Kate Nowak: Demon Mathematics
Kate posted a clip which exposes the profits oil companies make by working the rules of rounding to their advantage. It’s mathematically engaging and relevant and well worth dropping into some dead air at the end of class.
But I don’t know what the kids do with it.
Mostly, it runs afoul of the rule of least power which, for our purposes, means the medium has to hint at a question while leaving several square miles of pasture open around it for student exploration. This guy, in contrast, lays out an explicit thesis and supports it completely, leaving little room for inquiry.
Denise Gaskins: Quiltometry
Your mileage will vary, obviously, with your class’ enthusiasm for quilting. I appreciate this, though, because it doesn’t just beg that wormy chestnut, “what shapes do you see here?”
Three notes:
- Ask: “how many different kinds of fabric do you see in the bottom two rows?” a question which anyone, regardless of mathematical ability, can answer or guess at. (Similarly: the question “will the ball hit the can?” is a prelude to mathematical inquiry but isn’t, itself, strictly mathematical.)
- Then ask: “how much of each kind of fabric do you need to quilt the bottom two rows?” a question which is unanswerable without more information. This begs the very, very valuable student inquiry, “what information do I need here?” and the very, very cool lazy-student follow-up “what is the least amount information I can get away with knowing here?” ¶ From there you can go lots of fun places, some of which might involve the practicality of purchasing fabric in one-yard increments with a fifty-four-inch bolt width, something I would know absolutely nothing about.
- Textbooks ruin these problems:
Be less helpful, etc.
16 Comments
Kate Nowak
May 15, 2009 - 3:12 am -Except…that…he’s wrong… I feel like I am living in the Twilight Zone with this clip…running around shouting in people’s faces “Rounding is not unfair, just because a vlogger says so! His argument is logically flawed! LOGICALLY FLAAAAAAWED!” (as men in white coats whisk me away).
Ahem. He says “5-9 up, 1-4 down” therefore you round up more than down. But he left out zero. Sometimes floating point decimals come out with a zero in the place you look at for your rounding. It’s really “5-9 up, 0-4 down”. Half and half. Unless I am completely losing my mind. Which I haven’t ruled out.
What kids do with it is argue with it. At least a few will notice something is not right here. If I can get them to speak up, we can get a little more in the weeds about the details of rounding, which no-brainer that it seems like, lots of kids find a way to screw up regularly and spectacularly.
I know it’s not a mysteriously tantalizing picture that begs an irresistible question. I’m working on it, Sensei. :-)
Ben
May 15, 2009 - 5:14 am -Kate:
Wouldn’t your logic in turn be flawed?
The concept of rounding it to replace a number with another number not quite equal to it, but close enough to it that for all practical purposes it doesn’t seriously affect the outcome of your equation. Rounding is the process of changing a number (either 1-9), into a 0, by changing the number to the previous or next highest multiple of 10.
The 0 at the end of the number (or after the decimal point) is the goal and purpose of the rounding. Therefore, the number 0 isn’t included in the rounding argument because we don’t round the number 0 to anything. If my gasoline purchase landed perfectly on $12.78 and 0/10 of a penny I wouldn’t need to round because the amount ends without any fractions of a penny to figure out what to do with.
That, and I probably would have a very tiny car if I only needed to put that much in :)
Kate
May 15, 2009 - 6:19 am -How would you round each of these to the nearest tenth?
2.5938473
2.5823895708923
2.57123
2.564905689
2.5527346
2.543890589
2.53276
2.523957
2.5127463872634
2.50467234
You get 2.6 5 times, and 2.5 5 times.
Seriously, if this doesn’t do it, I give up.
Dan Meyer
May 15, 2009 - 6:27 am -Backhand volley down the line!
I wish this was on ESPN.
Jason Dyer
May 15, 2009 - 8:05 am -I recommend the take on the same video at Good Math, Bad Math:
http://scienceblogs.com/goodmath/2009/03/rounding_and_bias.php
Frank Noschese
May 15, 2009 - 8:51 am -Don’t forget Rhett Allain’s post over at Dot Physics!
“In the second Cat in the Hat book (I think it is the second one), the Cat reveals that he has more smaller cats under his hat. They are labeled A – Z with Z being so small you can’t even see. Question: What is the sequence of sizes for successive cats? How big would Cat Z be?”
http://blog.dotphys.net/2009/04/the-cat-in-the-hat-comes-back-and-gets-small/
A. Mercer
May 15, 2009 - 3:50 pm -Since crafting has been intro’d in the Quiltometry, I’d like to put a query out to the my fellow knitters there in Dy/Dan land (I know Sarah is one from her annual report)….
1. I can see lot’s of algebra in knitting esp. pattern knitting, but I’m pretty convinced it will not be engaging or obvious UNLESS the kids are knitting themselves.
2. I’m not seeing higher level Algebra, but I can see a lot of stuff that is suitable at elementary grades for laying foundations. Am I missing something Sarah (and others) at that goes beyond pre-Algebra?
3. I was about to start a small knitting group of students to test some of the “therapeutic” benefits, and I’m going to try to throw some math into the mix, ideas are welcome.
Thanks as always for letting me pimp on your blog.
BTW: I like how you “framed” the quiltometry.
Sarah
May 15, 2009 - 9:01 pm -Thanks for calling me out Alice. FWIW, I’m planning on converting Jackie next year too, (teaching her to crochet hyperbolic planes.) and am all for starting a math knitting group.
My precalculus teacher’s emergency lesson plan was to write a paper about how you use math in daily life. I wrote about knitting. Probably along the lines of altering patterns as you suggest in #1. But I completely agree, this would be as boring as any other way to approach the math if you weren’t already engaged with knitting.
For ideas, get on Ravelry and search for math. (I procrastinated for at least an hour when I shouldn’t have this week after Jackie got me looking at hyperbolic fun again.) The ideas do tend to be elementary or college level with a handful of geometry “standards” thrown in. (I’m afraid of not being able to post this comment if I have too many links. Check your Twitter. Future people, search Wooly Thoughts or Toroidal Snark.)
That said, I could imagine some experiments with gauge leading to discussions about ratio. Also in pattern building discussions looking at how the height of garter rows compares to the width of the stitch. Years ago I saw a “random” cable sweater that could be a tie-in to probability. (Perhaps a bit weak, but if it’s knitting club with math instead of math club with knitting I’m okay with the weakness.)
Those are my gut reactions. I haven’t tried any of this with students. They see me knitting at basketball and football games, but honestly, I haven’t done nearly as much since I started teaching. Keep me updated, and I’ll keep brainstorming.
Sarah
May 15, 2009 - 9:09 pm -Please, don’t turn whatever fun ideas generated into the standard math book problem. A la Polar Science Station.
Nancy Bosch
May 16, 2009 - 6:53 am -The Cat in the Hat problem looks like like a “Dan”. Here’s a t-shirt for ya. http://www.threadless.com/product/427/Hypotamoose
This company has a student t-shirt design contest called Threadless 101—maybe you could entice some of your kids.
A. Mercer
May 16, 2009 - 12:42 pm -If we keep this up, do you think we could succeed in turning Dy/Dan into a crafting blog? He already has pictures of pink fabric in this post…I kid, I kid.
So there is still agreement from Sarah that to make the knitting math connection, you have to have the kids doing knitting, which only seems to be taught in Europe, or Waldorf schools.
Sarah
May 16, 2009 - 4:10 pm -I’ve taught friends to knit since high school and plenty of little kids learn the knit stitch from me when I knit in public. But, yeah, knitting club with twist of math.
Dan Meyer
May 17, 2009 - 6:41 pm -Looks like I need to add a few new keywords to my blog’s spam filter. Heh.
A. Mercer
May 20, 2009 - 5:48 pm -Dan, I know each comment brings me that much closer to having my IP blocked…
SERIOUSLY, don’t you think that point about the kids doing the activity as a pre-req to doing math projects related to it is kinda key?
I suppose there are some activities, like pro sports, where you could be largely an observer. My dh is convinced he can’t do math, but spent most of his life following baseball stats, which involves a fair amount of math and analysis (really, what is a useful stat to follow in baseball, you could write a dissertation on it). I think this argues against stupid math problem setups like, how much of x do you need to make y when the kid doesn’t give a darn about making y and working with x.
Dan Meyer
May 21, 2009 - 6:39 pm -Sorry, Alice, missed the question the first time around.
I think that having students quilt a bit before they work the math could only help their understanding of the area problem. As always, though, we balance everything against time and cost and I don’t think the value added by classroom quilting justifies the time or dollar cost.
That line is different for everyone, though, and if bringing a personal hobby into the classroom makes you a little more satisfied in your job or the relationship between your students that much deeper, that has to factor into your calculations also.
A. Mercer
May 21, 2009 - 7:15 pm -Dan, I hear you on that. I would NOT do any of this lightly. I think we’re all on the same sheet of graph paper which is don’t just throw this stuff out there unless there is some meat to the lesson and something to hook the kids so they aren’t saying WTH.