a generalized version with variables, whereas Ned used a specific question. I was also able to give her help during class but not him, because he was out sick.
One issue with Jane’s is that perhaps because she is so quick to figure things out on her own, sometimes as the reader you have to do quite a bit of work to understand how she gets from step to step.
The step in #5 is something that other students in the class might be okay with, but the factoring needs some explanation in my opinion. Even if another student could see that it was true, I’m not sure that they would understand how Jane knew to make this move.
I have to give Jane a lot of credit, though, because she is aware of the fact that she is making connections more quickly than other students. She wrote a reflection at the end and in it, she wrote:
Some parts were a little hard to explain but I finally got through. I had the most trouble explaining completing the square than anything else. It was just a given thing to me but I understand why people would get confused.
This seems important to me. Even though Jane didn’t catch all the places where students might get tripped up, I’m impressed that such a bright girl, who previously has had difficulty responding with complete respect when unimpressed by her peers’ work, was able to come to this level of understanding.
The other cool thing about this is that the section Jane mentions, completing the square, is one of my favorite parts of her write-up. She used a diagram to explain what she was doing:
It’s a classic way of thinking about this, though we haven’t done it in class and it isn’t in our book. I’m not sure where she picked it up, but I can tell that she used it for the right reason and put the right spin on it.
Again, this is one of my tippy top students, but I think the other students are grappling with figuring how to explain things in similar ways. They’re just explaining simpler problems. One very interesting thing about this is that all students are on the same page, since they have so little experience explaining themselves. I must say, things have vastly improved since last time, which is encouraging.
But it still seems like it is a ton of work for these students to attempt advanced problems. At first I was a little disappointed when students were choosing rather basic things, like solving a not-too-complicated equation. Now I think I might encourage them to aim for more basic problems so that they can get used to getting very thoroughly digging through a problem. I’m worried that Jane is learning to only thoroughly explain PART of the problem, since there was so much to get into in her chosen problem.