Comments on: [Presentation] Math Is Power, Not Punishment

By: Ivy Kong

Ivy Kong — Fri, 08 Dec 2017 21:18:15 +0000

I was trying to come up with ways to teach the distributive property to my 7th grade intervention class. In my last few years, I tried many different ways, like using an area model, drawing the arrows, telling corny stories about talking to everyone inside the parentheses house, using algebra tiles, etc, etc. It dawned on me one day that the students probably might not even understand what was meant by 3(2x-5). So, whatever models I trying to teach were all non-sense steps to them.

Then I tried this this year: I told the kids that 3(2x-5) meant 3 sets of (2x-5) and made them expand the expression by writing out three separate sets of (2x-5). Then we combined like terms and figured out that it was 6x-15. I pounded in the idea that the ‘3 times’ meant ‘three sets’. The kids got the idea they needed three sets of 2x and three sets of -5. I hadn’t even mentioned the distributive property yet.

Then your talk came in… I wanted the ‘set’ idea to stick, so I gave them different headaches.

Power move.

I asked them to expand 7(6-8y)–minor grumbling… 1/2(4x+8)–they loved that… then 50(12x+7)–major whining. For a group of kids who were quite below grade level and also didn’t want to write (12x+7) fifty times, they came up with the aspirin awfully fast.

Then I taught them the convention and stuff. All in all, it was great and the kids felt super successful. (I also felt successful by using this strategy–I had a headache and you gave me an aspirin!)

By: Scott

Scott — Tue, 05 Dec 2017 16:52:24 +0000

It took me a minute to figure out why you needed a much bigger hammer to pound a stylus into the ground. Then I realized it was a stake…

I really like the coin problem and how it showed why arrays come in handy for counting. I’ve been working with our elementary math coach (I’m middle school) on using arrays. I am definitely sharing this with her.

By: Chester Draws

Chester Draws — Tue, 05 Dec 2017 05:07:30 +0000

In reply to Stacie Bender.

Is there any need at all for this theorem though Stacie?

It follows from two simple rules that students don’t usually have issues with — sum of a triangle and then adjacent angles on a line. As a result I have crossed this theorem off my list of ones to teach, since it can be quickly worked out from first principles — and I therefore I also don’t have to teach them when not to apply it (when the angle given is vertically opposite, not exterior) and have more time to teach the ones I do correctly.

I also don’t teach alternate exterior angles on parallel lines are equal. Again it follows from two simple rules we are already teaching, and is one less thing for them to confuse themselves about.

A plethora of rules they have to learn puts students off Geometry — so that’s where their headache tends to be. So I make it easier by cutting out surplus rules. If that means that some questions take an extra step, then so be it.

(I do actually teach both rules, because they are simple introductions to proofs. What I don’t do is expect them to add them to the list of ones they have to memorise.)

By: Dan Meyer

Dan Meyer — Mon, 04 Dec 2017 18:41:10 +0000

In reply to Stacie Bender.

Dig it. You’re provoking a combination here between the need for computation (“This would be easier if I had a general rule.”) and the need for certainty (“How can I be sure this general rule will always work.”)

Added to the document.

By: Stacie Bender

Stacie Bender — Sat, 02 Dec 2017 18:46:14 +0000

Hi Dan,
Here’s a recent headache of mine. My regular geometry students have a hard time with the “exterior angle of a triangle is equal to the sum of the remote interior angles” theorem. I don’t know if 6 problems is enough of a headache for my students to want the cure, but it’s a start. You’re welcome to copy to your directory and share.
Stacie
https://drive.google.com/open?id=15V-73Rw3VPVPMgndfpUaiqNTB30XHNk9

By: Scott McDaniel

Scott McDaniel — Fri, 01 Dec 2017 19:06:04 +0000

Yep!

I think this is the one that Dan was speaking of: http://math.ucsd.edu/~jrabin/publications/ProblemFreeActivity.pdf

By: Joanne Ward

Joanne Ward — Fri, 01 Dec 2017 14:30:13 +0000

Thank you for sharing the video!! :))

By: Dawn Burgess

Dawn Burgess — Fri, 01 Dec 2017 11:34:50 +0000

Dan, in the video you mention a paper teachers should read, but I didn’t see a link at the end. Could you point me in the right direction?