MAT: Mathematics + WRI: Writing
My first mix tag since I started the new blogging system. (How's that working out for you, readers?) It's pretty much due to Ron Lancaster. We'll get there. If you missed it, yesterday was Day 1 of OAME 2013. This is day 2.
|WRITING FEATURES MOSTLY IN PARTS 2 & 4|
1) Keynote: Annie Kidder
Topic: Defining and Measuring Educational Success in 21st Century
Annie (also on Twitter) is from the "People For Education" group, who are meant to provide an objective viewpoint on public education, with supporting evidence. Basically, moving away from opinion pieces on such a polarizing issue, going for statistics. Such as: only 10% of students take ONLY applied math; 62% have three or more applied math courses.
(Aside: For those not familiar with Ontario's education system... there are effectively two streams in Grade 9, the 'applied' and the 'academic'. If you enter at the applied level, you need two Grade 11 math to lead to University Calculus, as opposed to just one; both can lead to College.)
There is, it seems, a strong correlation between average family income for a school, and the percentage of students taking applied courses. That is, lower income area means higher percentage of "applied". So just because you have rich parents, you're better at math? There is also a correlation between family income and being a member of a band or a choir. See NY Times article No Rich Child Left Behind.
We're blaming failing schools for trends that are more the result of the behaviour of the rich.
-When you make a narrow definition, it defines where you focus your efforts. We need more USEFUL measures, not more JUDGING measures.
-How do we define SUCCESS? Then how do we MEASURE it, because it's not enough now to say "just trust us", society needs to see numbers. Related, why do we equate PROSPERITY with "Money! Jobs! Economy!" instead of "Equity! Joy! Citizenship!".
-There are problems with the system. (Chief among them, why do people say, "I know all about education, because I went to school!" more so than "I know all about surgery, because I had an operation!")
Topic: Powers of 2 and Exponents
My first Ron Lancaster session begins: Some numbers can be written as the sum of consecutive numbers. For instance, 5=2+3; 6=1+2+3; 7=3+4. These are known as polite numbers. What numbers do NOT have this property?
All the powers of 2. And only the powers of 2. And, I'm hooked.
We need to balance curriculum with the curiosity of the subject. In particular, just because something doesn't have an immediate "real life application" doesn't mean it won't DECADES LATER. For a simple example, RSA and prime numbers.
Writers! Have you tried Constricted Writing?
|THERE'S YOUR WORD OF THE DAY|
How many different combinations of vowels are there? For instance, 'a', 'e', 'i', 'o', 'u', 'ae', 'ai', 'ao'... and so on to 'aeiou'. (That's the math bit.) Now, can you produce a work using ONLY that type of vowel, or vowel combination? Canadian Poet, JonArno Lawson, did just that with "The Voweller's Bestiary". From aardvark to guineafowl. For instance, in the poem called 'Raccoons', he used only a's and o's.
Wow, I can't even. That's a lovely little challenge. Don't like that? How about every other sentence you write excludes a particular vowel. Or write a sentence where the word lengths constantly increase by one letter. (To a point and then decrease back, perhaps?) Will this necessarily be something you'll publish? No. Will it improve your skills and your vocabulary? Very possibly.
Back to the maths (more writing later!), here's an interesting pattern if you have a set of numbered cards. Starting with 1, you deal, then skip, then deal, then skip... then go back and deal the skipped cards the same way... until you're only left with one card. You might be fooled into thinking the pattern between total initial cards and value you end with is linear. It's not.
By the way, any readers from New York out there? Check out Math Trails.
-The best stuff sneaks up on you. Perhaps don't say 'prove this is always true', say, 'how might you convince someone that you aren't missing any case where this is false?'
-A reason teachers can improve over time is that students (and educators) can show new approaches, which you can then use again in later years.
Topic: Mathematics in Gaming and Architecture
Speaker (Jelena) who moved from high school to college teaching remarks that students don't know proportions, among other things. A student once said to her "I thought architecture was just about drawing" - without thought to, say, building code violations. How can we strengthen connections?
Interesting personal note: when she said "separate into small groups for open discussion", I inwardly cringed. I think this is part of why I don't do a lot of group work, it's really not my milieu. Of course, in the end it was fine. The few tasks provided to us as starting points also reminded me of others out there where students have to decide on what's important.
Notably, in a particular game, two line equations are given for a ball and a player. Now, is the slope merely the TRAJECTORY, or is the the RATE OF CHANGE (the speed) of the player? (If they run faster, does their slope increase?) Because, yeah. Definition shift between Grades? Also, leaving out units can be a key point of inquiry. Even in the United States where they're already in imperial (BECAUSE THEY'RE ANNOYING), they'll still need metric if they're going to buy anything from IKEA. (Ha!)
A possible summative task for Grade 10 Academic? You have two circles, moving on lines, getting closer together. How do you know when they touch/intersect? (Boom, circles, distance formula, triangles from start point to intersection... though I don't teach Grade 10, so maybe not?)
-"You can make things as complicated or simple as you want." A task is what you make of it. Measurements based on student SELF is also a way to lead to different answers, all correct.
-A continuum is nice; perhaps a Grade 10 task can be redone in Calculus, by adding a third dimension, or speed/related rates. ("This looks familiar.")
4) Featured Speaker: Ron Lancaster
Topic: Using Fiction and Film to Teach Mathematics
The main topic was "The Housekeeper and The Professor", a book written by Yoko Ogawa and translated into English from the Japanese. In brief, a housekeeper goes to work for a math professor, who has suffered a brain injury and only has an 80 minute memory. She has a ten year old son that the Professor nicknames Root, due to his hairdo.
And, I'm hooked again.
Yoko Ogawa has actually won awards in Japan. The book bridges subject areas and a colleague in Ottawa has read it to her Grade 7 class. It starts off right away with the date February 20th. 220. A friendly number (with 284). A hallmark of the friendship that begins between the housekeeper and professor. Yes, english math themes. It goes on... did you know all even perfect numbers must end in 6 or 8?
Ron supplemented his talk with pictures and a brilliant offhand remark... incorporate a photography component into an assignment. Why should a teacher have to hunt down a picture of a parabolic bridge when it's so easy to snap a photo with your phone these days? Even actually TEST whether it's a parabola or just something close?
The sum of any two consecutive triangular numbers is a square number. Proofs without words. Could you prove something to a classmate using only pictures and gestures?
Writers! Hope you read that bit. Here's your other hook: There are stories behind every picture. Ron told us some as he was showing them, about where he took them, what led up to them, like 'the missing bell'. Reality is stranger than fiction, but the next time you look at a picture - write a story about it. Or if you're blocked in your writing, do a random search, and write something based on the 3rd image hit.
|WHY DO YOU THINK I TOOK THIS PICTURE?|
WHAT WAS HE SAYING JUST BEFORE THIS?
The real kicker: the book was adapted into a live action movie in 2006. The book takes place from the Housekeeper's perspective. The movie takes place as a HISTORICAL RECOLLECTION from the perspective of ROOT, who is now a high school math teacher. It's called "Hakase no Aishita Sushiki", or "The Professor and his Beloved Equation". OMFG.
I now have a copy of the movie. This is going to rival "Nanoha The Movie 2nd" for my attention once I have spare time again... though I'm a bit worried that I'd spoil the book by watching it first.
-Why should it be so unusual for a math teacher to go to the school library to request a book? "Math on Trial" just recently came out; why aren't math educators more aware of fiction/non-fiction in their subject area?
-Followup to earlier: Don't say 'prove this identity is true', say, 'this is true... HOW ELSE could you write this?'
-Like the Professor, remember to thank students when they answer your questions; don't just charge on with the remainder of the problem.
5) OAME Meeting and Banquet
I like going to Meetings when given the chance, partly because I want to know how the process works. I don't often go to Banquets, but decided since I wasn't paying for the conference (as I presented), I'd go for it. Learned the attendance at OAME2013 was about 1800 people.
-For only the second time, we had a triumvirate of women heading OAME, as the president-elect, president, and past-president were all female.
-Just because you've always done something one way, doesn't mean it's the only way to do it.
|AT THE BANQUET, BY CHANCE, I PARKED BY RON'S CAR|
The banquet itself reinforced a couple of things: 1) My belief that every picture tells a story. (If you saw the license plate MAD4MATH, what would you think? Now, what if you knew it belonged to Madeleine?) 2) My belief in myself; someone said they were inspired by my talk, and were going to try to have some music in their math class. So, blushing.
Ron Lancaster also designed place mats with math puzzles on them, to work on while we waited to be called for the buffet. We were called by table, and there was a free drink in it for anyone who could identify the random sequence in which tables were called: 7, 3, 2, 4, 6, 8, 1, 9, 5.
No one got it. In retrospect, it recalls a conversation I had Wednesday night with Mike Campbell related to Data Management.
The answer: It was a random number sequence. The committee chair sat in the hall at some point during the conference, and asked passers-by to give him a random number from 1 to 9. (The first three numbers he got were ALL 7.) Numberphile actually did a video related to this.
Quick, think of a random number from 1 to 4!
You picked 3. Humans are very bad at random numbers.
Again, had lunch before the last featured speaker. Though also visited exhibitors before that. Apparently Brock University is starting up an online math contest for senior grades. I need to go back to check that out. Also, when I checked in with textbook distributors, they're moving texts to electronic versions... except, you know, Data Management. It's low priority, because the text is about 10 years old (from before the latest curriculum revision), and the course doesn't run with nearly the volume that calculus does.
You have no idea how backwards that seems to me. I was sitting with Tess Miller at the banquet, and she postulated that there wasn't the money in it, despite Data Management being of more use to, you know, everyone. (She also said that in PEI teachers won't go to any PD after the end of the school day. Different culture!) Also ran into Kate Mackrell, whom I know from QueensU and prior conferences, met Dan Allen through some tweets, and encountered Patti Walker, who knew ME through tweets, so, nice.
|I WAS REALLY THERE! SEE?|
Anyway. This took two hours to write and assemble. It's now after 1:30am. I should sleep, tomorrow I've got three more sessions, then a five hour drive back home.