Jonathan: And I think the relation to your description is this: that bottom hump often comes form kids feeling overwhelmed and just quitting. If you can find a way (and it sounds like you have) to keep them from quitting, you have a good shot at avoiding the lower hump. What I did was different, but to the same end.

My inverted bell curve hypothesis doesn’t have a whole lot of scientific ground to stand on, I’ll admit. It’s a pseudo-science rationale for the strategy you’re referencing. In a way I don’t have the energy to prove, the way I assess is keeping more of these bottom decile kids from quitting.

I mean, I’ve got a few kids rocking forty percents with a week and a half until finals who are convinced they’re going to remediate and pass. Thing is, I’m pretty sure they can.

I am also curious about why what you are doing appears effective. In wondering about several possible reasons, I don’t mean to dismiss the explanation you have offered.

I’m just struggeling with how to get my students to start thinking for themselves and how to assess this process. Then how to balance this with computational fluency.

So, I want them to understand the mathematics, be able to apply it to new situations, and be able to effectively communicate this thinking to others. Um, am I reaching too high?

Keep up the great posts – please understand that my comments are really just the questions I ask myself. However, I’m sick of my own answers and need input from others. Thanks.

Dan, when assessing one concept at a time, how do you assess your students’ ability to synthesize the concepts? Ability to problem solve? Ability to communicate mathematical thinking? In short, when do the higher order skills come into play?

Also, I’ve found that students often can do well when presented with one concept at a time. Yet when assessed on multiple ideas/topics at once, they don’t know what to do. I often hear — “I didn’t know what to do, because I didn’t know which type of problem it was”. Arghhhh! Basically it amounts to, ”tell me what to do and I’ll do it.” I then question — have they actually learned anything, if they cannot determine a strategy with which to attack the problem?

By testing in little pieces, one skill at a time, are they ever asked to put skills together, to use more than one at a time?