Sunday 27 October 2019

OAME 2019 Summary

Continuing the tradition of OAME 2013, OAME 2014, OAME 2015, OAME 2016, and OAME 2018, we have this post. OAME 2019 (the annual conference for the Ontario Association for Mathematics Education) took place starting Thursday, May 16th... and it was local to Ottawa, so I was helping out behind the scenes with registration. (I dropped by OttawaU's campus briefly on Wednesday night, not longer due to a Cappies conflict, always something.)

This means I only went to five sessions, so they should fit in this post. One on Thursday (last slot), two on Friday and two on Saturday.


T5. "Find the fraud! Using Benford's law in the classroom."


Presented by Tim Sibbald, Nippissing. (Also Gazette editor, asked me about a cartoon. It's so rare anyone asks anymore... regrettably, personified math has become a low priority item compared to the rest of my life.)

To start, Tim had us guess at $100 with 16.6% interest. Actual: $100, $116.60, $135.96... at 15 years, it reaches $1000, so good to use as a demonstration. (Graph shown. We see at year 2 we're over a tenth of the way, but amount still starts with "1".)


Benford in 1930s noticed early log tables were really worn in the beginning pages. He determined 30% of numbers start with "1". What is the pattern? Consider 0 to 15 years (DOMAIN) gives 1 to 10 (RANGE). Then starting at 10 again.

So how long are we 1 <= y < 2? For 0 <= x < 4.51. And 4.5/15 = 9/30, about 30%. If $ comes out sooner, recall that's a MINIMUM percentage. The funny thing is, this also works with areas of rivers, which isn't exponential. Now "2" at 16.7%, so half of data starts with a 1 or 2.

Explanation: MSD (Most Significant Digit, or leftmost digit). Formally do Inverse: x = log_(1.166)_y

Imperfection: National Debt doesn't work, it's inconsistent. Inflation and 30% rates of mortgage. (Inflation rate is historically 2%.) Debate: Good enough for evidence? Over 30% is possible, is UNDER possible? (Changing the initial investment?)

Tim went further: What about OTHER DIGITS? The 2nd (not MSD)?
-Are we looking at 30% of 30%? Moves graph up so no change in ratio?
-If eg. a "2", we sum the intervals 1.2 to 1.299999... then 2.2 to 2.29999... etc.
-Law of Large Numbers. Eventually Gaussian distribution.
-The percentages for second digit are about EQUAL now! Note that ZERO does come into this now. Zero is about 11.97%, One is 11.39%, down to Nine at 8.50%.

What about OTHER STUFF?
-Baseball stats are exponential? (Following Benfords Law)
-What if interest was quadratic instead? ("If you're slightly baffled, the students will feel like they can engage.") What about root function? (Also 30%+ for ZERO, ignoring a zero before the decimal, so 0.###...)

-Two Statistics Branches: Inferential Stats (90% of a school text) and Modelling Stats (the other 10%). Test Benford when the parameters change. Structure when you do an inverse, if reciprocal interest, self-inverse.

So how to create bogus data? 
y = (1.05)^(t+random/10) in a spreadsheet?
-Effect still applies to things like quadratics. Envelope function. (Shows sketch of MSD1 between 100% and 30% over time.) 100% from 1 to 2, and 30% as minimum (horizontal asymptote).
-The longer the fraud, the more evidence you have.

After that session wrapped up there was the OAME AWARDS WITH WINE & CHEESESaw TMC Twitter folks there, we talked outside afterwards for a bit.


F3. "Moving Beyond Basics in Data Management to Reach Every Student"


Presented by Chris Papalia. This is the one I really wanted to get to, since I end up teaching Data every year, and want to get better at it.



-Chris has tried to change context (podcasts like freakonomics radio, news like 538), excerpts, spiralling and tech. Emphasizes projects over tests.
-"Thinking Classroom" in data? (Tell me a story.)
-Mystery Data: graph shows lots of data at a high number. Turns out each dot is a day. Distance on y-axis, number of steps on x-axis.

-Starts his course with the 1-var and 2-var data. Normal Distribution, still a challenge; NOT counting (perhaps too challenging to start).
-Google form for that first day of class, use that data (handedness, etc) later on. Have a question "try to make option B the 2nd most popular here".
-"The Canon" by Natalie Angier. Chapter 2. Faking heads/tails.
-Hans Rosling. Alan Smith TED talk.
-"Compound Probability Applets".
-Test alternatives.

There was much more at the bit.ly link provided, and I downloaded a number of things. This past September, I tried starting with an overview and one variable data. (Is it going better? Maybe?)


F5. "Project Based Learning" (+ bonus)


I was a late signup on this, because not much was happening with registration any more. Presented by Marieta Angjeli. She noted it was "not based on research", but was a natural extension of things she did. Student feedback asking for something more engaging/inclusive.

You have to commit. J-Curve. It will go worse before it gets better. We then got given a cylinder with strings sticking out of it. "orange toy". RULE #1: You have to come up with the problem.

"Before you start solving it, I want you to suggest what the problem is." ... Length of string, weight, what interior looks like?
-Realization comes: "they're not all the same, different boxes". Light rattle? Can trap object?
-Marieta admits she can't say "you're right, you're not right"... when she built them, she forget to mark which box had which design.
KEY POINTS: Process is more important than Product. Messy learning is what sticks.


-MDM 4U looked at "Mathematics of Mental Health". (If you feel grades is the only way to a good life, we have a problem.) First issues, what IS mental health?
-http://vroc.ca  "Virtual Researchers On Call"
-They thought Grade 12s would be more stressed, turned out to be Grade 9s. (bias of study, etc); looked at 10% of school, every class.
-Every Friday was PBL (Project Based Learning) time.
-http://view.wirewax.com/8078587

-To Grade 9s, a project for every unit (done Fridays). Still do tests. One project each, as it's hard to cross strands. Mural of Algebra Tiles for mental well being (find cost of tiles?). Needed Word Problem that connects to a problem in the community. For Measurement, cars project. She went through the various units.
-In 3U, for Desmos, image for Student Identity. Cultural Heritage.

(I had to pop off to see someone about a bookshelf and transporting it. When I returned they were looking at samples of the work. After a bit I went to catch the end of Marian Small's address:)

BONUS Marian:
Marian was looking at Application questions versus Thinking questions, and how Communication is packaged with Thinking. And difference between Thinking and Knowledge/Understanding? (Thinking has finite solutions, Knowledge is simply 'neg times pos is neg'.) -"In the end, it's our beliefs about what math is."

(Incidentally, bit.ly/oame_slowmath was written on the board.)

That wrapped up Friday (had to get home to the little one, with the bookshelf on the busses), and on to Saturday. When Alexandra turned 11 months old. Huzzah!


S1. "Talk! Talk! And More Math Talk!"


MATH TALK! was put on by Connie Hamilton, from Corwin Press. They had "Visible Learning" books for math (#VLMath) and a handout package.

-First: Differentiate between Prompt (mirror) versus Cue (microscope). One looks inside, nudge out while the other looks carefully at information in front of you.
-One cue: "A sound or visual that isn't your voice to cue students to give their attention."
-When we pose "What was", we don't notice turns, and talk could be dominated by one voice.
-Paraphrasing is good for listener and speaker. (We did an exercise talking to a person near to us.)

For a successful paraphrase? Helps to know it's coming. "A conversation involves both listening and speaking." It's typically the listening component that's absent.
-To be an effective speaker, be an effective listener.
-How does listening fit into the Ontario Math Processes?
-Shoulders should be squared to speaker. Have students communicate what someone ELSE said? (You listen with a different purpose, to communicate later, versus wondering what I'll say next in response.)

Professor Hattie, statistician, "a study of studies". Quantified as effect size.
-The average is 0.40, the "hinge point". Defined as "a year's worth of learning in a year". Dialogic instruction has an effect size of 0.82. A year's worth in half the time.
-Turns out just giving a hint isn't more effective in the end. Consider ACCOUNTABLE talk. Begin with a paraphrase and add. (eg. "I agree with, another way to look at, I used to think...")
-We thought of more talk stems ("This reminds me of") then shared them around the room. Shifted to just writing on the handout.

-What is your role during conversations? When you interrupt students, you change the dynamic, it becomes guided instruction. Only do it with purpose.
-Students can find misconceptions on their own, given time.
-Bring a chair, model learning. Look at group, not speaker, so they don't only talk to you.
-Something inanimate to break the silence (not your voice), easier to talk then. Also "It's the timer shutting down talk, not me."
-We lined up by birthdays to be grouped.

-Triad Protocol, can be done in as little as five minutes.
-Three roles: Questioner, Respondent and Summarizer (who does NOT speak). Three rounds, each shifting who takes on each role. If there's a chatty person, perhaps give them summarizer as first role.
-After questioner and respondent go, the summarizer has exactly HALF of talk time to sum up. (Eg. If given 90 seconds, have 45 sec)
-My summarizer notes were based on "how to use today to support", and there was some back and forth. (Do kids really want to talk math? Not really.) It segued into immersion schooling and oral traditions (we had an indigenous teacher in our triad).
-Possibly relevant, what language are we speaking in such talks? Someone's second language?
-Books were given out randomly. (Furthest trip to get here, etc.)

I'd kept the second slot free on this day. Went back to see about helping with packing up registration, and to catch up on grading papers.


S3. "Debates in Math Class? I object!" (AGAIN)


I'd signed up for this session before the April PD Day in 2019. So this was a repeat of the previous month. But I figured I'd still look at it with the lens of the other participants. Introduction was much the same, noting students "like junk mail more than the textbook" and debates idea coming from the dual characteristics of light.

-Credit card activity. Remarked on that "pre-approved rate" means this is the rate before we approve you... could go UP after approval. (Yikes.)
-Thought of comparing cards versus comparing a card and no card. (Who would a certain card be better for.) For instance, don't worry about low interest rates if you're always going to pay it off, look for other offers (eg. cash back).
-There's also comparing credit versus debit. Credit card purchases ARE refundable, while debit comes right out of the bank account.
-There is cancelling at 9 months before the bad interest rates kick in (after initial offer) and they bet on us forgetting to do that.
-Put Post-Its onto papers in this iteration. (I think that does work better.)


-Cars activity. Done faster than in April, less fine print. Depreciation was mentioned. Also, to challenge yourself, consider reasons for the other side.
-Rules for testing fuel economy have changed! This is why a newer car looks worse than the listing for an older one. (If the older were checked under the new standards, it wouldn't be as good.)
-Quadratic/Exponential graph activity was mentioned.
-Had time to look more in depth through the landlords activity this time. What they want/need versus the residents. Noted that (in Ontario) a landlord can't ask for a security deposit any more!
-"Those not engaged have a chance to talk." (don't recall the context)
-Mention also of classroom design/redesign problem, square or not.

When that finished, I went back to registration to see if any help was needed for teardown. Got a red "?" shirt, was told everything was in hand, so went to join up with my wife and daughter at the tulip festival (after their meeting for a tea picnic).

And that concludes another (belated) look at the Annual OAME Conference. Not sure how this will work next year, when it won't be local, but I will still have my daughter at home.

Did you learn anything interesting? See a possible extension? Or have any thoughts about related mathematics? Do feel free to drop a comment below. As always, thanks for reading.

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