Represent!

Posted on May 2, 2017

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https://kgmathminds.com/2016/09/29/adding-subtracting-tools-and-representations/

Loving the idea of using language to talk about the learning process.   Students discussed what it was like to represent subtraction with number lines, blocks, equations, etc.

Grumpy and not sure why.   (Usually means something in the diet is out of whack…)

Also reading http://ccrc.tc.columbia.edu/media/k2/attachments/modularization-developmental-mathematics-two-states.pdf   having edited yesterday’s comment to be less grumpy and peevish.

Executive summary — modularizing in discrete units helped some students but in both four-week discrete units and “do 3 of whichever units you need” formats, there were significant struggles of the usual “math is hard” sort.   If this stuff is going to work, those issues need to be addressed.

The blow by blow:

So far it’s talking about the marvels of modules — chunking everything into discrete pieces.   I do see the “concept” word mentioned here:

modestconceptualcore

Okay, I think this is basically saying:   “intro math is mostly procedures, and computers help with the rote practice, and by the way you get graded on doing the practice a lot.”

I’m mildly galled that this seems to be an accepted status quo.

… and mirabile dictu the next paragraph does call this into question. It doesn’t address it at all though (?!?!?).   It just notes a bunch of Stigler-in-all-the-citations articles about concept issues (not including the one I cite most often).

There’s just one more paragraph saying that by the way, online courses haven’t been found to be particularly helpful to students with lower GPAs to start with.

Then the article just shifts to what the community colleges are doing.

Oh, but it’s okay!   It says so right here that the goal is to learn the concepts!!!

math_concept_quote

Where’s my shovel?   I’ve got asparagus to fertilize and this is strong stuff.

But this is interesting:

” Using interview data, we examine instructor and student experiences with teaching and learning developmental math content in both course structures, with attention to other theorized goals of modularization: personalization and mastery.”

Okay, I’m piqued .

First course structure:   crunchy, discrete four-week modules.

There’s a nice graphic of how students placed in the five modules.  Number two is the lowest, and I didn’t have to read to guess that that’s fractions.

From the comments, it seems the modules are very modularized.  To wit:

“So we are in fractions: We didn’t do anything else, no algebra. When we’re in decimals, we do just decimals. And then, once we get to [module 3], it’s all algebra. So really, you don’t use module 1 or 2 really in [module 3]; you usually add whole numbers with variables.”

And this piece of honesty:

“It makes it difficult to connect concepts all the way through, and it’s always possible for someone to say, “When you’re teaching this, you just show them where all of this stuff connects in.” And ideally, you do that, but then in a four-and-a-half-week class when you’ve got to give two tests and a final exam, it can get difficult to cover all the new material.”

Which is to say, even teachers who *want* to teach concepts find things too constraining.

The completion stats aren’t great, but this article isn’t about effectiveness (there’s mention of research that addresses that… later :))   There was some thought that success should be better in the higher levels because if you made it that far, you probably know more — but I would question that.  With discrete crunchy modules all you did was pass that module, per that first student quote. And if you’re one of the ones still doing everything painstakingly then… it’s not going to transfer smoothly.  (Oh, and administratively this was a “scheduling nightmare” b/c of the different drop/swap/withdrawal issues.)

The next structure was the “course shell” wherein you signed up for a 3- or 4- credit hour course and took whatever modules you needed.

My favorite quote so far:

“[T]he real surprise hasn’t been the ones who’ve floored the accelerator,” according to a 2014 blog post on the topic; “it’s the ones who ordinarily would have 27 given up and walked away, who are slowly plugging along” (Reed, 2014). Participants in our study affirmed this perspective to some degree, with some arguing that the flexibility afforded by shell courses is particularly appropriate for allowing developmental students to master content. As one faculty member explained, “The students who truly need more time to grasp a concept, they have that opportunity.”

Imagine, if you can/will… that the instruction is also designed to develop concepts.

… but to continue with the article — the big fat administrative downside to this one is that well, if you don’t complete enough modules, you don’t pass the course.   And no, the stats aren’t really good for this, either.

I agree with the conclusion in the Educause write-up when in the context of the whole article (because it includes the messy pedagogical and administrative ups and downs):

“…the lessons can also be applied to college-level courses. Students with weak proficiency in math and/or poor academic self-regulation will be more successful in computer-mediated courses that include strong structures to bolster student motivation, and create accountability for meeting course deadlines. Tweaking a computerized course to add more structure and clearer demands can push students to make it to the finish line.”

Could we improve the instruction along the way, too?   Concepts?

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