## Sunday, 30 December 2012

### Math 4 Ever

I recently read an article by a friend of mine, entitled "Why We Love Things That Won't End". It referred to TV and anime shows, book series', soap operas and the like. Ultimately, one theory was that we love them because while they're ongoing (and even afterwards), they foster creativity and community building.
 It's also freaking awesome to see how characters grow up over time.

It got me thinking. Perhaps partly due to a joke my brother-in-law told me around the same time, about my "Taylor's Polynomials" math series. He said I'll have to keep it going forever, because the Taylor Series is infinite. Which raises a good point.

Math doesn't end.

But I don't mean that in the sense of integers continuing on forever. Nor do I mean it in the sense of "when will this period ever end". No, I mean it more in the sense of mathematics being all around us, and that there are always more discoveries to be made. (For that matter, Godel's Incompleteness Theorem even proved the existence of mathematical truths that cannot be proved.)

Now, the big news in discoveries for 2012 was whether Shinichi Mochizuki has found a proof for the ABC conjecture. But in May, there was also the matter of a teenager in Germany solving a 300 year old riddle by Newton. And who says discoveries have to involve theorems? A fair bit of statistical discussion also occurred recently, surrounding Nate Silver and his election predictions. We have the rover on Mars. And Canada got rid of the penny this year, so that's going to make a number of textbook questions irrelevant by 2015. There's always something going on out there.

Yet students think that, once they have the answer, "I'm done".

The system is partly to blame for this. We need something we can mark, be it a finished essay, a completed piece of artwork, or a solved math problem. Though society is also to blame. Mathematics is often met, not with wonder, but with fear, uncertainty, and the remark "well, I was never good at math". This results in a desire to have it be "done", as opposed to continue indefinitely. And of course, a solution being "the end" may ultimately have it's roots in the first QED (Quod Erat Demonstrandum, 'what was required to be proven').

Yet when the student perception of "I'm done" changes, it's wonderful.

Students form 'communities', both in and outside the class, in order to help each other out. (It's not enough that I've found an answer - you haven't.) They compare answers, finding new ways of reaching the same outcome. (It's not enough that I've found an answer - there was another path.) Sometimes they even start asking questions to extend into later problems. (Ideally less with "when am I ever going to use this" and more with "so what comes after degree mode".)

 Stop memorizing rules!

The new question for an instructor then becomes, how can we change the "I'm done" perspective? More to the point, how can we do it without unnerving the student, while simultaneously keeping within the framework of all the standardized testing the government wants? (Even demands?) This, I dare say, is a work in progress. A work, perhaps, without end.

But that's not automatically a bad thing. Because it has created communities of mathematics educators, who are coming up with new, creative ideas. So here's to learning that never ends, and all the people that we meet along the way. Hope it was a good 2012!

## Thursday, 13 December 2012

### Day as Math Educator - Limited Edition

In August 2012, the Ontario Liberal Government recalled the legislature early, in order to pass Bill 115 (the "Putting Students First Act"). This Bill gave the provincial Education Minister the power to preemptively shut down any strike action by public education workers, and impose contracts onto them at the end of 2012, should their unions not reach deals with school boards of a "substantively identical" nature to what the government wanted.

Of note, from the Bill:
14. (1) The Ontario Labour Relations Board shall not inquire into or make a decision on whether a provision of this Act, a regulation or an order made under subsection 9 (2) is constitutionally valid or is in conflict with the Human Rights Code.

 There's Pros and Cons

But this blog post isn't about that. Nor is it about how a deal was tentatively negotiated between union and board two weeks ago, only to have the minister suggest some additional language before ratification. Which killed the whole thing. No, this is about the aftermath. This is about education workers doing what we can to get Bill 115 repealed, so that we can actually negotiate fairly, and do the jobs we were hired to do.

This is...

### A Day in the Life of a Math Teacher: the Job Action aka "Limited" Edition.

(In other words, this is what a day would be like if we clocked in and clocked out the way many in the public think we do already. I'm all about the teachable moments.)

Thursday, December 13, 2012

4:44am - Good lord. It must be tradition that on DITLife days, I wake up early for NO REASON. Though here it may also be due to me still trying to shake off a cold. It takes over a half hour and some kleenex before I'm back to sleep again.

6:30ish - My wife wakes up, turning off her alarm before it sounds, creeping out of the bedroom. I'm vaguely aware, still mostly asleep.

7am - My alarm goes off. Get out of bed, listen to the news. Then wish my wife well as she heads off to the gym.

7:30am - Dressed now, breakfast, scan through Twitter.

7:55am - Head out to school. Need to be a little earlier than usual, since there's a logjam of cars when everyone (including parents) arrives at the same time. There's what looks like sillystring outside - I learn later it's freezing fog. Weird, wish I'd thought to take a photo.

8:10ish - Traffic circle. ^_-

8:15am - At work even earlier than I thought. Position my car well, then wait inside it listening to Crush Rush (radio quiz show).

8:20am - Head for school doors. Chat with some colleagues. Our parking lot, by the way, is a bumpy skating rink, all ice since last week. Someone remarks, "that's what you get when you hire the lowest bidder".

8:25am - Our contract officially says to be present 15 minutes before classes start, so this is when we head in. For the second time this week, I'm the first person in our prep room. By about 2 seconds, but still, this is REALLY WEIRD if you know me.

8:30am - Down at the office photocopier. Last night I recalled a handout I used two years ago about trig triangles in a completely different course. Found it, now running off a set for the class.

8:35am - Back to class before the warning bell (no one else was copying this morning). Don't recognize the "get to class" music, but the music before this was "Total Eclipse of the Heart", reminding me of a Twitter conversation a week or so ago.

8:40am - PERIOD 1

This class we're currently doing sine and cosine laws. There were problems yesterday when a couple of the textbook solutions were wrong. Yeah, I didn't doublecheck those (and I can't blame it on job action, I usually only check the trickier ones anyway). So lost time there affirming that methods were correct, textbook sucks.

I bring it up because it almost looked like we were heading for the same situation today... but the problem was a calculator that had slipped into radian mode. (Crisis averted?) I advise looking at one question in particular, give them time to do it - lending out my textbook and my calculator (to different students) in the process. Makes taking it up a tad trickier, plus my form on the board sucks today.

Decide we should to move next Tuesday's test to Wednesday, unless there's objections. (Nope.) Then summary note of cases on the Smartboard after, followed by some application. Decide to let them work through the actual mechanics of it for homework and sing in the last five minutes: "Cosine It". Not one of Kristina Maria's more well known numbers, but was getting more airtime a year ago. So, solidifying concepts through earworm.

9:55am - Period changeup. I take the opportunity to write up the solution to the application question to show tomorrow as the next class comes in.

10:00am - PERIOD 2

Data Management - test tomorrow on statistics. I hand back their last test, and have them do a self-evaluation on goals for the next month. (Did it with other classes earlier in the week, wanted to return at least one more item to the Gr 12s first.) A number want mark updates. Yeah, I haven't had a chance to make any printouts - promise something before the Holiday.

Rest of the class is review time; oh, recycling gets taken down by a volunteer, and I have them do self-evaluations, which I try to get to once a month.  Then I go around answering questions, suggesting to the one guy he stop doing his English, wishing best of luck to a couple students doing the arts performance tonight (nuts, writing this I realize I missed one), and allow a couple students to go work in the quiet of the library as long as it's open, and they check back in with me.

On a roll from last period, and to try and lighten the mood at the end, I do a reprise of "The Medians", a song from last week. Normally don't do callbacks, but again, hoping it helps earworm some information in.

11:15am - LUNCH

Start by checking email. Also write solutions up on the board for a quiz I'm giving this afternoon, to speed things up. (I can slide another board over it to hide them.) I'm a tad concerned about my afternoon pacing, but need to give another test before the Holidays. Dropping trig identities until January as it is.

Just before I head back to the prep room, a student asks if she can borrow my metre stick. The LAST person who did that (on Friday) never returned it, I only got this replacement yesterday from a colleague... but I teach this student, and she assured me it will be returned by next period, so alright.

Grab my lunch from the fridge in the prep room. Briefly chat with a colleague who teaches the same course and level as my Period 1 to mention I'm moving my test. She is too, so that works nicely. I decide to vary things up today - I go to the staff room. (Yesterday I also varied things up by leaving the school, coincidentally the same day the Elementary Teachers were doing a one day walkout.)

Today, I'm in the staff room for probably the first time since my last DITLife post, during our PD Day. Feels like more teachers in here than usual, but my "usual" is about two months out of date. Topics range from politics to the weather to music. Head out about noon with another brainstorm - I run off some photocopies of the unit circle for my next class.

12:05pm - Travel time. Get my metre stick back.

12:10pm - PERIOD 3

This is the U-level class, we're quizzing on Sine and Cosine laws, then I'm introducing trig on the cartesian plane. (I've tried doing it the other way - also how the textbook does it - but feel like I lose people with the four Quadrants, and never get them back when we hit the 'laws' later. So I'm trying to keep people with me as long as possible. Something that needs feeling out with every class though - I might have flipped it here, if only I'd had an extra two days before the Holiday.)

So a little over half an hour for the quiz, then the dramatic reveal of the answers, and we talk about those. In the last 35 minutes, I introduce terminal arms, related acute angles, the Quadrants... and the dramatic reveal of the Unit Circle and (x,y)=(cos,sin). With accompanying handout.

I know I get far too carried away here (think I called it "the most exciting ten minutes of this unit"), but I'm hoping some of it rubs off. One guy remarks that I'm funny - I counter I hope he doesn't mean funny looking. When the period ends, I overhear at least one student commenting on Tangent being Slope, so I feel like my job is done.

1:25pm - Period changeup. Similar to the morning, I use it to fix up my slide a little so that I can upload it onto the web.

1:30pm - PERIOD 4

This is it, folks. This is the only 75 minutes I have in my day to prepare lessons and quizzes for three classes, do all of my marking, my data entry, plus respond to parents, and set/verify exams for January. I've done bits of all of that the last four days... needless to say, haven't been checking Twitter from work lately.

But this is exactly what some of you thought, right? Teachers can do all of that and still knock off work at 3pm? Heh, okay, just kidding - normally I'd have a 37 minute duty thrown in there too, once every four days. But with the job actions, I'm not doing it, the same way colleagues aren't doing lunch supervision duty.

Where was I? Right, now I have 70 minutes. (Slowness of my computer and the internet combined to make me lose 5 minutes.)

1:35pm - Make some modifications to tomorrow's lessons based on what happened today. I'd like a better example in one case, but know I won't have time to find it. In fact, I'm going to have to forgo this prep altogether pretty soon; fortunately I CAN improv lessons from old notes, just not my preference. Ten minutes max. Turns into fifteen. DARN it!

1:50pm - I need a quiz for tomorrow, Period 1. I have a number of old questions I can cut and paste, and a quick glance in a textbook inspires me for another. Done. Printed.

I've lost track of time checks.

I need a quiz for Monday... and since one student is leaving early for the Holidays, I actually need it for TOMORROW, so they have it before the weekend, to write their test early too. Bit harder to find a good example in old files, but done. Printed.

Go to get printouts in prep room, then down to the office to copy them so that I don't have to deal with it in the morning. Which now in retrospect is silly, I have to go to the office every morning to check my mailbox anyway... this wasted a perfectly good two minutes in walking time. There's a message in said box about the assembly next week. I scan through it.

Get back to my classroom with all my handouts.

2:25pm - Glance at clock before responding to an email from admin regarding work for a suspended student; also send a message to a student regarding some work we did today.

2:35pm - Related to that student writing their test early, I need said test before Tuesday! I'll be adapting from a couple sources, so I start pulling them together. Get the skeleton of a test done as the bell rings. Time to shut everything down. Didn't get a chance to do ANY marking. DARN it!

2:45pm - Shut down computer, try to quickly tidy desk, back to prep room, grab a printout from desk regarding the Problem of the Week to take home (think I printed that at lunch?). Have to change back into boots, my shoes get stuck, I'm grumbling.

2:55pm - Leave school. Since I'm positioned well in the parking lot, and a number of the early parents left five minutes ago, takes less than ten minutes to be on the road.

3:25pm - Arrive at home. It's still light out. CANNOT get used to that this far along in December. Take advantage of it though; I shovel the walk a bit more, as it's warm enough to remove a bit of the ice. Don't fully hit pavement, but it's better than the school parking lot.

3:40pm - Actually go inside. Realize I haven't had anything to drink all day. Rectify that. Earlier this week I already changed lightbulbs and cleaned the kitchen, so pretty much head for computer to catch up on email and Twitter. As well as blogs... I find I have more time to comment now.

5pm - Start writing this post. Do it on and off; my wife arrives home at some point in there.

7pm - Dinner. Except here's the thing. I'd rather not be having dinner.

I'd rather be at the school's art night, watching some of the students I teach perform.

I can't.

It might be mistaken as supervision.

And I get it, I do, if something were to happen, I'd be in trouble if I interceded, and probably in worse trouble if I didn't. So best to avoid the situation entirely. No collateral damage that way. Same situation for coaches, who now can't be in the stands; in fact, we're lucky the arts night is going ahead at all, it's thanks to the principal being awesome and stepping forwards to take over.

But it sucks.

I can console myself with the fact that I saw one of their rehearsals. And they were AWESOME. (One of the acts still needed stuff like, uh, props and costumes though, I hope that came together.) I can now use this time instead for... well, blogging. Which includes the fact that my Math-Tans series will probably return in January.

Here's another thing, about how the math crunches down:
1) With 75 minutes in a day to do the non-teaching parts of my job, that's 25 minutes per class. Could YOU prepare a 75 minute class (including quizzes) in 25 minutes? Abiding by the curriculum standards? And have it actually be something worthwhile?
2) Ironically, I also have 75 students across my three classes. My tests are four pages. If we assume it takes me one minute to mark a page (it doesn't), assuming no interruptions, it would take four days to get through a set. Ignoring quizzes, we're looking at a set of tests every 2.5 weeks, on average.

So that's 12 days, 36 lessons (well, 30, let's not count the review day and test day). Lose 4 to marking (should be 5 owing to not a minute and always interruptions, but I'm going bare minimum). That's 8 days of 75 minutes, or 600 minutes to prepare 30 lessons. We're now down to *20* minutes per day for one lesson prep. Now, some teachers are fortunate enough to have two of the same class, but even then, this 20 minutes ON LESSONS assumes NO communication with parents, or discussion with colleagues, or marking BACKLOG (I have a hell of a one), or organizing field trips...

Yet this is what a portion of the general public believes we can do. All that crammed into 20 minute slots. I know this because they figure we still have plenty of time for extra-curriculars. Like sports practices, organizing busses for games, or doing band and choir, or helping to run math contests, all of those things. Or like arts nights.

Well, surprise... is it any wonder we normally work past 7pm? And into the weekends? And during holidays? And pretty much ALL the time except "the summer"? (And even in August there is prep going on.) For the record, Bill 115 also imposes it's maximum of 10 sick days, etc, etc, on custodial staff, and office staff, who have to go into schools - albeit maybe on reduced hours - through said "summer". Teachers are not the only education workers, which even the MEDIA forgets. CONSTANTLY.

But anyway. Went off on a tangent there. Where were we?

Yes, DITLife.

9pm - Caught up to the present, so I ponder how to spice things up here image-wise. Also let it sit for at least an hour to make sure I can edit if needed.

10:30pm - Return. Edit.

11pm - Watch "Daily Show". Go to bed, hoping that this isn't going to become the norm.

So there it is - an atypical day, but just possibly it's the sort of day the public thinks I do all the time.

EDIT: Noticed an error this morning, went in to change it, somehow ended up deleting the entire thing. Blogger, I hate you. I've restored most of it from a text file, there may be some minor inadvertent editorial changes though.

## Wednesday, 12 December 2012

### Blog Publicity Experiment

So over the last few weeks, I ran an little experiment in self-promotion.  Results in a moment, first a couple initial thoughts:

### 1) I don't Blog like I read Blogs

When I'm reading, I tend to prefer the shorter entires. I scan through, possibly leave a comment, move on. If they're too long, I find either I start 'skimming' later paragraphs, and/or I don't find time to comment, and/or I flag it for later and then never find time to get back. (If I had time in the day 'set aside' for blogs, maybe this wouldn't happen, but I don't do that either.)

When I'm writing though, it tends to be the culmination of several days' thought emptied out onto the internet, so you end up reading a lot in one go. More than I might be willing to read if I were in your shoes. Despite knowing this, I don't see me being able to change my style.

Now, there are exceptions to every rule (certain math blogs that I follow tend to suck me in regardless), but it makes me wonder if this is a common thing, or something only common to my personality type, or what. And do people who post shorter entries prefer reading longer ones?

### 2) I only track comments on my Blog

When I comment somewhere else, that's probably it - if you have a rebuttal comment to me outside of 24 hours, I'll miss it.  (Sorry.)  The reasoning is partly I have way too much email to track already, so I'll only track back to see followups on things that stood out... and partly because the first few times I ever commented, I didn't get much response anyway (outside of #mtt2k).

Yet at the same time, I feel personally obligated to respond to comments here (likely NOT within 24 h), to acknowledge that I did see your remark, and appreciate the feedback.  So again, if I assume other people are like me, they'd never see my response anyway.  So why this mental obligation?

I have no answers, but I found these things curious.

### The Experiment

I made a posting to my Other Blog (the personification of math web series) in late November, three weekends ago.  (Just a roundup of stuff happening here, though it had one new card.)  I then said absolutely nothing about it.  No tweets, no Facebook, no Google+.  It took a week to get to 3 views, and is now at 8.

I made a posting to This Blog two weekends ago.  (The Identity Crisis one, about the annoyance of dealing with multiple online accounts.)  I then said absolutely nothing about it, same as above.  It took about three days to get to 3 views, and is now at 13.

I made a posting to This Blog last weekend.  (Spoilers and thoughts for the movie Looper.)  I then posted about it everywhere.  It took less than a day to get to 3 views, and is now at 12.  (A maximum of 4 went to my prior entry based on this one, according to the stats.)

So what does this tell me?  I think it tells me that lots of publicity earns a lot of early hits (a "bump"), but then from then on, it's just a constant trickle in terms of additional views.  I know there are confounding variables (the fact that people who didn't want spoilers would avoid the last, the fact that they didn't all go up at the same time, etc.) but it doesn't seem unreasonable.  Which brings up the question: Is it worth doing the publicity every time? Or should it only be for really KEY posts?

I'm not sure I have an answer to that, but I'm going to publicize this posting too, to see what happens.  And to those of you who started following me on Google+ lately (which I am almost CERTAIN is thanks to a comment I made on MPershan's blog Rational Expressions, though I have no proof), and are wondering when I'll get on about the math again - that would be soon.

The plan is for my next post to be another Day in the Life posting. Because now I'm taking Job Action, and effectively doing the job many in the public THINK I do -- in at 8:30am, out by 3pm. (Ontario teachers are protesting the government's plan to simply impose contracts on us in three weeks.) And before you start thinking this is EASIER... I've done the math. It means I'm never going to be caught up. Ever.

By the way, happy 12/12/12!

## Saturday, 8 December 2012

### Looper Roundup: Spoilers

I know what you're thinking - this guy's a little late to the party, isn't he? The movie "Looper" has been out for over two months. No one's really talking about it anymore.

Okay, first of all, I'm not expecting much traffic, this is (as is so often the case) a way to download thoughts out of my head so I can stop thinking about them. Secondly, I would have posted it earlier but I received a text message from my future self telling me not to see the movie until today. It seemed legit. Or possibly I'm kidding about that last one.

Anyway, at this point, lest you question my credentials as far as time travel goes, I will point you at my page where I catalogue Time Loops, my earlier blog post where I go off on the Amy/Rory farewell episode of Doctor Who, and mention that I wrote something like 300,000 words about a group of teenagers finding a time machine. I grant "Time Trippers" is not published, in part because I made it a tad too date specific, and it needs more re-edits... and in part because I don't have time to see about publishing. Suffice to say, I am perfectly well versed in the two main temporal theories:
(A) Unchangeable Past (the "Frank" theory)
(B) Multiple Time Tracks (the "Carrie" theory)

Contrary to popular belief, I do not see them as mutually exclusive. I see incursions as leaning more towards theory (A), until a tipping point is reached, at which point you have (B) - which itself can collapse down into a changed history. All of this temporal babbling also serving to act as buffer space because obviously there will be MASSIVE SPOILERS for the movie Looper. It's in the title of the blog, so don't say you weren't warned!

There will also be a large number of links below for those of you who want to see the opinions of others. Yes, I do my research.

 Looper? I don't even know 'er. ....yet

### PART 1 - WHAT THE INTERNET SAYS

First, let's start the roundup with a few review sites that I've been to:
WIRED: Looper's Time Traveling Hitmen Kill Boredom Dead
SCREENRANT: Looper Review

The gist of these and most other review sites is, it's not really a time travel movie - time travel is the vehicle to generate the situation - don't overthink things. Oh, but I'm all about overthinking... and I find that for the most part, the movie holds up. Part of it's power (as with all time travel) is to allow the viewer to fill in the gaps. For instance:
- Why don't they kill them in the future and send back bodies? Because death triggers something that disappearance doesn't, or there needs to be a live body involved - we can hand wave that stuff.
- Why do they have Loopers kill their own selves, not each other, since the latter avoids the time paradox in the first place? I'm thinking mobsters have a sick sense of humour.
- Why doesn't the protagonist shoot off his hand or something at the end? Because that would BLOODY HURT? Not to mention there's no hundred percent chance of success there. (I really don't see how this is a complaint, particularly when something like this YouTube 'How Looper Should Have Ended' is more a more obvious flaw.)
...and so on.

But I'll get to that "flaw" in a moment.  Let me address the timeline problem first. There are two (main) such infographics floating around out there on the internet:
1) WIRED: Looper, Visualized: Spoiler-ific Timeline Shows How Film Defies Time Travel Genre

2) FILM.COM: Looper Infographic Explains It All

There is also a third one here at Back to the Feature and a fourth one here (more texty), both of which come closer to nailing it (IMHO), that I stumbled across. Yet none of these address what I thought was a rather key scene, to the point where I'm almost wondering if the film itself looped only in the theatre where I was watching it. Almost.

Recall the sequence of events:
- The FIRST time Young Joe has a chance to kill Old Joe, he DOESN'T. He then goes back to his apartment, falls out of a window, and
- The SECOND time Young Joe has a chance to kill Old Joe, he DOES. He then lives his life until being sent back, and
- The THIRD time Young Joe has a chance to kill Old Joe, he DOESN'T, and we get the majority of the movie.

That FIRST time is (in my opinion), really, really important. Yet it's being consistently missed in all the top hits I get in my Google searches. (Meaning my post here is liable to be buried with the others who've spotted it, that I also haven't come across yet, but whatever.) That FIRST scene tells us two things:
1) Suicide is not a way out. Because that's effectively what happened. Young Joe fell out of a window, and died, meaning he was not alive in 30 years, thus was not sent back, thus... had no reason to be falling out of a window, thus it didn't happen, thus... time effectively resets itself back to the chance of killing Old Joe. I was nodding at that point. We're already stuck in a time loop. Something has to give. Something does. Old Joe isn't able to avoid getting sacked, and so he dies.
2) There's an element of quantum uncertainty involved in breaking time loops. Given that "something has to give", when events play out, they won't necessarily lead to exactly the same outcome 100% of the time. (Perhaps 99.9% of the time?)

I already hear you protesting, since you've seen the movie, but no, suicide is not a way out. This may please some who consider it a rather Awful Time Travel Trope. (Which I kind of agree with.) Now stick with me here. Or alternatively, try to follow the logic from these other analysts, then come back:
Nick Hurwitch: A Time Traveler's Analysis of Looper
"So was Joe's sacrifice for nothing? Uh... yeah. Kinda."

Ken Flagg: Looper and the Problem With Time Travel
"The only way for the plot to make sense would be for time to be linear for those who have been sent back in time and non-linear for those who have not..."

### PART 2 - WHAT I SAY

We're getting closer to the situation, but we're not quite there yet. I refer you back to my theory (A) above, unchangeable past. The Wired video Observation Deck makes the point that "It's not the big arcs that can kill time travel, it's the details". I'm going to argue the flip side, "It's not the details that kill timelines, it's the big arcs."  The confusion comes from the fact that WE don't know which details constitute big arcs.
 I prefer this personification to the old man and hourglass

Consider going to work. You have two possible routes, and vary them up day by day. One day, there happens to be an accident, so you take route two. This may have no consequence whatsoever. Or you may have just run into the episode "Turn Left" from Doctor Who (where this one action kills thousands). You have no way of knowing. But the time streams (or the personifications of time, if you will) do know. Moreover, if you decide to "Turn Left" time can manipulate the situation so that it would be as if you turned right.  It won't bother to do this in all cases. You have free will.  But it will for the important ones.

The natural state of things is actually that Young Joe does NOT kill Old Joe, and Old Joe escapes. (We saw this the FIRST time.) But this leads to the window fall, and a temporal loop - so it's resolved by having Old Joe die. Interestingly, whatever is going on with the Rainmaker is happening completely independent of this. Something else acts as the trigger for him. Again, the details don't matter - only the big arc. (It's sort of like the Terminator movies, where Skynet is going to happen no matter what, it's only a question of when. I think it's also telling that director Rian Johnson made a passing reference to those movies in an interview back in July.) So Young Joe lives out his life.

But then, as Old Joe, he is sent back in time. The natural state of things is that he is NOT masked and killed by Young Joe, and he's got his rage issues to help. But if he IS going to survive, he has to save his younger self from killing himself later by falling out a window. Thanks to a "random" flashback memory, and some doctoring offscreen, this occurs.

And now we have something seriously interesting.

 Or seriously messed up
If Young Joe dies, Old Joe can't have saved him at the window, so he would actually be dead there. Yet he simultaneously WOULDN'T be dead there, because he was only IN that position because of Old Joe's trip. There's a serious amount of quantum entanglement going on here (I am probably misusing the term terribly - temporal entanglement?) to the extent that either:
#1 - Young Joe lives on, becoming Old Joe with the same major life events occurring in order to close his own loop as the rest of the world continues on it's merry way.  (Represented by Old Joe's memories.)  This is why simply deciding "never to leave the farm" for instance, won't work... events will conspire to turn him into Old Joe, no question about that.
#2 - Young Joe dies, and (by necessity) he ends up back at the point before Old Joe arrives... where both killing him and not killing him result in temporal loops, so effectively Young Joe has to have a heart attack and die on the spot.  (This reset obviously didn't happen.)
#3 - The third option, being what the movie did.

Let me now look at that, and clear up the remaining loose ends.

### PART 3 - WHAT THE MOVIE SAYS

The movie effectively says that Young Joe can kill himself (duh), which not only wipes Old Joe out of existence (okay), but maintains all of their interactions to that point.  That's the bit that has me thinking the most. (Even Star Trek usually has the sense to punch the reset button at that point instead.  I'm not saying a reset button is GOOD, but it is tidy. Now, for some Trek both good AND tidy, highly recommend the DS9 Millennium Trilogy by Judith & Garfield Reeves-Stevens, they wrap a time loop on itself like nobody's business.) Anyway.

The last scene with Sara, where she actually sees Joe's body, that's the REAL poser and paradox for me. If Old Joe never existed, what sequence of events brought Young Joe out to that field? (With all that money?) And how does Sara obviously remember them? I suspect there's a link here to the fact that the whole Looper organization got shot up to pieces, but I can't quite make the connection. So my best answer for this is that since Joe already existed in a state of temporal entanglement, interactions by all Joes got a "get out of physics free" card. (I've seen another theory that Joe is actually the father of the Rainmaker, who is Cid's BROTHER, but that didn't quite seem to work out timewise.) If you've been able to follow the logic to this point and see something, by all means comment.

 A more useful comment, perhaps?

A couple other loose ends:
1) People are claiming that "Joe created the Rainmaker". Not initially, no. Bear in mind we have no idea WHY all the Loopers loops were closing - it IS a criminal organization, maybe Rainmaker was once a good guy*. I buy that a new Loop was created as soon as Old Joe and Young Joe were both alive in the same timeline, and that he could have come about as a result of their actions, but I don't think that's the case in the original timeline.
*One theory out there is that Cid would ALWAYS grow up twisted, until Joe helped him accept Sara as a mother; I think I buy that theory the most.

2) The whole mutilation thing with Seth, that can still fit my theories. Gruesome as it is, severed appendages can be reattached, and memories wiped, and bodies placed in cold storage. I also think that whole bit was simultaneously necessary (so we know why Joe can't be teaming up with these guys) and unnecessary (because REALLY, you couldn't just use a hypnosis trigger phrase, or some sort of poison pill with a thirty year capsule dissolve or something??).

In conclusion, did Joe's suicide actually solve anything?  Well, it destroyed the cycle of loops.  It apparently didn't wipe him from existence, which along with failure of anyone to learn a lesson, is my usual argument against this sort of thing (people are better off in this world because YOU are here, dear reader, whether that be because you're a great comfort in times of need... or a thorn in someone's side prompting them to greater things). So he got lucky. But we don't know the fate of the Rainmaker, and now Joe's not in a position to help one way or the other.

Did he have an alternative at that point? Narratively speaking, no. It was an interesting movie, and I think the time travel holds up better than others might think.

## Sunday, 2 December 2012

### Identity Crisis

Prove the following:

Okay, no, not that sort of identity crisis. I'm talking about the dividing line between work and home. You know, like what they've mentioned on Bones, except here I'm going to take an electronic communications angle.

Consider: For work, you have a work email, a work number (perhaps even a mobile phone provided by them), a social account (or online board) for discussing things with coworkers, and likely key browser tabs or a work webpage (even as a teacher, I use one to post up the lessons of the day). For home, you have a personal email, a home number (perhaps just a mobile phone), a social account (Facebook, Twitter) for discussing things with friends, and likely key browser tabs or a webpage (where you may blog about stories you're writing).

Very clear dividing lines between the different accounts though, right?  No overlap between work and home?  Yeah, right.

So here's the crisis part. Do I really want a more professional website linked with my personal YouTube account as connected to my more laid back Twitter feed... where I admittedly about tweet work related things? Because Gmail seems really serious about making all of that (along with G+) interconnected - and once it's together, it's devilishly hard if not impossible to break the links. (I suspect the cloud is to blame. We're not supposed to have multiple clouds?)

Someone else has already discussed the idea of online identity better than I at that link, but I'm going to outline my personal struggles anyway. Quick context for the following: I have three primary emails. My work email (Work), my personal email (Home), and an email for my math webseries "Taylor's Polynomials" (MathTans).

CASE ONE: I created a YouTube account back in the summer, after deciding that I would participate in "Mystery Teacher Theatre 2000". I ultimately decided to make my video an episode of my webseries. And found I couldn't disassociate the YouTube account from my Home email to switch it over. I had to make a new account from MathTans.

So I now have two YouTube accounts, one where I'm following Math related things (Home), and one where I've started following Song Mashups (MathTans)... which is kind of reversed, but I can't be bothered disassociating each set of links in order to swap them.

CASE TWO: I created a LinkedIn account on my Home email (not with Work because it's more a job networking site). I then started following a Teacher's Group there. So I'm getting work related information flowing through my Home account - and there's another source of crossover too, in terms of using the Home account to follow Ontario political issues outside of work.

Add to this, the fact that a few years ago I created a webpage for a course I teach. I wasn't doing this through a Wiki (though again, another place needing an email to sign up...); this was done through "gmail sites". So again, my Home email. I've since expanded the site, and am using it for all my courses... but of course, when I'm at Work I need to log into my Home mail every time I want to update. Just like when I'm at Home, I'm getting Work related messages.

CASE THREE: I created my Twitter account through MathTans, my web series. I figured I'd be using it to tweet updates and other things of interest, as well as to see what Twitter was all about. Plus my home email was getting cluttered already via CASE 2. Then owing to circumstances, my web series went on hiatus.

I've continued to use Twitter, but usually not while logged in as MathTans. It's asked on occasion whether that's still my account, and it also wants me to hook in with Google+. But I have two Google+ now too, personal and web series related, and I don't want to forge a permanent link to MathTans Google+ when I use Home Google+ more often.

Corollary: I followed math blogs on MathTans and personal blogs on this (Home) blog. So most of my comments on blogs pointed back to MathTans. Now I'm using this blog more, but my comments still point back there. Should I be switching? For that matter, I don't even know the answer as to who would be more likely to follow me sporadically here, versus regularly on MathTans, versus both? (Or neither? Though c'mon, if you've read this far...)

CASE FOUR: Facebook. When I first signed in years ago, it was a strictly personal thing; I politely turned away colleagues. I was trying to make a definitive line somewhere - you can't necessarily walk into a store without seeing a student there and being seen as a Teacher. So this was going to be a place totally separate, where if I chance to grumble about marking, or post of pictures of me on vacation, it would take an unusual chain for school colleagues and students to find out. (Not that I didn't want them to see some things, but I'd prefer to tell them in person.)

Now, I've been feeling less restrictive there lately. I do still only have about a hundred FB "friends", very few of them being ones I haven't personally met at some point in my life... but I've again hooked in a page for my math webseries, and most of my hesitation in expanding now is that I'm not sure if I'M ready to see pictures of coworkers on vacation, as opposed to the reverse. So I'm not sure where that sits... do other people out there friend a lot of Work people on Home FB?

--
I guess what I'm saying is I have to keep logging in across multiple accounts. (I have even another for my personal webpage, in fact.) But that's what I wanted. Separation. Order. In fact I know there's people out there with two Twitter accounts, used for different purposes. Yet I can't seem to make some of the links where I want to - and once links ARE made, it's so difficult to uncouple them, if you'd prefer they were set up differently! Or gone altogether! (Or maybe it's easy but I've no time to find the site that explains it?) Instead, the web does things like encourage you to be signed in to multiple accounts at once. So we're at the point where I avoid linking. I'm left with the impression that electronically, we're trying to jam people into a lovely box/cloud, which seems to me to have two consequences:

1) People may learn more about you than you intend. Which will either give them a false impression, or make identity theft easier.
2) It can become more difficult to stretch outside this box, which in it's own way is encouraging stereotyping.

So, to sum up, it's not that I have a problem with doing Work related things at Home (or vice versa) - goodness knows I spend enough time at home marking papers. It's that, well, my online life is becoming cluttered, and I'm not sure how to clean it up. I don't think connecting things even more is the way to go, but diversifying too much results in too many damn passwords to remember. So... yeah. Until I think of an alternative, my blog comments will likely remain pointing at the web series I'm not updating? Feel free to offer suggestions.

As to the initial crisis, try multiplying LS by 1, where 1 is defined by RS/RS.

## Sunday, 18 November 2012

### Week as Math Educator Roundup

So, before we go back over the five school days, let's have a quick look at the weekend...

Saturday, not much done related to work, in part because of catching up on sleep, on Twitter, and a D&D gaming group I'm involved with that meets periodically on Saturday evenings. I actually feel kind of bad about not getting back to the marking. Though I did respond to an email question from a student.

Sunday, did get back to marking. Also did some finance prep for Monday's class. Over four hours work in total, amid talking to people online and my afternoon yoga class (we learned the rockin' cobra). It does feel insufficient.

Final thoughts will be categorized into headers.

### 1) Teaching Week Itself

Monday-
Approximate words: 2590

Tuesday-
Time Blogging: About 2.5 hrs (dedicated)
Approximate words: 3650

Wednesday-
Time Blogging: About 2.5 hrs (mixed)
Approximate words: 2660

Thursday-
Approximate words: 2600

Friday-
Time Blogging: About 3 hrs (dedicated)
Approximate words: 1900

Weekend-

TOTAL WORK WEEK: About 50 Hours
(Lunch is in there, but it's less than 45 minutes (on a good day). Balance that with travel time, which is roughly 45 min per day (>3.5 hr/wk) and we're back over 50 hrs. At 7 hrs sleep/night, I'd be sleeping less per week than working. But I do sleep in weekends.)

CONCLUSION:
I felt like Monday and Thursday were the most "typical" days; maybe Thursday was a bit more hectic than usual. Tuesday is typical of those days where my head is a bit off. Wednesday was obviously the outlier, yet I usually have at least one long work day per week too.

Interesting thing I discovered about the jobs of other teachers, when I had the chance to peruse their posts - their schedules vary by day! (Not 3 teaching classes, 1 prep period, rinse, repeat.) Some have what seem like very different schedules depending on the weekday, up to 8 separate periods, and may not see the same set of students every day. Huh.

### 2) Shifting Narrative Perspectives

I wanted to try changing up the narratives, both to see if I could do it, and so that people would have something different to come back to every day.

Thus in order of most to least difficulty:

5) Friday- Third person plural, that was more of a mess than I thought it would be. (Yeah, three hours of dedicated writing to produce the smallest entry.) I wanted to avoid the cop-out of 'they = this guy and his thoughts', but using 'they' as a teachers collective made me worry educators would read it and say 'I wouldn't have done that at all', hence everything sliding into the theoretical. Not so pleased with the result, but satisfied.

4) Wednesday- Third person singular. Kept slipping into first person. Part of the trouble is a phrase like "Prep period ends, test still hasn't been written" could work with 'His' or 'My'. Pretty sure I caught all the slips at least, as I tend to reread sentences as I go. Didn't have time to give the posts detailed editing after the fact.

3) Tuesday- Second person singular. Surprisingly, a bit of a toss up between this and Thursday, but since multitasking was done with the latter, I'll claim this was the harder perspective. The hardest part was that since YOU meant the blogger, I could never use YOU for the reader. I had to refer to readers in third person.

2) Thursday- First person plural. About the same difficulty as Tuesday. The 'job shadowing' excuse made it easy enough, yet there were some difficulties. The 'our wife' remark towards the end was actually rooted in a few earlier attempts that had to be rewritten. 'Our car'? 'Our formal wear'? Not wholly accurate. Plus I did start to feel a bit like Gollum, and I'm not big on LOTR.

1) Monday- First person singular. Obviously the easiest. You're reading this perspective now, and most blogs follow such a format. I probably should have saved this for the END of the week, when I was feeling tired... but then, reversing the order might have turned off first time readers, and Day 1 is the day with the most hits. (My first ever post to pass 100 views actually. Day 2 still under 70.)

Of course, there is the lurking variable that Thursday and Monday felt like more "typical" days. Would it have been easier to do third person on a day that didn't run so long? I don't think so, but I can't say for sure. I do wonder if people found the variety interesting, irritating, or simply didn't care. Feel free to comment below.

### 3) The Personified Math

Well, the two people who've actually read my web series followed me over! The lack of ANY other remark leads me to think that the web series will continue to tool about in my subconscious, as I spend former 'blogging time' in the coming week doing other things. The series WILL be back, make no mistake, you're not getting rid of them. (Sorry?) But I may not throw myself back into ramping up the story buffer (including Hevvi) until the holidays.

With respect to the actual characters I used, Tangent surprised me a bit, both in her selection and that she's a bit more kindhearted than I'd imagined (as well as mischievous). As I said in the comments, maybe I can get students to sympathize with choosing her ratio? Hevvi got short shrift, saddled with the hardest narrative perspective. The conics were par for the course (I didn't offer Hyper because I had no card prepared for her). And Para...

Um. I really am crushing on Para a bit, aren't I? *^^* Most entries, quite by chance, were about 2600 words. In part due to her asides, she blew past that by an additional 1000. The quadratic does strike me as someone teenagers could relate to though - often misunderstood, causing trouble even though she's never trying to be difficult, insecure in particular when she's compared to Expona... so yeah.

I still think I need to find a voice for Para too, for video episodes. I'd co-opt my wife, except I've made the Quadratic a singer. I'd ask my friends, except I'm a bit worried about their reactions. It's funny, I'm really good at male voices/accents, but I'm much better at drawing female characters (plus, X chromosomes = algebra), so now I'm in trouble.

Yes, I am putting far too much thought into something that's only really yielded any professional dividends in terms of stretches and compressions. But it's fun, damnit.

### 4) Topics for Comment

Finally, a few key things that come up over the course of the week. As I'm still interested in opinions for them, if this is the only post you're going to read, I'll summarize:

1. ROUNDING. In mathematics, rounding is generally bad. It introduces error if you're about to multiply by a large number, it throws off ratios, and we prefer to use "exact" radical values most of the time anyway. Yet on Wednesday, students were mentioning that in science, rounding is mandatory, related to the number of significant digits in measurement. This seems like a necessary disconnect, but how are we supposed to deal with that in the classroom in a way that minimizes confusion?

2. CONICS. I really am curious where this is in other curricula. It was removed from the (Gr 11) Ontario curriculum back in 2003 when five years of high school got compressed back into four. (That's also when proofs were removed, because when it was proposed removing calculus instead, post-secondary institutions were up in arms.)

3. JOB SATISFACTION. This came up on Thursday, with the remark that when students "are getting it", a teacher feels happy - in fact, may feel it a bit even if it's second hand and not their own student. Does this work the same for other teachers, and what about people in other jobs? What is 'satisfying'?

4. THEME SONGS. I threw those in on a whim after making an offhanded remark on the first day. Did anyone actually click on the links? If so, did you think they were interesting? (This kind of relates to my web series too, since I always had at least a link a day in them... but not much point doing that if no one follows links.)

Finally, for those wanting more, there's now a tumblr site for all the posts of all participants: http://DITLife.tumblr.com/

I think that's everything. Thanks for joining me this week! I hope you will consider checking in on me again from time to time, or following me on Twitter. (Or, y'know, telling me why you'd never do that so that I can at least be more aware of my follower demographics. :) )

## Friday, 16 November 2012

### Week as Math Educator - Day 5

You don't know me. Well, maybe you do know me, but I know you haven't seen me like this before... my name is Hevvi. And the H is silent! I'm also known as the Heaviside Step Function. I mean, you didn't think this was the complete cast of math-tan characters, did you?

Welcome to Day 5 of "A Week in the Life of a Math Educator".

As to a theme song for today, well, yesterday's was impossible to top. So, unless we can piggyback on some more famous tune... I'm guess I'm like, f(u).

Funny thing about today though - it's a Professional Development (PD) day. So if you've ever wondered what goes on during such days... this is not the posting to read. Because Ontario high school teachers are, as I mentioned at the start of this week, taking job action. Which means that, while normally the agenda would be Board directed and effectively a Professional Activity (PA) day - oh, there is a distinction between PD and PA - today teachers are making the choice to do self-directed PD instead.

For context, here's roughly how the last PA day went. After arriving, there's breakfast, a presentation from our Police Liaison about the problems of sexting, a presentation from another teacher colleague about Technology in the schools, some group work involving strategies for difficult students, break for lunch, then meetings in departments to discuss the school improvement plan (SIP) and assessment and evaluation policies of the Board. Which is valuable (well, most of it), but at the same time, is geared more globally than individually.

So, if a teacher didn't HAVE to do that, if they could throw out the agenda and spend a day doing self-directed professional development... what would that look like? What might such teachers end up doing?

They might do the following.

### MORNING

They might again wake up before their alarm, wonder why (stress?), and head to their computer to catch up after a night of blogging instead of having read posts. They might finally think they had the time to fully read the DITLife blog of someone else (who commented on theirs), and comment back. They might also not wear a tie, end up leaving the house just after 8am without worrying about being late for class, and even take a moment to muse about the frost on the grass.

They might hear Katy Perry on the radio while driving in, and start singing along, except using the tune "Polynomials" instead of "California Gurls", because it's more mathematical. Well, okay, I find this last possibility highly unlikely for most teachers, but statistically speaking I suppose stranger things have happened. Math educators can be an odd bunch. (Also, that's correct spelling for the original song, because apparently "Poor Literacy is Kewl". Also again, one more more traffic circle yesterday and again today, well done keeping track.)

Such teachers arriving on a PD Day might potentially then get to the prep room at 8:25, the time they'd normally be going to class, and walk down to the staff room with another colleague. Which I'll say is a lot more likely, even taking into account the fact that this would be one particular teacher's first time into the staff room this month. Yeah, it really is way off in the corner of the building, almost like an afterthought after the planners put in the cafeteria.

Anyway, the colleagues might soon find themselves chatting with others while in line for breakfast - ones they rarely have the chance to interact with on a regular basis. The group may even end up sitting together at a table, all the while discussing such topics as: Formal Day Thursday, the format of PD Days past, how having kids can change opinions on teaching, the state of the school play, the fact that Christmas displays are up too early, and the fact that it's colder in the building without the body heat generated by students.

The principal (who was required to create a PD agenda for the day anyway) coming by the staff room is also an option, particularly if it's to bring some flowers to present to the cafeteria staff for a job well done.

Ultimately, teachers in this position might head back to the prep room at about 9:25am, whereby they might work on refining a lesson delivered a few days ago. Seeing as there's no time to really revise such things once they're done, needing to be so focussed on where they'll be going with it tomorrow. After all, revisions, they can happen next time that lesson is needed - like next semester, yes? Or, alternatively, now. Teachers might even relish the opportunity to do a lot of this revision planning, spending most of the morning on it.

While some colleagues clue in to doing the above, others, and this blogger in specific, might be doing some marking. For instance, resuming the marking of papers that had been continually getting chipped away at all week. Of course, teachers doing this might have occasional brief interruptions, such as when a Vice Principal comes by to reassure that things will be in place for the Math Contest next week, and then again when they decide to check both their board and internal email... and of course there are occasional conversations with the other math (and family studies) educators.

One teacher remarks in passing that they can't recall last time a PD day was this productive. Another is getting memories of Thursday confused from reading this blog. (John C. Reilly? Okay then.) Yet another has computer issues. And notable, a comment regarding a student from a senior math course, who has a mark under 60. Is this student misplaced? Is this student being forced to take the course by their parents, or their choice of career? No. This student knows they aren't very good at math, but has said they are taking this extra course "because I like it"! Thus perchance they have a greater incentive to continue, compared to other students.

Lunch, in many such scenarios, would be announced before noon. Teachers who are like the one blogging though, who are close to finishing the set of tests? They might prefer to keep going. They might also be inclined to ponder the fact that they've done 2 hours of marking as self-directed PD. But when you consider that there are PD days at the end of the school year, which are pretty much only for frantic marking in order to get totals together in time for commencement... it's not that unusual. Moreover, this stuff has to get done, so this might actually free up a couple hours on Saturday. Then again, since test totaling is yet to be done, probably not.

### AFTERNOON

It's a reasonable assumption that most teachers on this day would eventually get upstairs, to the library, for lunch, before 12:15pm. There, they might have the chance to talk with some educators who are different people from that morning. Topics now being such things as: Sports pools, how factors in getting teachers together during a regular day might include school size and necessity, the troubles with the economy, and how classes are going in other departments.

After lunch, teachers are willing to help put away the plates and cutlery, as leftovers are brought down to the custodial staff. They'd then all return to their offices. Again with an eye to this blog though, there is the matter of a car still at the garage... and checking voicemail reveals a notice to phone to arrange a pickup. This is done. Then, having made one phone call, an educator may feel they're on a roll, and they would then phone parents regarding missing assignments - this being the calls that were not done late yesterday. (Hating the phone, that's not necessarily unusual, but phoning earlier rather than later can alleviate stress.)

By this point a certain teacher, or perhaps by extension most teachers, would at least consider networking with someone else teaching the same course as them. At 1pm this happens here, and they both look over a course summative as suggested by another who taught the course previously. Though this being finance work, and there being those who find it worse than phone calls, it does necessitate actually going through and creating a personal solution set too. That done, they can discuss tweaks, leaving only the final individual planning for Monday.

But with it now being 2pm, why not finally do some more fun self-directed PD? After all, in addition to the songs by the math-tans, there are many other students and staff in the world setting math concepts to music. This is the point in the day when they turn up... the f(u) link "theme music" was found at this time, along with some others that also connect to calculus concepts. These songs can be added to a certain list being compiled, even if they are a bit beyond high school.

Conceivably, there is also the opportunity today for all interested teachers to fully catch up on email. Connected to this, they might scan through the email links to a backlog of "Technology Times" articles, a weekly publication within the Board. (A couple items are bound to be Tweeted later, if anyone's interested!)

Finally verging on 3:30pm. Many have left since the day officially ended a half hour ago, but some remain. They may still have a few key things left to do, such as creating a summary file of teacher courses for their Gr 12 data class. Not being aware of any easy way of grabbing this data, it's entered manually, flipping between windows, which fortunately only takes about half an hour (and saves needing to do it Monday).

Teachers, they came and go at all times, and this time of year, it's usually dark for the goings. But there is still light at 4:15pm when they might be leaving to pick up their car, were they to have left it for service at a garage the day before. Upon arrival, the loaner can then be swapped out, and the car with new winter tires would get driven home.

The blogger and his math-tan thoughts, they are indeed home for about 5pm, which means they are the first arrivals at the house. At this point, there is a good chance they choose to write up their blogging, but fall asleep in the process, waking up only at midnight, having completely missed dinner.  They would post, and go back to sleep.

BUT HERE'S WHAT REALLY HAPPENED...

### EVENING

They begin a writeup of their blogging, including doing some additional sketches. Their wife comes home, and they have something quick and microwavable to eat. Eventually, before 8pm, they head out to a birthday celebration for a friend.

Following that, and returning home before midnight, the blogging resumes, until the point that has now been reached. It takes longer, in part because writing in third person plural style is somewhat more difficult than many might have first anticipated.

As for the somewhat hypothetical nature of this entire post... well, again speaking as Hevvi (the H is silent!), I may also be theoretical. Certainly I'm non-canonical until Logan's Gazebo chances to find me. Whether that happens sooner or much later will have at least some connection to the interest, or lack thereof, on the Other Blog, of Math Personification. The one involving the characters you have seen this week. So feel free to comment here or there; worth doing?

Final thoughts on this entire experience will be posted this Sunday, so come on back then!  And as always, Tina's roundup of other educator posts is at her site, Drawing on Math: Day in the Life, Part 4

## Thursday, 15 November 2012

### Week as Math Educator - Day 4

My name is Tangent. I win by two votes. In an election where only two votes were cast. One of them calling me 'tan-tan'. >.<  Politics these days - I'm sure I wouldn't have won if my older sisters, Sine and Cosine, had run an ad campaign worth millions of dollars. But, they didn't, so I guess you're stuck with me blogging about Day 4 of "A Week in the Life of a Math Educator"!

I'll effectively be shadowing the actual blogger all day today. We should get some positive energy going to start, what do you readers think? I'm thinking lots of you are teachers, so how about a theme tune of "You Have Made A Difference", which you can listen to in English at this link, or alternatively in French at this link ("Vous Changez la Vie"). If nothing else, carry that with you into tomorrow, okay everybody?

### MORNING

On to the day... we know we need to be leaving earlier than usual, since the car is getting a tune-up, rustproofing and some snow tires; appointment was booked last week. We wake up before the 7am alarm (again!) and are out by just after 7:30pm. Drop the car off, pick up the free loaner (it's a wonderful garage, just ask for info if you're local!).

Root(64) am. (See what we did there?)  Leaving the place in the replacement car, need to reset the clock to daylight savings; lots of the radio presets are okay though, they've even got CBC. News: It's five weeks after Amanda Todd's suicide in BC. The 15-year-old was was cyber-bullied, so we get some press about Bullying Prevention Week at last, from her mother. Oh, and British Columbia's Education Minister told the mother not to attend an anti-bullying conference, after 'expert advice'. What is that I don't even. Moving on.

82*100 am.  We get to school - it's formal day, so we've got the pink bow tie, jacket, and cardboard top hat. The latter seems to be the big hit as we head to the office to empty our mailbox. We're back in the class fifteen minutes before the bell; students start arriving pretty soon, on account of the test (drawn up last night) and there still being questions.

One student verging on tears is wondering if she can do the test next week. Personal policy hasn't changed - if you can bring in a valid note from home indicating there's external issues, okay, otherwise, life goes on here. She elects to write. Another student is also looking miserable with similar hopes. Tell him that if work on the summative task next week is better than what he does here, we can reassess, but no note, we're proceeding.

Warning bell; the underlying theme of the "get to class" music is recognizable, it's Yankee Doodle, but this is the jazzed up instrumental version that we haven't located on the web after five minutes of searching, so you'll need to visualize. We're busy answering questions of students at this point anyway. Incidentally, a couple of the guys are also observing the formal day, looking nicely dressed.

DCCCXL am. PERIOD 1: Gr11 MIXED. Playing of the anthem, and morning announcements. From there into the test. Four absences, one we know about (death in the family, haven't seen her at all this week), the others will be getting calls. Once everyone's writing (some spent more time with their notes first), go to check mail on the computer. We get a little popup... Norton Antivirus is upset. Why? "Computer does not have all available operating system updates installed."

First, we don't have the authorization to install anything. Second, we're not even sure what the OS is, so we check... "Microsoft Windows XP Professional Version 2002: Service Pack 3". Yup, that seems about right, so what's the problem? Whatever, message is gone now. Forgetting our email, we scan back through the test, notice one of the questions could be seen as ambiguous, thus jot a clarification on the board.

A bit later, a student asks something - an answer seems wrong, but she can't spot her mistake. We tell her to keep doublechecking, even as we suffer a momentary panic attack because we don't immediately spot it either. Is it possible we created a question with a nonsense solution? No, we reassure ourselves... but at the same time, it's finance. So useful, yet we're probably as anxious about finance questions as other people are about trig identities. We don't broadcast this, obviously, but don't pretend we're an expert here either.

The period wraps up, some students will return to finish at lunch, a couple others think they'll be able to take ten minutes off their second period class if they check with their teacher. We allow them to do this. Then we suffer another little panic attack - we're missing one of the graphing calculators! Nope, it's on the desk. Okay, deep breath, need to get going with next period.

By the way, any of you out there started reading this like we're Gollum yet? We likesss the mathematicsss, the math is our precioussss... while we hatesss the finansssse. (Sorry, that was evil of me, now you probably won't be able to unsee that perspective for the rest of the post, huh? Hm. So is it wrong I find that funny?)

LOG (10^10) am. PERIOD 2: Gr12 DATA. We ask students if we should be taking up yesterday's sheet first, or saving that for after they have time to work today in class... in other words, no point taking up homework if it's not yet done. Vibe is, launch the new topic. That would be causation. So we present a silly scenario, discuss, then hit them with definitions, and fifteen to twenty minutes to work on either last night's stuff, or new stuff, while we circulate to answer questions.

As well as get Summative Topics from those who haven't come up with them yet. Secondary sources are due next Monday after all, plus we need to come up with groups before next Wednesday! Eventually we regroup to discuss the scenarios of today. Then a little discussion of the Placebo Effect, not strictly in the curriculum, but how can you not at least mention it when dealing with causation?

Also this period, we remember to give a notice to a student about an event happening Monday, the recycling for the room is brought by a couple students down to the loading bay when the announcement is called, and of note, about the same percentage of students as first period going in on the Formal Day, including one female.

DATE am. (11/15) LUNCH. First dealing with students returning to finish their tests. Gives us time to deal with attendance, checking mail, and saving files to upload to the course websites. One of the missing students from this morning turns up! Said she slept in, wondering about writing now. Lunch is shorter than a period though, so we offer them same rules as always - if she can get a note, Monday will be okay, otherwise both now and after school. She goes to phone her mom. Comes back - she'll have a note Monday.

Once students are finished, to the prep room to phone those still missing! We reach one parent, child wasn't feeling well, for the other we leave a message. Also check our voicemail, but the garage hasn't phoned back yet about our car. Our heart soars a little now at the discussion going on here... colleague is saying how it's so satisfying "When they [students] see trig and are getting it, realizing how x is cosine...". (We ask to quote her here, she's good with that.)

Question comes up: What gives OTHER people job satisfaction? Coding something really nice? Making money for a company? For us, it's students. For you? Comment below, maybe?

Conversation shifts to introducing quadratics; suggested to do it by throwing things around the room. Better suggestion is raised - attach a streamer to the things you're throwing. Hah! Have to head back to class after less than ten minutes though... we have students arriving early for next class, regarding the task they didn't write Tuesday. We do compliment another teacher on her formal dress in passing though. Which she says she's supplementing with a shawl to conform to the dress code.  (Yeah, so my midriff baring top would not work out here... anyway, that's a whole other identity.)

We get to the classroom, answer some student questions prior to class, then we're immediately on again. Had time for a mouthful or two of food in there.

### AFTERNOON

Time: The amicable number pair of 1184
(1184's divisors: 592, 296, 148, 74, 37, 32, 16, 8, 4, 2, 1)

PERIOD 3: Gr11 U. More students dressed in formal attire this period! We compliment one guy on the sweater vest, and ask one female student how she got her hair pinned that way. Notably one student spilled his drink in the hall as he hurried to class from lunch. But in the chaos it was handled by a VP and care staff member nearby, before we could suggest to said student that he get some paper towels.

Start this period by doing a Seat Switch - finally, we remembered to do this again after the success of two weeks ago! (Forgot this morning, and blogged about that back here.) Then flashing up yesterday's notes for the five people who'd been legitimately absent, and address any questions based on yesterday's work on exponents. Very few questions, and most of them are working in new groups now discussing the unit. Well, this is awesome.

Some of them ask for the quiz early; we make sure all of them have it with 40 minutes left in the period, to allow for ten minutes to take it up at the end. The level four question, solving an exponential equation, is engaging a number of them. We like this. Many are now seeing they need the same base, but aren't sure how to proceed from there. (Logarithms is Grade 12.)

Bit of a hiccup as one student gets a spontaneous nosebleed. The math is that exciting. He goes to the washroom, the person sitting behind him is a bit perturbed by the sight of a couple blood spots on the desk. We go to wipe them up, problem solved. A little thereafter, we take the quiz up, they seem to follow the logic of setting exponents equal! Collect in quizzes to have a look, remind them of test next week.

(11^2)+(3^2) pm: PERIOD 4 aka PREP PERIOD. Before we can get going here, there's commotion in the halls. Long story short, someone has sprayed odour of foxglove around (it's not a good scent), so we phone the office while another teacher asks students about this. Principal comes, we learn this also happened upstairs, and identity of person is likely known.

This seemingly dealt with, we go back to the prep room. Phone is in use, so we double back to class to respond to an email that connects to the math contests we're coordinating next Tuesday. (A student asked about them at some point today too, forget when.) Another student arrives at this point about writing the test which he couldn't do after school yesterday. Right, he has a spare now.  Got confused as to when he was coming by.

We give him the test, then double back to the prep room. Phone is free, we check our voicemail, one message... the parent of the absent student from this morning? No, the garage about our car. We phone back, talk for a bit, even sit down briefly; the tech is going to check on the availability of a cheaper brand of winter tires, we'll phone him back later.

That's one thing about teaching - no one can reach you during the day, unless it's an emergency. Car tuneup, dinner plans, online chats, all of that isn't emergency, therefore impossible during the day. (But those sorts of things don't happen much in other jobs either, do they...?)

Double back to check on student, organize desk, talk with him, he's done all he can. Back to phone the garage. Again long story short, no cheaper tires but other minor savings, and won't be picking the car up until tomorrow. This changes things! We won't need to be leaving the school before 5pm. So we take a half hour to finish our lunch and do a quick Twitter scan. (Haven't checked Facebook since Wednesday morning as it's blocked at work...) Respond to an @mpershan tweet.

Now 490/2 pm. End of school day. Student comes by to write task, as we prepare the next day of teaching (which would be Monday, given the Professional Development day tomorrow). She finishes after 4pm, about the same time we finish getting everything arranged. We go to photocopy necessary handouts. No one else in prep room when we return, but then a couple coaches come through after practice. Chat briefly.

At this point, we would phone some parents of students who have outstanding assignments, but job action is such that we're not communicating outside of school hours. It can wait until tomorrow anyway. Check voicemail once more though - good thing, garage wanted clarification on something, phone them back before they close. Then, a knock at the door - a student is wondering if one of the coaches is still here. No, they left... which is bad, because he left his cell phone in a room that is now locked. However, we may have that key.

We go and rescue his cell phone, asking to be reasonably certain it is his. We have now "saved his life"... oh, good for us! After 5pm now. Would start marking, but since nothing can be handed back tomorrow, typing up minutes for the math meeting last Monday takes priority. Also brief distractions online again. As well as taking a moment to set up the following photograph in our room, since we're blogging about it... remember, Formal Day.
 Actually my classroom. Rare photo!

Verging on 6:30pm, one of our students chances by in the hall (back from some event, presumably). He's surprised we're still here, asks how long we normally stay. We say this is about right. He's... impressed? We hope that's the emotion. He moves on, Meeting Minutes done, about time to get going in order to get to the drycleaners before they close at 7pm.

### EVENING

Home a little after the aforementioned 999999/142857 pm. We chat with our wife (our wife? Oooh, okay, the first person plural is failing us a bit on THAT remark... maybe we'll drop that now), and she was able to hear a radio broadcast related to a friend of ours and NaNoWriMo. He may well be reading this now too, all the best to him in his efforts! There's a bit more chatting about the day, decide that for dinner to just toss a pizza in the oven.

A bit of final work is necessary on the Math-Tans membership card at the top of this post, not having entirely anticipated the Tangent result back on Sunday... yeah, bad enough that the students forget me as soon as they learn Triangle Laws, now even my own creator is handling me after Sine and Cosine. But it's okay. I have Lyn to hang out with whenever I'm neglected on the Trigonometry side. :)

Continued blogging through 'Elementary' and 'Daily Show' which brings us to 11:30pm and time to post up. In fact, think this day was the most typical of any of the days blogged so far!! Glad I could share it with you! Remember, "You Have Made a Difference"... and perhaps I have too.

Tina's roundup of other educator posts at her site, Drawing on Math: Day in the Life, Part 3
She'll also be posting her day today, if memory serves.
We'll be back tomorrow... or will we?