Saturday, 4 May 2013

MAT: OAME 2013 Day 3 - Laments

Thursday was OAME Day 1. Friday was OAME Day 2. This post is about the half day Saturday, now that I've made it back home. At least one person has told me (in person) they liked reading about a session they didn't get to, so hey, here we go again.


1) Keynote: Bob McDonald

Topic: Vacations in Space

This would indeed be the host of CBC radio's "Quirks and Quarks". He spoke of how they measured the Earth in 220 BC ("stadia" used to be a unit of measure), the shuttle that allows one to experience weightlessness (G-Force 1), and moving out into the universe. Notably how people will pay large sums of money to be rocketed up there. Solar sails may be big in future too (ooh shiny!) and I liked the idea of a "weigh" station in orbit that has different gravity in different areas, to adjust to the gravity of your destination.

-"Our ignorance is greater than our knowledge." We still don't know where a large part of the universe's mass is, nor how to turn off gravity. If you drop something, inertia says it should STAY there, in the air... unless you're close to a large mass...
-"We are the centre of our own personal universe." We see things from our present frame of reference, which can get interesting if someone jumps into a swimming pool that's actually a rotating ring keeping the water in place. Or when you're not sure where a student is going when tackling a problem.

2) Session

Topic: Free Falling - Letting Go of Textbooks, Worksheets and Units

Bruce McLaurin talks about risk, and working without a net. Not necessarily just a flipped class (though it came up) but a class where you introduce all topics at the beginning, then can cycle through the curriculum, without chapters, without units. One day, ask "what's the difference between (x+1)^2 and x^2+2x+1"? Another day, incorporate actual news items into the classroom, like sinkholes, the russian meteorite, or Felix Baumgartner's free fall from space.

Bruce posed six questions over the course of the talk:
1. Do you ever allow students to explore problems that you don't know the answer to? (Is it a problem if you already have the answer?)
2. What's wrong with textbooks? (Participant answers included generic, structured, language used, contrived...)
3. What are the advantages of working without units?
4. What's with the flipped classroom? (Setting aside watching videos, it shifts the responsibility. Students aren't used to LEARNING, they're used to BEING TAUGHT.)
5. What is the problem with worksheets?
6. Does "free falling" take a certain personality type, or does it take the confidence that comes with experience? (Both?)


The article 'Right now, we build minds the same way we build cars' came up, and the fact that it can be scary for us to give control to the students... in part because many come up with lame questions on their own! But they also see stuff we don't. "The Mathematician's Lament" was mentioned. Also, a possible summative task: "Design an experiment to demonstrate at least 2 functions of the course (3M) using a string, a weight, and a monkey." Consider visiting Bruce's Blog, he started it last month.

-"When standing on the brink, don't look down. Look forwards, and have faith."
-"If they don't hear it in your classroom, when are they going to hear it?"

3) Session

Topic: Mathematical Ethics

Douglas Henrich also mentioned "The Mathematician's Lament" (it seems to come up every year, I should get a copy...). Though key to the session was how mathematics also has a social dimension. There were two main aspects that I took away with me:

1. Ethics can be seen as Consistency. This is what we strive for (in notation, etc), yet we're not great at it. For instance, when you draw two triangles with equal sides, we say they are "congruent". Why not "equal"? Well, is there anything physical that is truly identical the way an equation is? Is our use of the word "equal" consistent? Alternatively, in Grade 9, "zero" isn't "nothing", particularly with regards to slope, or zero pair algebra tiles. So if "zero" and "nothing" were equated before, that's not consistent. There are social inconsistencies in math... times when we "cheat", and/or teach abridged versions, which might encourage students to do the same, or tune us out.

2. Ethics can (should?) be a component of a mathematical answer. The example given was: "XYZ Corp are making a product in demand, but contaminants are adversely affecting a population of dove-tailed turtles. The higher the turtle mortality percentage, the less items are bought, and the lower the profits. Given the following equation, find the optimal dove tail turtle mortality rate that will maximize revenue."

There's an element of social responsibility being lost to the hard numbers. Follow up question: "As the mathematical consultant to XYZ Corp., are there any ethical considerations you would bring to your client's attention?" For instance, the problem of cumulative effects, or multibillion dollar lawsuits down the road, that would offset these short term profits. To me, this seems especially pertinent of late, given all the recent news about labour conditions in other countries.

Douglas did point out that such questions are not simple to come up with. He also runs a senior computer science course where the summative is to hack into a particular computer on the network (subject to some constraints, like no physical damage). There, the learning comes from the experience, not success.

-"Can we do this in math? I don't know, which is partly why I do these talks." (Linking back to the prior session - asking questions that we don't know the answers to.)
-"Do we want students to use math to READ the world, or to TRANSFORM the world?" (Effectively an individual context versus a social one.)


At the end, I went back to the larger 'featured speaker' room; I didn't sign in for any today partly because my Thursday was ALL features, but that doesn't mean I wasn't curious. A colleague coming out said a statistic from the "Dyscalculia" session is that for every 14 studies on Dyslexia, there's only one on Dyscalculia. Huh. Also ran into Kate Mackrell and Jimmy Pai again before I left.

So there you have it. I hope you were able to find something useful within my posts of the last few days.

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