Chapter 17 - Homework Reflections

Homework is an essential part of a mathematics class. Students are expected to do homework, because teachers know that students learn best when they work on problems, and practice their skills. Hopefully, each homework assignment is discussed in class, so that the students find if they have any errors in their work. Teachers know that it is important that students not only recognize their errors, but also learn how to do those problems correctly so that they will not make those errors again. Writing corrections to their homework assignments is a valuable task, one that will reinforce the students' understanding of the concepts.

In my writing-intensive geometry class, I was also interested in hearing how the students felt about their homework assignments, their struggles, their errors, and their triumphs. I asked them to select a few homework corrections for their portfolio, and to write reflections on those assignments: why they chose the ones the picked, and what (if anything) they learned from the correction process.

Of course a few always wrote about how they thought homework corrections were "a pain", and that they didn't really like to do them; but most of the students felt it was important that they find out exactly what their error had been, in each case, and exactly why they had made that mistake. They agreed with me when I said that if we did not find the source of our errors, we were doomed to repeat them. This also allowed them a way to vent their frustration at those errors they, themselves, called "stupid mistakes". (One wonders if there are "smart mistakes"!)

In her Homework Reflections, Malia wrote: "I chose to put this piece in my portfolio because I feel that homework is something that shows the amount of effort you put into a partucular class on your own time. I am proud to say that I have always done my homework, and if I did not understand a problem, I made sure it was explained by a classmate or the teacher. I should have taken the time to draw an accurate diagram. If I had just drawn the diagram below, I would have gotten the problem right. I sure won't make that mistake again!"

Keenan wrote "Although I have to admit it, I think homework is a great factor in how well you do in class. Homework also reflects how much effort a student puts into the work. If I feel that a particular assignment is challenging or easy to forget, I circle it in my homework reflections. Then I know exactly which problems to review before the next test."

Shelly had some excllent ideas about methods for handling homework. She wrote "I keep a notebook with each homework assignment, and I write all the solutions clearly for each problem, step by step. Then, when we go over them in class, I circle in red the ones I got wrong. I write notes to myself saying what I did wrong, like 'forgot to square it' or 'I was thinking area and it was supposed to be perimeter'. (I think it's dumb to write something like "I made an arithemetic mistake" - the point is, what was the mistake, exactly!) Then I study these before the next test."

Jan began her corrections with the comment "In general, proofs are not my favorite part of math, but I've learned ways to get better at them. Mostly, writing clear notes explaining (to myself) exactly where and how I went wrong is what works for me. Then, before the next test, I study what I wrote so I can do better the next time."

"It is easier to square the circle than to get round a mathematician."

Augustus De Morgan (1806-1871)