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Elizabeth:

Am I imagining it, or are the participants (posters and respondents) mostly male? I’d love to be wrong about this. If I’m not wrong, then why would that be the case? And more importantly, has anyone noticed whether there is there any difference in class participation between female and male students when these are used in class?

I don't ask for your gender during the registration process so it's hard for me bring any data to bear on the question. But if I allow myself some conservative guesses, it seems that at the time of this writing:

  1. the top ten most perplexing users are all male,
  2. nine of the top ten most perplexing first acts were uploaded by males.

So help me, I can't figure out how the interaction on the site (ask a question and click "skip") or the nature of the tasks (a context and a question) preferences men. The reviews are all blind, too. I'm looking at a photo. Maybe it was uploaded by Candice Director. Or maybe by Dan Anderson. It's impossible to know until later.

I'm highlighting Elizabeth's comment to see if anyone can help me figure this out. I'd rather this didn't turn into a general complaint window, though. I'm interested in locating the source of any gender bias, not in airing out any other grievances.

BTW: My adviser has done a lot of work in gender and math. I should probably check in.

Featured Comment:

Too many. A really great discussion down below. Here's a link to my summary.

Hola, amigos. I'm back from Spain, back in the game after sidelining myself for a helluva comment thread. It turns out that NCTM President Michael Shaughnessy designed the task that I critiqued in a recent post and he stopped by with a few notes on my redesign.

Michael Shaughnessy:

Not all math problems have to be posed everytime in a a high tech environment. Sure, it’s ‘cooler’ that way, but i completely disagree with your comment on this one, about ‘how the problem was posed.’ It’s only boring in the beholder’s eyes, depends on how it’s pitched to a group.

The last line seems to contradict itself, though. Either boredom is in the eye of the beholder, in which case we should just pose the task however we like and accept that it simply won't engage some students or engagement depends on how the task is posed, in which case we can discuss productive ways to pose it. They both can't be true, though.

I figured there were three productive ways to pose that task, three revisions to Shaughnessy's original problem that would open it up to a few more students. I'm quoting my original post here:

  1. Show how this new, difficult problem arises from an old, easy problem.
  2. Make an appeal to student intuition.
  3. Introduce abstraction (labels, notation, etc.) only as a necessary part of solving a problem that interests us.

What's interesting is how many critics, Shaughnessy included, saw a video and assumed I was aiming at something "high-tech," "cool," and "hip." But those are beside the point. The point is helping more students access an interesting problem. Video was the means, not an end.

Shaughnessy also reports having "gotten a LOT of mileage out of this problem with middle school kids, high school kids, perspective teachers [sic]" without anything fancier than the paper the problem was printed on. I don't doubt that's true. But if that brief video opens the problem up to even one more student, my only question is why not? Why not get a little more mileage out of the problem? What's the downside?

While most critics decided early on that I was just trying to buy off the YouTube generation with something shiny, I was grateful that Tom I. critiqued the redesign on its own terms:

… it seems like Dan is always recommending that we (more or less) apologize to our students for the abstractness of math. The abstractness makes it hard, but must we assume that it makes math pointless and uninteresting for our students?

Abstraction doesn't make math harder. Abstraction makes math possible. It's one of the most powerful and satisfying tools in the mathematician's box. The trouble is that you can't abstract a vacuum. You start with something concrete (not necessarily "real-world") and then abstract its essential features. Again: you start with something concrete and then abstract it. Over and over again, though, math curricula provide both the concrete and the abstract simultaneously, one on top of the other. This is unnatural. (R. Wright puts it artfully: "This is a charming problem when posed simply and innocently, not flayed alive by terminology, labels, and notation.") Unnatural abstraction is boring and intimidating. When we put abstraction in its rightful place as a tool for simplifying the concrete, it's interesting and empowering.

Other Featured Comments

Debbie:

By starting off with a very familiar problem-style and seeing you apply your approach to it I think I’m finally convinced that this isn’t a one-trick pony but something that can work with all sorts of maths.

Bowen Kerins:

I also want to point to some language used in the discussion here. The initial problem is “insultingly easy”, while the later problem is “trivial” (Alexander’s comment). This is in the eye of the giver of the problem, not in the eye of the recipient.

This is a strong point and I'll mind my manners going forward. Rephrasing: the goal isn't to start with a problem every student will find easy. The goal is to show how something relatively simple quickly turns into something relatively more complex.

Tom I:

I bet 9 out of 10 readers of this blog thought [Shaughnessy's original] was a fun problem and felt an itch to solve it. Why wouldn’t students feel that way?

Because there isn't a one-to-one correspondence between things math teachers like and things students like. They aren't like us. Please: do whatever you can to imagine what it feels like to walk into a math class as a high school freshman who's been convinced since fifth grade she's stupid, who's now on her third year of the same Algebra class. She isn't thrilled by the same mathematical investigations you and I are. She's threatened by them.

If I cut my teeth teaching honors kids in Fairfax County, I imagine this would be a very different blog. I'd have a very different career. As it is, they tossed me to the wolves in my third year teaching and I had to make friends in the wild. I couldn't be more grateful for the empathy that experience required.

Carlo Amato:

What program do you use to construct this video?

Dvora:

On the tech side of things… how did you create the video? What programs did you use?

All Keynote. Let me see what I can put together for Keynote Camp.

Bob Parker Nails It

Bob Parker, in the comments, re the speed of cash transactions vs. credit:

Credit can’t be slower then cash – Visa told me so. They told me I am a social pariah if I pay in cash.

I believe he refers to this ad spot:

Teach Like An Elective

Jerram Froese, taking offense that anyone would walk out of a conference session after it started:

Damn. If only our students could stand up and walk out of class at any time. Wow, people.

That's a mixed metaphor right there, but an essential hypothetical for any classroom teacher and especially for core subject teachers who are (overall enrollment notwithstanding) guaranteed an audience year after year.

Cigotie, Ctd.

Cigotie and his mom stopped by this weekend to register their opinion on the obstacles to creative growth facing today's students. Both are extremely good-natured, especially since they are responding to a post entitled, "How Do You Solve A Problem Like Cigotie?"

Cigotie: I also see many kids online doing the same exact thing, as inspirations like Video CoPilot, Creative Cow, etc. And I also agree on how people are getting too sucked into a world, full of copying and project file manipulation, that they have lost all creativity themselves.

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