TCH: A Month Of Teaching

I've been recording hours worked per day for a month now. I was going to do some reflection on it this weekend, but then ended up doing a special episode on fractions for my web serial instead.

Still, it's occurred to me to simply present the data, and then see if anyone else has thoughts. That way when I finally analyze (who knows when), I can actually address particular points people would like to hear about. Assuming there are any.

TEACHING DATA

Fri Apr 12: 6.5 hrs
Sat Apr 13: 4.6 hrs

Sun Apr 14: 10.6 hrs
Mon Apr 15: 14 hrs
Tue Apr 16: 13.5 hrs
Wed Apr 17: 14.5 hrs
Thu Apr 18: 12.5 hrs
Fri Apr 19: 14.5 hrs
Sat Apr 20: 0 hrs
  WEEK: 79.6 hrs

Sun Apr 21: 4 hrs
Mon Apr 22: 9.5 hrs
Tue Apr 23: 11 hrs
Wed Apr 24: 7 hrs
Thu Apr 25: 11.5 hrs
Fri Apr 26: 7 hrs
Sat Apr 27: 4 hrs
  WEEK: 54 hrs

Sun Apr 28: 0.5 hrs
Mon Apr 29: 9 hrs
Tue Apr 30: 11.5 hrs
Wed May 1: 8.5 hrs
Thu May 2: 8 hrs
Fri May 3: 8 hrs
Sat May 4: 4.5 hrs
  WEEK: 50 hrs

Sun May 5: 1 hr
Mon May 6: 9 hrs
Tue May 7: 11 hrs
Wed May 8: 8 hrs
Thu May 9: 8 hrs
Fri May 10: 8 hrs
Sat May 11: 0.5 hrs
  WEEK: 45.5 hrs

Sun May 12: 2.5 hrs
Mon May 13: 9 hrs
Tue May 14: 9 hrs
Wed May 15: 10 hrs
Thu May 16: 11 hrs
Fri May 17: 8.5 hrs
Sat May 18: 0 hrs
  WEEK: 50 hrs
   MONTH OF MAY TO DATE: 124.5 hrs

Any Qs? Note that some questions, like the ground rules, may have been answered in my initial post. I'll probably keep tweeting times, using #TchDay, until I tire of it or someone says "hey, stop that".

TCH: Two Teachers Per Class

The more I think about it, the more it makes sense. Have two teachers for one class of students. And I'm not talking about one teacher (or educational assistant) who deals with those two "difficult" students in the corner, while the other teaches, I'm talking about having two teachers. Hear me out.

ORIGIN OF THE IDEA

I've been tweeting hours worked for the last month or so. I plan to have a roundup post on that at some point, but one thing I'm starting to realize is that the job is potentially doable in a regular 8 hour day. Assuming you don't do any marking, or extra curricular activities. (Effectively filing off the worst and best aspects of the job.) If you must do those things, well, sacrifice sleep.

Today in particular, as I marked, I wished I had a day just to do only marking. (Which is what the weekend is for. Yet I blog. Yeah, I'm stupid like that.) I also listened to the latest "Infinite Tangents" podcast, where there was mention of "laying out a class" based on overall curriculum expectations - hopefully collaboratively. Thus with help. Okay, so what if I had a FEW days to mark student work, because we'd arranged that someone ELSE was currently teaching the next unit? I'm not saying I'm hiding out, I'm still helping the classroom during the day, but when I'm not there I'm MARKING rather than PREPPING.

This means I can focus more on the problems with the last unit, even having time to make changes so it's better for next time, rather than trying to figure out what I have to be teaching tomorrow. Our next unit, the two teachers switch it up, so that it's not one person tasked with all the marking all the time. Notice I also flagged this post as "teaching" not "math", because I think it's workable in other subject areas too.

I hear your objections. But bear with me as I work through this.

COMPARISON

Advantages to Two Teachers Per Class:
1) Teachers don't get to observe enough teaching. Boom. Fixed.
2) We emphasize group work, yet we teach in solitary. Why?
3) It's a chance to share (equitably) what always feels like an impossible workload.
4) A second set of eyes in the class can more easily pick up on problems students are having. Also allows for constructive feedback to colleagues.
5) Pretty sure this would reduce teacher burnout and increase retention rates.
6) This might even allow for better flipped classrooms, as it generates time for teachers to create flipped content. Or just any content.
7) Creates jobs, which is good for the politicians and prospective teachers out there. Alternatively, may mean the bureaucracy can increase class sizes, but as long as they're not doubling, we'd be looking at less than what we have now.

Disadvantages to Two Teachers Per Class:
1) Seems to require units. I'll deal with that below.
2) Personality conflicts. Two teachers with different styles may not mesh well, or issues may erupt if students seem to "prefer" one teacher to the other.
3) Continuity. Students may have difficulty handling a different teacher for different topics, and teachers may have difficulty picking up where someone else left off.
4) Coordination. Two teachers now have to assign one mark per student.

IT'S ALL ABOUT PROS AND CONS

ABOUT DISADVANTAGES

It doesn't require units. It might make more sense to have units, where Teacher A takes 1, 3 and 5 while Teacher B instructs 2, 4 and 6, but not necessarily. Picture a classroom where all the topics are laid out within the first two weeks. Teacher A can then do an activity on trig (perhaps even based on current events), have an evaluation of some sort at the end, and while they're correcting that, Teacher B does a few lectures about solving equations. Then Teacher A is on again, and they could do something on quadratics - or, y'know, even FOLLOW UP on their activity from two weeks ago. (Seeing it again before the final exam? Madness!)


I can't immediately see why this can't apply to other subjects too. Teacher A instructs on World War I, Teacher B on World War II. Teacher A does chemistry, Teacher B jumps in with some physics. Teacher A does the poetry unit, Teacher B gets ye olde Shakespeare. Teacher A does perspective drawing then Teacher B moves into watercolours. I suppose you could argue we may get too specialized, but is that a bad thing?

Personality conflicts is a bit harder to reconcile. This whole idea would need to be a collaborative exercise, not a competition, yet there's always people out there who have a personality type that leans to the latter, or who might take things too personally. (I may even be one of them.) Students would not help matters, tending to be judgmental, or simply wanting to see what happens when you pit two teachers against each other.

But on the other hand, there are some really good teachers in my department doing some great things with group work and... that isn't me.

I'm an introvert, who is bad at judging personalities and gathering anecdotal evidence. So I don't do a lot of it. But if I was paired with someone who WAS good at it, not only would the students benefit, I might get BETTER at it. Meanwhile, that teacher... would get to see me sing about Trigonometry. Um. So they might feel they're getting a raw deal, but they could be paired with someone else next semester. My point is, play to individual strengths and evolve as a teacher, rather than get stuck in a rut.

As far as continuity goes, most times students get different teachers from year to year anyway, so it shouldn't be all that confusing. And as to continuity with teachers - again, it's not that you vanish for a week, you're IN THE CLASS, observing what is being taught, it's just you can deal with marking and self improvement rather than all the prep work. Because of that, I can't think there would be huge disputes about mark assignment either.

Heck, in terms of implementation, this could even translate to just having a couple "floating" guys in the department. They teach collaboratively with Teacher A for one term, then Teacher B during the next term. You know, kind of like student teaching, except with pay. So this might be particularly beneficial to young teachers, as they build confidence and find their place.

THAT SAID

The major disadvantage, of course, is that this has to be sold to the public. I say "public" not "politicians", for two reasons:
1) Despite the politician's apparent penchant for doing whatever, then selling it as "the right thing", surely there are some times they have to bend to the will of the public. Like, election years.
2) The public thinks teachers "have it easy", hahahaha, kill me now. They're the ones to convince of the benefits of such a system, and why more money would be needed for education to implement it. (Maybe if we take some of that tech money, eh? Then again, my ten year old computer says new tech would be helpful.)

Well, I'm not a salesman. Nor am I sure how I'd advocate for this. (Nor am I even positive it's a good idea.) That said, is this NOT what they do at the post-secondary level?? Hiring teaching assistants to mark papers and answer questions, so that professors can focus on research? My system improves on that, as I'm not passing the drudge work on to someone else, but making it more equitable, distributing the workload fairly between two professionals. Doesn't this make sense?

I feel like it makes sense. In the comments, someone please tell me why we're not doing this.

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.

BOB POINTS OUT HE'S LEFT HANDED, RIGHT BRAINED

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.

Takeaways:
-"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?)

OR YOU'D BE ON IT, GOING NOWHERE

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.

Takeaways:
-"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:

ALSO, ONE POUND
IS NOT 500 GRAMS!

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.

Takeaways:
-"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.)

Miscellaneous

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.

MIX: OAME 2013 Day 2 - Write Stuff

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.

Takeaways:
-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!")


2) Session

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.

Takeaways:
-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.


3) Session

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?)

Takeaways:
-"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.

Takeaways:
-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.

Meeting takeaways:
-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.


Miscellaneous

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.

MAT: OAME 2013 Day 1 - Key Notes

As I said recently, I want to record more Professional Development. That entry was meant to be a warm up for OAME 2013, the Ontario Association of Mathematics Educators Annual Conference, now taking place in Toronto, Ontario. It's the 40th anniversary. So this post tracks my lineup of sessions.

LOOK, I'M A FOOTNOTE!

1) Keynote: Stephen Lewis

Topic: Education: The World's Greatest Force for Good

Essentially talking about Math and Social Justice. Not hugely mathematical, but definitely relevant for EQUALITY. Just when you think we've come a long way, you hear about what's happening to women and children elsewhere in the world... or even close to home. (I still do not understand what's with all the rape cases making the media lately for the wrong reasons.)

Also, it's terrible how money tends to be the bottom line for anything. Particularly education, as strings get attached to loans, and what once was free is no more... is it any wonder Massive Open Online Courses (MOOCs) are seeing an upswell, given the cost of education in the world?

Takeaways:
-Education grips young children. Particularly those who haven't been able to experience it.
-There's enough injustice in this world already without creating more injustice.

2) My Session

Topic: Musical Mathematics

I actually missed a bit of the keynote making sure I was in a position to be able to present. ^_^ Had about two dozen people. Felt like my pacing was a bit off and I say "Uh" too much, but got a number of laughs, and the comments ranged from "Thanks" to "Outstanding", so I did something right. Good point raised as to how much the singing in class actually helps/correlates with results on quizzes and the like. Need to figure out how to gather that sort of data.

Takeaways:
-Someone out there is doing a music based math summative. I gave her my card, I hope she contacts me.
-My TMC13 presentation probably won't suck.

3) Featured Speaker: Dan Meyer

Topic: Making Math More Like Things Students Like: Video Games

The room had two screens, and they weren't synchronized, so Dan had to ask the audience for a second Mac projector adapter and coordinate two clickers. He started with some Angry Bird statistics, the answer to "How long will a student spend on a homework question until they know it's impossible" (12 minutes), and took a dig at Justin Bieber. (Meyer's more of a Ryan Gosling fan.)

Some key ideas (paraphrased):
"Make math more gamelike, not games more mathlike."
"Teachers risk not developing questions enough. We find the answers too exciting." (I am SO guilty of this at times.)
"A benefit of an open middle is that my way to solve [from beginning to end] may not be your way." (I love when a student does something different.)
"Adding a timed element only makes something more challenging, not more interesting." (I hate timed games. I don't play Set.)

IT'S DAN MEYER.   #DANMEYERFACTS #TWITTER

The six key video game elements to incorporate in math class:
1. Get to the point (as fast as possible).
2. Real world, bah (real is relative).
3. Have an open middle (self determination).
4. Grow more interesting as you grow more challenging.
5. Instruction is visual, only as needed, embedded in practice.
6. Reduce the cost of failure (don't lock in tests).

4) Featured Speaker: Jason Brown

Topic: The Connections Between Mathematics and Music

Pure tones are sine curves. Why are so many of our trig applications about angles, and repeated phenomena, and oscillating objects - and not music? Even the scale is taking a continuous blend of tones and making them discrete... based on ratios. In the equal temperament scale, that ratio is 2^(1/12), or the twelfth root of 2. (12 tones in a chromatic scale.) And why does the diatonic scale use the sequence 2212221 (TTSTTTS)? Due to network graphs that seek a "maximally even" orientation.

Some of that theory may have passed you by, so again, key ideas:
"Hearing 'beats' between two similar notes comes from a trig identity." (sin A+sin B=...)

HE WAS THERE WITH A WHOLE BAND

"Transformation is used all the time in music: move the motif up or down, reverse it, invert it, speed it up." ...Then show function notation? (Rap music generally only uses repetition, this may be why I personally find it less compelling.)
"Beatles tune 'I Wanna Hold Your Hand' uses f(x)=x-3; they don't start on the downbeat. You don't realize until they start the vocals, and your brain is fooled every time you hear the song, even if you know about it." (A constantly rising chromatic scale was also a brain teaser.)
"A 3 pattern versus 4 is a popular trick." (eg. Emphasize every 3rd note while bars are 4 beats. Resynchs every 3 bars.)

I actually got Brown's book as a gift for being a presenter (it was one of a few book choices), and he signed it for me. I bought his CD too: "Songs in the Key of Pi".

Miscellaneous

There was lunch there between the two featured speakers, after which I checked out some of the exhibitors. Renewed my OAME membership. Cube for Teachers is an online resource that tracks lesson items by Ontario Curriculum. Talked to the University of Guelph guy about a wallet card for Statistics. (And, I fear, stumped him when I asked how he would personify a Normal Distribution versus a Binomial Distribution.)

I was the guy at the start of the day who got the people in the Presenters room to post up the code for opening the MagLocked tech desks. Then at the end, I went to the Wine and Cheese and ended up talking more musical math. Now looking forward to tomorrow!

ETC: Doctor Who's Pacing

"I say stuff." -The Doctor
"My turn." -Me

So, the recent episode "Journey to the Centre of the TARDIS". It bothered me. But not for the temporal aspects, as remarked on by some, including at io9 in the article "We're mighty sick of Doctor Who stories where time travel is magic". I think the show got the temporal aspects RIGHT, for the most part. The trouble was in the storytelling, and to a certain degree, in the staging and pacing.

Ok, spoilers ahead.

By the way, speaking of staging, there's storyboards up for the episode.

Also, here's a review from someone who apparently liked the episode a lot. More than their first comment, at any rate.

Have I mentioned that I've written time travel fiction? I also wrote about the movie Looper and "Asylum of the Daleks".

Also, you realize I'm just killing space here, because SPOILERS!  Hello!

You DID catch that, yes?  Sure you want to scroll?

Okay, just checking.

BIG FRIENDLY BUTTON

So, let's start with: There isn't necessarily a problem with a reset button episode. Not when it's done well. I should know, I've seen a bunch and written one into my "Time Trippers" story. In fact, I did mine in a way which, upon further analysis, is not completely dissimilar from this episode. (So, okay, biased.) Yet I think that's also why I find this Doctor Who episode simultaneously really good, and yet rather aggravating.

I think that the point to a reset button episode is character development. Bear with me, I know that sounds weird since the characters don't remember it... but the point is, WE DO.

In this case, we get to see the Doctor being rather manic about who Clara is, while she does the same in turn... we're effectively afforded the chance to look inside their heads, and learn how they would react to certain things, without those things actually occurring. That's NOT a bad thing. It's only bad if it's never brought up again.

Now, there are other ways to do this aside from time travel. "The Zeppo" comes to mind, from Buffy, season 3, episode 13. We see the story from Xander's point of view, we get new insight into his character that the other main characters do not. We can now look at him in a new light. The people in the story don't know what happened, so they lack that ability. Of course, we don't get the benefit of Xander really interacting with the others.

There are also ways to botch this using time travel. "Year of Hell", the Star Trek: Voyager two parter from Season 4 comes to mind. The resolution made no sense, and the actions of the characters (like Chakotay, in investigating temporal paradox) were completely isolated from the rest of the series itself. For an example of it being done well on that show, go with "Timeless", sixth season.

Doctor Who's "Journey"... the rules are consistent, not magic, but it falls down in execution.

TIMELINES

Now, here's why it works. We're effectively seeing the second iteration of a time loop. The same plot device, by the way, as used in Stargate Universe's Season One Episode "Time". (There are no new plots?) In the grand scheme of things, here's what happened:

TARDIS gets zapped. Doctor appears, tells himself how to fix it, time loop gets fixed, end story. Which is (in theory) all Clara knows. But that's barely even a teaser.

So here's what actually happened:

TARDIS gets zapped. Big problems, temporal echoes, people die, maybe even Clara actually dies, then Doctor has a flash of insight, sends the critical device back in time, inscribing it with a message to tell his future self to push it. Bringing us to second iteration. Clara retrieves device, still big problems, still temporal echoes, still people die, this time Clara survives, helps Doctor with his flash of insight, and this time he has the time or inclination to actually interact with his prior self. Time loop closes.

We only see the second part of that run. Which is part of the problem, but at the same time, we don't necessarily want to be subjected to a replay of Haruhi Suzumiya's "Endless Eight". So I can forgive them that. The trouble is, it's not obvious unless you make a habit of thinking four dimensionally.

For instance, the "time will reassert itself" issue discussed in the io9 article comes from the fact that the group is effectively trapped in a room that will burn them alive. The Doctor's 'plan' is that the two salvage guys separate. His theory being that, according to future history, when they die, they get fused together. But if they stay apart, that can't happen, meaning the beings now trapping them won't actually exist, meaning they can get out.

Time hates when you try to rewrite it though. Even future time. Just ask my character, Carrie. So that failed.

Moreover, it seems to me even had separating the guys WORKED, they'd become trapped by two SEPARATED future salvage guys. So that's where even more of the theory falls down. Also, to even be with me at this point, you'd have needed to notice the burn victim parallel, which is where the rest of it potentially falls down. Which brings me to the bigger problems.

PACING

A HUGE problem with the show itself lately is the pacing. Everything is frantic, and the characters talk so fast that I miss chunks of dialogue, and it's all an action adventure, and really? Does no one sit and talk anymore? I watched the episode a second time, and here's a few rather KEY bits of dialogue that breezed by me on first viewing:
1) "This little baby can disable entire vessels." Okay, so THAT'S why the device was so helpful. I was trying to figure out how it acted like a reset.
2) "You're my guides for this." Okay, that's at least a possible reason for the Doctor to trap them inside... they do know salvage, and his ship is a bit of a wreck. He didn't know the half of it.
3) "So that's who." Which I think I only got on the second viewing because I saw a reference to it on the 'net. Maybe cut away even faster and have Clara whisper quieter next time, then no one will get it.
4) "Recent past." Aha, so that's how the Doctor was able to set the time rift. (See? It's never that easy, honestly.)

I also thought the first time that ALL of the salvage operators were androids, because that bit of dialogue was unclear. Oh, and I missed the swimming pool. Yeah, lots of people mentioning the pool as I browsed the net, passed right by me in the initial viewing. Don't blink.

Now, I realize part of the point is that they WANT to pull us into multiple viewings, but can we not always be lurching from crisis to crisis? The bit in "Cold War" when Clara is reflecting on the people who died was genuine, and important in the grand scheme of things.

There was time for that sort of thing here. Just nix some of the stuff where the salvage people are wandering around trying to salvage the TARDIS, with it trying to stop them, because that turned out to be pointless. Or at the least, it could have been done SO much more intelligently. ("Let's split up!" - how was that NOT the plan in the first place?!)

Which brings me to the other big deal...

CHARACTERIZATION

Maybe it's the lack of female writers. But when The Doctor was talking about putting the TARDIS in basic mode for her, and then the talk about driving, my jaw nearly hit the floor. Also, it took how long for The Doctor to realize Clara was still inside? And the way he described her? Oy. (Maybe he was overcompensating after that, what with the self destruct?)

Clara wasn't much better. "A hug is really nice"... pardon me? This guy has just said he saw you DIE in the past, and YOU'VE just recently seen yourself dead, and a hug is nice? No. Just no. A hug is now scary, and this guy you thought you knew is acting kind of creepy insane, and you're smarter than that. Or you should be. And you COULD be.

Again, the point of a reset button episode is CHARACTER development.

Show me Clara giving The Doctor what for about his secrets, and/or the Doctor sincerely apologizing. Show me the Doctor scared; I bought it in "Hide", I didn't buy it here, the script forced him to act too manic. Heck, show the Doctor collapsing to his knees or something when he sees the engine, actively distraught over the TARDIS. Maybe show him choosing the TARDIS over Clara. Show Clara standing up to The Doctor, or leaving him.

SHOW ME SOMETHING OTHER THAN PEOPLE RUNNING AROUND.

Oh, and then there was this gem:
"Don't worry. You'll forget."
"I don't want to forget. Not all of it."

Which leads to... pardon me?! I'm thinking there are a few things you'd want to remember ASIDE FROM A RANDOM NAME. Writers, don't use your "vanishing" episode to drop hints ABOUT THE PLOT. Either state the plot OUTRIGHT (as the characters won't remember it), or have a discussion. About whether they'll still be the same people if The Doctor manages to repair the damage, or whether they have the right to do this if the future is already written (and wanting to assert itself), or what will become of the salvage people should none of this ever have happened. You could have made time for that! Easily! Then people won't end up annoyed in this way.

For that matter, it would make the end line of "Do you feel safe? I need to know you're not afraid." ring true, instead of hollow, as it did for me at the end. Sure she feels safe. Apparently she always has. Boring. Instead, wind back a bit to show me a Clara who's overcome, who isn't sure she can go on, who has been wounded, physically and emotionally, and who isn't sure she'll ever trust again.

THEN reset her and ask her if she feels safe.

If she does, that's not only better foreshadowing, it's far creepier for the audience than a noise in the dark. Don't you think?

MAT: Tile and Error

You know that we like using 'x'
To do algebra is not that complex!
Physical models can help you out. (oh oh)

A small square will be one by one
The area, the area is how it's done!
Unknown length shows 'x' without a doubt.

-Avril Lavigne ParaB Conic, "Y-Squared Tile"


Blogging about PD (Professional Development) here. I should do more of this. That way, I'll remember it better, and it could be of more use to others. I sort of did it as part of DITLife, but here it wasn't part of a school day, it was a Saturday morning. The "Ottawa Valley Spring Math Forum", as presented by Claire Bonner, Rebecca Black, Robin McAteer and Anne Holness.

Topic: From Patterns to Algebra.

In other words - at least for me - the bridge from middle school (Using: Input x 3) to high school (Using: 3x). Immediate diversion to write about what's in the parentheses there... since when does "take the number and triple it" become "triple of some unknown that looks like a multiplication symbol"?? Answer: Nowhere in the curriculum. Just, you know, one of those adjustments we expect Grade 9s to make.

Along the same lines, we tell students to always do the parentheses first, before exponents. Then we start writing parentheses as multiplication, and wonder why they have trouble with order of operations. Yeah.

Anyway, here's some of my "take aways" from today:

1) Students - and people - have a tendency to look down the table for patterns (+5,+5,+5,+5) rather than across (value times five). Putting things in order does not help them make the transition.

2) A mistake textbooks make is giving a lovely pattern of squares, then immediately saying "create a table". That changes the context. One should be able to come up with a "rule" even WITHOUT a table. Along the same lines, you don't want to introduce 'x' and 'y' too early, or you're probably doing a disservice. They're very abstract - patterns are concrete.

3) Pausing to ask a student "Why? Explain yourself!" is important not just for that student. Granted, it forces that student to try and articulate their intuition. Good. But it can also allow you to see whether they're seeing what you think, and perhaps more importantly, give OTHER students additional time to think about things.

4) Why DO we kill mixed numbers as soon as students enter high school? If you have "6 times 2 (1/2)", you don't have to do "6 times (5/2)", you can do "6 times 2" PLUS "6 times 1/2". Boom. Distributive law.

5) Patterns show equivalent expressions. Consider "3x+7" and "3(x+3)-2". Equivalent? Well, put down 3 "x-tiles" and 7 "unit tiles". Now put down three groups of "x-tiles" & 3 "unit tiles". Include two negative units. Zero pairs. Boom, same thing. No algebra.

6) Cutting up the "x-tiles" according to values of x makes more sense than swapping in unit chips for x. Which I'm not articulating well, but we sort of need elasticized tiles to represent x. Ones that students won't fire at each other.

7) Possible group activity for solving equations: "You're the right side (3x-4). I'm the left side (2x). We're equal. So of what value are our 'x' tiles to make it work?" (No stealing my tiles! But you can give me zero pairs, aka 'Thanks for nothing!'.)

8) Sequences, which start counting at '1'... I've blogged about that issue before. But it occurred today that RECURSIVE sequences DO run down the table. You need to know entry 98 to figure out entry 99. Inefficient, but there's the connection between recursive addition (of a constant) modeling a linear pattern.

And I'm doing recursion this coming week. I have no idea how much use that connection will be, but here's hoping I remember to incorporate it.



And that's whyyyyyy I smile, it's been a while,
Since every day and everything has felt this riiiight,
And now. YOU turn it all around...

-ParaB  Avril Lavigne, "Smile"