My Monday SAT Prep class had some very interesting discussion. Since I taped that session, I am able to go over the discussion which we had in class again, in greater detail. I would like to reflect on the whole class, but highlight that discussion.

I was just wrapping up the following slide on proportions…

When the question was asked by KJ: “With proportions, is cross-multiplication and division the only way to simplify?” My answer: “No,” and some elaboration led to a bunch of student voice stemming from some mass confusion.

As I look back on the slide, the step where I multiply both sides by 12 could have been elaborated upon, or taken a little more slowly. It is interesting to wonder if that was the root of the ensuing 20 minute discussion.

A few students were confused about what it means to “multiply both sides by 12”, and one student, AO, asked about where we were multiplying 12 in the numerator or in the denominator.

Another student was confused that we didn’t just compute (doughnuts/package) and then multiply by 5. At which point I realized that students were not confident that I could take the inverse of both sides of the equation, i.e. to have doughnuts/package on both sides, and thus get the same answer for x.

When one student (F.R.) pointed out that this method would work when the numbers weren’t so neat and tidy, I thought we were making headway, but just then… a student asked “But why does it have to be that difficult? Why can’t you just say 12 divided by 2 times 5. Why is that so hard?”

And another student chimes in: “I get what SL just said!”

“Maybe this question wouldn’t have been so hard if the numbers hadn’t been so easy,” said another student.

“Why do we have to be taught the more complex way?” says SL.

After about 8 minutes of students taking positions on cross-multiplication-and-division, or the algebraic method, we get at one root of the matter.

“When you write something over another number, it just looks so much more confusing than it has to be,” says SL. We conclude that fractions are scary. And that you have to work on them until they aren’t so scary.

“Fractions are, like, my worst enemy,” says SL. And a couple of other students agree.

I have to say this animosity towards mathematics is very interesting, and a little dismaying. No other subject seems to be determined to make the learner feel stupid. No other subject seems to offer simplicity and then once a student is lulled into thinking they understand, there is a sudden change in difficulty.

Overall, I think the first half of the class was very valuable. I think many students had chances to voice their frustrations or challenges with the content. I need to keep those students in mind when I prepare a lesson. I need to brainstorm other ways to connect the math to those students so that it feels authentic and non-threatening. I am really thinking that a Mighton-esque approach where the numbers are easier at first and then the problems only get minutely harder as the student progresses.

The second part of the class (slightly better camera angle) was a little silly, but folks seemed attentive. The break seems to be very helpful, and students seemed refreshed and ready to go after the break. After I gave out the homework handout many people interpreted that as the end of class, that wasn’t so helpful, but it was used by some to get some work done.

This was the first class where I tried both a handout in class, and giving out the homework and letting some class time be used on it. I don’t think I will get any better return or completion rate on the homework by doing this, so I may not do it again. I was able to collect quite a few worksheets that were done in the first half of the class.

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