Friday, August 30, 2013

Reasonable Numbers, Unreasonable Nutrition

I just went to a McDonald's to eat and use the wi-fi to get some work done. Here's how it went down:

• Ordered 20 pc meal (stop with your judging eyes)
• Cashier kid heard 10 pc. I didn't notice until after I had paid.
• He called over manager. She decided to see what the price of the 20 pc meal was ($7.50), look at the receipt ($6.19), and charge the difference.
• She asked the kid what the difference was. He was pretty satisfied with his answer of $1.20. She found an item for$1.15 and charged me.
• Everyone involved was very nice and helpful, and works too hard for too little money.
There are a lot of failure modes for mental arithmetic, but there are some simple checks that you should go through. Here, anything that doesn't end with 1 is impossible. It's easy to come to $1.41 or maybe$1.21, but $1.20 shouldn't pass the smell test. We've been doing some curriculum work at school, and the math and science departments across all four divisions are convinced that this sort of answer-checking is something that kids have to have. They're right. It's a habit of mind for a scientist or mathematician, and it's something that we have to spend time with our kids on if we want them to learn it.$1.30 as an approximate answer's pretty good, and that's something else that we should work with kids on - coming to first approximations before solving a problem, so that we have some idea about what we're supposed to get, not falling prey to the "writing down whatever the calculator spits out" syndrome. These approximations can be about rounding numbers or about using a first-order Taylor series or squaring off a curve or whatever, but this is a skill that's even less frequently explicitly taught in schools than checking answers for reasonableness. Dan Meyer's "Give me a number that's too high, give me a number that's too low, give me a guess" is a great way to start.

There's certainly a lot of content to get through, but these mathematical practices are arguably at least as important, not least because they'll often survive after the content is forgotten. Don't we want to live in a world where people have these tools (even non-academic folk)? If the answer's yes, then put your class time and assessment questions where your mouth is this year - make time for work on reasonableness-checking and approximation.

Saturday, August 17, 2013

Whiteboard Loudly

I came across "University Buys Bulletproof Whiteboards" today. It's about a move by UM-Eastern Shore to buy 200 18"x20" bulletproof whiteboards - at what seems like a cost of $300 a piece. The idea is that students and teachers can use these as shields in the event of a school shooting. Those logistics aside, two things: 1. This is a far cry from the$2 Interactive Whiteboard! Portable whiteboards are cheap and can instantly transform a classroom into a place of doing, rather than a place of hearing. While it's great that some of these whiteboards are going into UMES, I hope that they're also being used to change the environment of the classroom, rather than sitting next to desks waiting for bad news. For the price, they could buy/make a $2 whiteboard for every student at the school! The cost/benefit analysis here isn't really my point, but if these are worth$60,000, maybe it's also worth it to spend \$5000 to outfit every room in the school with a set of student whiteboards, and worth the cost to train teachers to use them effectively to increase student engagement and learning.

2. I generally try to stay away from the bottom half of the internet, but the comments in the CNN article speak volumes. Almost everybody there cannot conceive of whiteboards that are not the exclusive domain of the teacher. (some disturbing images ahead, and, as usual, even more offensive stuff in other comments on the article, so follow those at your own risk)
• "Sure is a publicity stun[t]. Dumb one at that because it's pretty obvious that a shooter can figure out how to walk behind a white board."
• "How does a bullet-proof white board, which is mounted against a wall, protect anyone from bullets, which would be fired from somewhere inside the same room?"
• "The point derpmage is making is that all these whiteboards are mounted (i.e. screwed into the walls) typically in these classrooms. So, if something started, what is a teacher supposed to do? Are they supposed to somehow rip a bulletproof Kevlar Reinforced whiteboard off the wall somehow in order to use it to protect themselves and others? Not going to happen. A waste of taxpayer dollars."
• "There's a hook for easy hanging. Did you honestly think that you were the only one smart enough to realize that having it bolted to the wall would be problematic? It may be a waste, but they did have the foresight to consider the access issue."
• "Many whiteboards are used as standalones next to the blackboard... not hung on walls..."
• "Most schools got away from blackboards and use large whiteboards attached to the walls and use markers. This is really too small for classrooms. It wouldn't hold much information. Besides, the teacher may be safe but not the students. One University building has more then 200 rooms."
• "You take it off the wall and use it as a shield."
• "Is the professor supposed to hold the whiteboard -all the time- in preparation for the moment a gunman comes charging through the door? Otherwise they'll be dead before they get to it."
• "Also, I reckon these whiteboards may be more handy for a crazy gunman than the professor trying to hide behind it. Simply take out professor and ... BINGO, the gunman now has a shield against law enforcement to hold off their position! Super dumb in my opinion."
Even folks that notice the small sizes of the boards go through contortions to imagine them on the wall, in the professor's hand, etc. I haven't seen a single comment understand the idea that the whiteboards are for the students. If you're whiteboarding, don't keep it a secret! It's pretty infectious, so let some teachers see students working actively with whiteboards, figuring things out, collaborating, being skeptical... ; it got me hooked!