Comments on: NCTM President Michael Shaughnessy Responds To My Revision Of His Geometry Task

By: dy/dan » Blog Archive » [LOA] The Place Where Language And Math Make Friends

Fri, 20 Jul 2012 00:09:39 +0000

[…] My response one year ago to a commenter who said I was always recommending that math teachers apologize for the abstractness of math: Abstraction doesn't make math harder. Abstraction makes math possible. […]

By: hodge

hodge — Sun, 08 Jan 2012 20:46:48 +0000

The Benezet article is really worth a look, if for no other reason than to get a peek at education in the 20’s & 30’s. He argues that paper & pencil arithmetic gets in the way of logical reasoning, and experimented with abandoning all but mental arithmetic in the first few years of school. He gives a lot of specific examples and anecdotes that still ring true today, as well as transcribed exchanges with classrooms from the 1920’s and 30’s.

By: Sue VanHattum

Sue VanHattum — Sun, 08 Jan 2012 15:40:55 +0000

Also, if you're near any math circles (check here for possibilities), that might be a way to help him continue. Or check out Art of Problem Solving.

By: Dan Meyer

Dan Meyer — Mon, 02 Jan 2012 16:39:03 +0000

Hi Brooke, thanks for the comment. I'd never heard of Benezet so I've added him to the reading list. Also, FWIW, my mom homeschooled me up until the point (eighth grade) that she could no longer teach me math. At that point, we used a VHS series and after that point, I went to public school. I'm not saying that was the right or wrong course or action. I'm just sympathetic to parents who find themselves in the challenging (but probably rewarding) spot of facilitating their kids' learning in every subject. Yikes.

By: brooke

brooke — Fri, 30 Dec 2011 21:25:03 +0000

I’m just reading through your blog … so late to the conversation that doesn’t probably exist anymore. So, it’s really just a comment for you.

I’m a homeschool mom who has a passion that my kids learn subjects in ways that actually benefit their thinking skills. I like what you are trying to say/get across. Your goal clearly isn’t “use video”, rather your goal seems to be teaching students to think. It reminds me of the Benezet articles I read years ago. (I’m assuming you’ve heard of him, but there is a series of 3 articles online that attempts to explain his approach. I wish I had more on him.) The basis really is that crossover between intuition and exactness. I think some people, such as my nephew, are really born with math intuition that extends quite far. Others have to be coaxed towards it, such as my oldest son! The goal isn’t to be catchy. The goal is to extend that intuition, the actual understanding of a problem, so that there is little to no jump in performing the math required to gain an exact answer. Your approach, whatever media or paper or illustrations you may use to get it across, gives students the belief that they CAN understand, they CAN think, that math CAN make sense to them.

However, this all really intimidates me! I’ve made it easily to 7th grade math with my kids. I have no problem causing them to think, explaining it in an understandable way, keeping it interesting to a degree … but looking at the levels which you are teaching makes me think, there is NO way I can get that far with them unless I go back to school!

By: dy/dan » Blog Archive » [3ACTS] Some Really Obscure Geometry Problem

dy/dan » Blog Archive » [3ACTS] Some Really Obscure Geometry Problem — Tue, 25 Oct 2011 18:39:13 +0000

[…] 2011 Aug 29: My response here. […]

By: Jason Dyer

Jason Dyer — Thu, 08 Sep 2011 19:29:59 +0000

Sorry for the super-belated; I responded to this, but it looks like the Internets ate my homework.

this strikes me as stronger presentation of the puzzle

Why?

I should be clear I didn’t mean stronger than the video, I mean stronger than the original presentation.

It is not practical to make everything a video (at least at the moment?) So techniques to improve dead-tree problems into better dead-tree problems are helpful.

By: Bowen Kerins

Bowen Kerins — Thu, 01 Sep 2011 03:56:10 +0000

Good point about the “dry problem”, let me try and rephrase what I meant. I guess what I was going for is that after students work on a difficult, interesting problem (dry or otherwise) they’ll have some perspective on the ways they thought about it, or even parallels between the problem they solved and something else. I try to block off a lot of discussion time for students to describe these ways of thinking. I’ve never had kids make videos, but that’s what I was getting at.

Yeah, the other way sounds like “Here’s this pig, you put the lipstick on it, kids.” That ain’t good, and it sure ain’t math!

At some point, though, don’t there have to be some “dry problems” in a curriculum? Sticking with geometry, here’s a dry one: “What happens when you connect the midpoints of a quadrilateral?” This is a great problem with plenty of “legs” (it can be revisited several times) and students have a terrific time exploring it. I don’t see how a video introduction to the problem could work without killing the “aha”.

Good luck to everyone starting the new school year!

By: Brian Frank

Brian Frank — Wed, 31 Aug 2011 23:28:35 +0000

@zeno Here’s what I’m thinking. Without the transition, I don’t think its really challenging your intuition. It’s almost like “here’s an easy problem you can intuit”, and “now here’s a hard one you can’t”. By showing the easy problem continuously morph into the hard one, I think your brain’s intuitive systems stays on the whole time. Dan’s premise is there’s value in taking intuition to the edge, and I think this betters ushers me to that edge.

By: Zeno

Zeno — Wed, 31 Aug 2011 22:47:56 +0000

@Dan: Why is the visual interpolation of the two frames important?