Monday, 30 December 2013

WRI: Putting My Serial Together

There are many articles out there talking about how to write a serial. So many. I have NOT found as many talking about how a single individual actually DOES it - it's mostly summary tips for others. Tips, suggestions, pitfalls... heck, I even wrote my own post with tips.

My cup runneth over

So this will be a post about how I actually ASSEMBLE my serial. I'm doing this partly as a window for other writers, but I'm also hoping:
1) That you'll comment if it's different from your creative process. Be it serial writing, math blogging to a schedule, what have you.
2) That you'll comment if you see ways I could be more efficient, or how I might improve the process.


I have a text file where I place the ongoing story. I like to have a buffer of at least a couple weeks, so in theory, every two weeks I'll go in and write four more episodes. In practice, there's times when I write more, and times when I'm scrambling to get a few episodes in on the day before I need to publish. I just published #203. I've written through #208.

What makes the writing tricky is bringing each scene to a stopping point after about 10 paragraphs. Effectively trimming out all the florid details and cutting to the heart of the matter. I think this is something I'm fairly good at; for a teaching analogy, it's sort of like highlighting the core ideas of a unit. No idea if the big picture is emerging though, as that's up to the readers.

At the bottom of the file I have a bunch of miscellaneous ideas, links, and aborted dialogue, which I turn to when I get stuck. As the file fills up (every half arc, which is 15 episodes or so), I store it, transfer the ideas, and continue the process in another file. Back when I split the party (in Series 4), I tried having a file for each group, but the back and forth became too difficult to manage.

I also edit when I write, in the sense that I reread at least two prior entries before beginning my next one. Partly to pick up the threads of where I was, but also to catch silly grammar errors. So when it comes to edits in step two, most of the basic stuff has already been caught.


This requires a different mindset. This pass isn't even for spelling and grammar so much as it is for titles and links. Every episode needs it's own title, something more interesting than "Episode 17". And every episode I do includes at least one weblink, be it to a math blog or a funny YouTube video. I like to think this distinguishes me from your average serial.

Head shot of a "bunny girl"
Sometimes where to place a link is obvious. But more often than not, it isn't, which requires doing some online searches - and I don't want to pick the first hit, I want to pick the one that might be the most useful. Titles are also harder to come up with than you think, as I tend to enjoy wordplay. I even keep a separate file that includes all my titles to date, as I have this worry that I'll end up repeating an idea.

The other thing I (try to) do at this step is see that I'm not abusing pronouns, and that referring to Para as a "bunny girl" has enough surrounding context for new readers. This gives me a titled, linked episode. I'm halfway there.


I've previously blogged about why you should draw for your story. I've also gone in depth about drawing for a webcomic (aka serial), to illustrate my process. For me, there are 3 types of pictures:

Body shot, more "factors" to consider
1) Head shots. Pretty easy, maybe a half hour from start to finish.

2) Body shots. Harder, because proportion comes into play, and I have to figure out what people are doing with their arms and hands. At least an hour for those; harder to draw, longer to colour.

3) Group shots. These take hours. I have to figure out relative heights, often going back into my archives to see how tall I made a character previously. Or this means sketching out a setting, which requires some perspective work and online research.

Group shot. Why do I torture myself?
I try not to do group shots that often, but sometimes the serial necessitates having one, or I simply want to challenge myself a bit. There's also the matter of synching the writing to the image. It doesn't happen often, but sometimes I'll have drawn something slightly different from the narrative - it was easier to show the character with their hands behind their back rather than gesturing, for instance. So I tweak a couple of words.

I'm very much into reusing art clips where possible, which is why a lot of the images are generic, and why new art is only featured in every other update - if that.


With all the pieces together, it's time to post. I generally give the entry a final read first, then cut and paste. Then alter the font defaults to be what I use. One additional consideration is where the picture is located - for instance, if you have a picture on the right, staring off TO the right, you're leading the reader off of your page. I take care to avoid that; put a right facing image to the left.

This is also when I give captions to the images - it's rare that I had any plan for those. Of late, I only tend to caption the larger images. Back when I started, this would all be done on a publishing day; since shifting to the blog, I can schedule ahead. I only schedule a couple updates in advance though... perhaps living in eternal hope of a remark altering a future update.

Do you see things as I intended or not?

One slight hassle at this step is that I created the serial blog with my mathtans account, but started the original series (and it's index pages) back on my personal google account. So I have to change mail accounts in order to update the index page. That's why the index update is often done a day or two after the fact.


That's pretty much how it goes! In fact, my blogging procedure is somewhat similar. Any insights, suggestions, or offers of assistance are now welcome. For other reading about my serial, check out:
-Rewrite recaps. Highlighting when execution has differed from idea.
-Why I write series 5. And why math is suicidal.
-Author Explains: Word Wide Web. More about the wordplay itself.

You're also welcome to read the serial too! It's a mathematical personification fantasy story. Yeah. Let me know if you find my audience.

Monday, 23 December 2013

ETC: We've Got Elder Sign


The following is from a game that took place Dec 21, 2013. The characters, randomly chosen:
-Carolyn Fern (Psychologist; Scott M)
-Jim Culver (Musician; Greg T)
-Wilson Richards (Handyman; Tom M)
-Rita Young (Athlete; Scott D)

Up against: Shudde M'ell
 (Power: World Cracking)

This game features an unexpected ending.

(Quick background about the game: Six adventures cards are dealt out. Museum Investigators attempt to fulfill those missions. Some successes give Elder Signs, which can then prevent the Ancient One from coming through - but the clock is always ticking, and Doom Tokens can awaken the Ancient if you take too long. You can also lose Sanity and Stamina - if those reach zero, the investigator dies. The missions are completed by rolling dice to complete the tasks on the cards.
The Dice: There are six green dice, each having: 1 investigate; 2 investigate; 3 investigate; terror; peril; scroll/lore. Bonus yellow die replaces Terror with 4 investigate. Bonus red die replaces 1 investigate with 4 investigate and Terror with Wildcard.)

Carolyn goes first, opening the "Another Dimension" portal. She then succeeds with that card, portal card gone, back to six cards. Jim goes next; he fails on attack. Which is when the insidiousness of Shudde M'ell becomes clear. The card is removed from circulation, placed under the Ancient One and NOT replaced, leaving only five cards. If all the Adventure cards go, it's an automatic loss. Oh good.

The clock ticks around to midnight a few times. The available cards gradually get whittled down as investigators fail. There are some successes, even some Elder Signs, but in the grand scheme of things, those will become irrelevant.

One of the cards, "Wicked Old Man", curses Carolyn when she does not succeed. (This gives her the black die, randomly canceling out a result.) A replacement card, "Ominous Portents", then had the effect that "At midnight, all investigators become cursed". With Carolyn already cursed, this would remove her from the game.

Fortunately, Rita won at taking that card out, with the side effect that she became blessed. (This gives her the white die, an extra as she rolls.) The very next round, Wilson becomes blessed by playing a spell card he'd obtained. Also somewhere in here, Jim defeated a monster which caused the clock to tick around an extra pulse - meaning that Rita now begins each round (instead of ending it).

Investigators (cursed Carolyn in particular) start playing it safe, visiting First Aid and Lost & Found on turns, rather than engaging in missions. Given the stalemate developing, an eye is cast towards Shudde M'ell. To defeat him requires rolling three terror. Jim ends up parking two terror dice on spell cards as he works on a mission, and it's thought they might be useful for the endgame - until it's realized that three terror are needed for EACH "doom token" (of which there would be ten). An additional annoyance is that few of the remaining cards dealt include Terror requirements, making it hard to "unpark" the dice.

Ultimately, there is ONLY ONE Adventure Card in circulation. This is often left to Wilson (who can control the yellow die) or Rita, who bought herself an ally - Anna Kaslow, who allows a reroll of up to two dice. Anna only goes away by losing sanity, while Rita's power ensures she doesn't lose sanity on any successes, helping to keep Anna around. (Yes, you can lose health and sanity by succeeding, in some cases.)

Rita defeats the latest Adventure card. Next card out: "It's Quiet". If this card is still active at the next midnight, it is removed from circulation and not replaced. Game Over! Fortunately, Jim has a spell card allowing for replacement of a card on the board - he uses it on this. (Since it's not a failed attack, Ancients cannot interfere.) Play continues. Another portal card comes into play: R'Lyeh. Who also gets the Wizard Whateley placed on him, which locks up the red die! That's the safer card to attack at the moment - defeat doesn't mean instant loss.

It's thought the portal card could be attempted multiple times. (This turns out to be a misinterpretation of Shudde's power - in the end, it won't matter.) Jim hops on to try even though Wilson, up next, has better chances. Jim fails, but Wilson also fails, and (right after midnight) Rita succeeds. (So though the card SHOULD have been mulched by Shudde the first time, all it did was grant three elder signs - which don't end up helping - and two cards to Rita from ally Ruby Standish - which she doesn't have occasion to use.)

The remaining Adventure card ("The Hall of the Dead") requires expending a health to defeat. Thought best to leave this for Rita, who doesn't expend health on success. But before she can act, it gets monsters summoned to it! Two at the end of the current clock tick, and the new midnight causes a doom token to go down, Shudde summoning a third. This ups the requirements.

The monsters include Wizard Whateley (again?!) who locks up the red die, and a Chthonian. Problem: The Hall needs 5 Investigate, the Chthonian needs 7, and there's at least 4 OTHER requirements, meaning it is absolutely IMPOSSIBLE to succeed in one shot - there aren't enough dice! But NOT succeeding in one turn means automatic loss of the game! Ergo the players can do NOTHING at this point, except tool around and heal up; the ONLY chance for victory comes in taking on the Ancient One himself. Yeah, right.

So the players trade in for items, and as it turns out, the very next tick of the clock adds two more doom tokens, which wakes up Shudde M'ell. On the bright side, curses and blessings are dispensed with, so Carolyn is free. On the down side, the red die was still pinned by Whateley and is now forever lost - hence Rita's red die cards are useless.

There are five cards under Shudde M'ell. (Should have been six, due to the R'Lyeh misunderstanding! Makes things more difficult!) One is turned over, then the players have their round, then another card is turned... should there be no cards left, the game is done. So no direct attack on investigators, it's a battle of attrition. As mentioned before, three Terror need to be rolled... for EVERY active doom token, meaning ten times.

Four players times five turns is twenty chances. So there needs to be a fifty percent success rate.

Two turns in; of the eight player attempts, five successes. In part by using spell cards to hold dice, clues to re-roll, and Jim's ability to park a die once per turn - even on success. This means 3 turns left (12 attempts) to get 7 hits, with fewer tricks available. Three turns in, still 5 success are needed.

I am the Terror that flaps in the... wait.
Rita declares her last spell card, and manages to park two Terror dice. When play moves on, Carolyn rolls a third. Down to 4. Jim just flat out rolls three Terror on six dice. BANG, down to 3. Wilson also manages to score three terror on a sequence of rolls. Four turns in - last set. Two more successes are needed.

It's pointed out that while the yellow die has no terror, it can be brought in to create an extra roll (discarding the yellow die upon failure). With this in mind and her rolls, Rita manages to pull off three Terror. Bringing us to Carolyn - who mops up by using her last clue to reroll non-terror dice! BANG. Ten success out of 18 roll attempts - with 2 to spare. Every player nailed their roll during each of their final attempts. The Ancient One is dead, ultimately defeated by the once cursed psychologist. You're welcome?

As I said in the beginning... this game features an unexpected ending.

Thursday, 19 December 2013

AMV Friday Roundup I

It was the last Friday of September. We will not say I was bored, because I'm a teacher, there's always something I'm supposed to be doing; let's go with I needed a break. Since I never have time to watch anime these days, except whatever the club is watching Friday at lunch, thus was born...


After watching a few Anime Music Videos (AMVs), I tossed my favourite one out on Twitter and Facebook, asking if people would like this to be a thing. I got about as much response as I do for my web serial (meaning hardly anything), and figured what the heck. So for the last three months or so, every Friday, I've posted a new AMV on Twitter. With the fourth update, I instituted the hashtag #AMVFriday. (Granted, someone named Rachel Nabors had already used that tag back in May, but just the once.)

Below is a roundup of the first twelve AMVs. Those selections were not completely random though! Thus I present the (never before seen) qualifications I have:

A) Posted by Creator. The channel should involve the person who made the AMV. First, because I strongly believe in giving credit to the originator of an idea. In fact, even if the comments area says "This is a great video by xxx, check out his/her website" (and by the way, the AMV culture is pretty good about giving credit) - not enough for me. Because, second, I want to be sure that the creator is fine with it being streamed. There's a lot of AMVs on (check it out!) which may not have been intended to be posted elsewhere.

B) Few subtitles. This is just a personal preference. I find the subtitling detracts, because my mind automatically tries to read it (comes from years of anime watching) - which pulls me out of the experience. I understand that maybe the AMV creator had no alternative, but including a shot with subtitles only works for me if the dialogue complements the music or what's going on, which is rare. Will I still watch? Of course. Will it make AMVFriday? Unlikely.

Let me try to hook you up...
C) Low View Count.  I didn't really start with this qualification. I knew I didn't want to post something from a 'BestAMVs' channel, I wanted to be less mainstream, but I didn't pay much attention to "Views". Until the end of October, when I was feeling down, and it occurred to me that my prior AMVFriday had already garnered over 100,000 views before my plug. They didn't need me to bring them traffic. I wanted to highlight someone who hadn't been quite as fortunate. So, since Fri Nov 1st, I've been keeping the view count in mind.

D) Single Song or Single Anime. Again a personal preference. If you're going to be cutting together a few different songs, stick with one anime. Similarly, if you want to combine a bunch of anime together, do it to a single tune. Let's not make the world any more Attention Deficit Disorder than it needs to be.

E) Not a Slideshow. In my searching, I've discovered that playing music and tossing down a new slide every five seconds seems to be a thing. To me, that's not an AMV. It's not that you have to have animation (very good AMVs have been made using manga pages), but a haphazard sequence of still shots is not good enough to clear my bar.

And that's pretty much it! How does it all happen? I take between 30 and 60 minutes to search 'AMV' and an anime (or song) that's on my mind. Watch some results, and suggested links off those. Eventually post my top one. But at this point? I'll take requests too!

You read that correctly: If you think there's an Anime Music Video out there that fits my qualifications, and is worthy of a plug, let me know. You can either comment below, send me an email, or @mathtans me on Twitter. Will it improve your hit count? Probably not, I'm rarely seen, often forgettable. But you will get at least one additional view!


1) Marmalade Boy. Song: Kiss the Girl. "Kiss Miki"
Channel: Celia SMV
Views when found (approx): 29,200 (Sep 27/13)

2) Magical Lyrical Nanoha. Song: Crush. "Nightmare AMV"
Channel: xValkyrieAngelx
Views when found (approx): 45,300 (Oct 4/13)

3) Karin ("Chibi Vampire"). Song: Part Of Me (Katy Perry).
Channel: SmilesR4All
Views when found (approx): 32,900 (Oct 11/13)

4) Tokyo Mew Mew. Song: Genie In A Bottle (Christina Aguilera).
Channel: AliceIkuta
Views when found (approx): 3,500 (Oct 18/13)

5) Fairy Tail. Song: "This Little Girl" (Cady Groves)
Channel: NaviProductions
Views when found (approx): 285,000 (Oct 25/13)

6) Read Or Die. Song: The End (Groove Coverage).
Channel: Faith (Kawaii Productions)
Views when found (approx): 1,800 (Nov 1/13)

7) Fushigi Yugi. Song: "At The Beginning" (Donna Lewis/Richard Marx)
Channel: JessieChaos
Views when found (approx): 2,000 (Nov 8/13)

8) Initial D. Song: Give it All (Rise Against)
Channel: Sztyanime
Views when found (approx): 2,165 (Nov 15/13)

9) Gatekeepers 21. Song: "Open the Gate" (No Doubt)
Channel: Vernon Jettlund (A Studio-Pink Prod)
Views when found (approx): 845 (Nov 22/13)

10) Bubblegum Crisis. Song: Self Control (Infernal)
Channel: VanVarnel
Views when found (approx): 605 (Nov 29/13)

11) Martian Successor Nadesico. Song: She's the One (Robbie Williams)
Channel: JordanWulff
Views when found: 92 (Dec 6/13)

12) Various! Song: Summer Sunshine (The Corrs)
Channel: xxxShanaxxxx
Views when found: 429 (Dec 13/13)

If you want to read the little blurbs I posted with each AMV, search #AMVFriday. If you want to comment, do so below!

Monday, 16 December 2013

TCH: Talking MTBoS Is Hard

Pic by Errol of Debs and Errol
Intro: Back in September, I signed up for "Explore MTBoS", an eight week event connecting math educators online. This is the eighth post connected to that event. If this is your first time on my blog, welcome! For the record, I post about writing in addition to math teaching. I also have a second blog, "Taylor's Polynomials", a story about personified math. Find it here:

This final mission came from Sam Shah (@samjshah). It asked us to share something we found out through the missions with someone else.

You know what? I sensed it would be something like that. Yet this is not merely something outside my comfort zone, it's out of synch with my personality. I'm posting now (three weeks later) because I hate to think I gave up in Week 7... plus I wonder if anyone else out there thinks like me.


Here's the short explanation for why this mission felt beyond me: It involves me telling people that I know better.

Please keep reading through the longer explanation.

There's a club for everything these days.

Let me start with what I'm NOT saying:
1) I'm NOT saying that "telling people I know better" was the intent of the mission. If anything, the intent was the exact opposite - it's right in the title! This mission was to reach out, to offer new ideas, to tell people that there was a place online where they could go for support, possibly even for new friendships. To share as equals, not to preach from on high.

2) I'm NOT saying that this was a bad mission. Again, I even sensed it would be something like this. If you've just seen a great movie, don't you want to tell others about it, and encourage them to go? If you're part of a wonderful community, don't you want others to join in, particularly ones whose opinions you value and respect? The motivation here is sound. The goal is noble.

3) I'm NOT saying that the MTBoS (Math Twitter BlogOSphere) is itself any sort of high authority. It's a group of wonderful people with thoughts on mathematics education. One may even aspire to be like some of those individuals. It is NOT a group spouting the godspell which others need to follow, and if my post causes you to see the MTBoS that way, I'm painting an unclear picture.

With that said, here's what I AM saying.


I've posted before about my introvert tendencies. I don't usually initiate conversations without cause. The reason may be anything from "I need help" to "How was your day" to "We could both use a laugh". That said, if I'm bringing up things from the MTBoS in conversation, there must be a point to it. After all, if someone randomly told ME about it, I'd be wondering why. And not all of my thoughts would be positive.

You: "There's this community of educators online."
Me: (I'm aware, I would have joined if I'd wanted to, are you blind?)
Me: (I wasn't aware, but I'm going insane here, how can I possibly make the time for something else, shoot me now.)

You: "I saw this lesson and think you might like it."
Me: (I have no idea how to pull this activity off and who are you to tell me this is better, if it is I hate you because you're better than me.)
Me: (I wish I had time to find things like this, I'm so envious, I hate my life, I'm doing everything wrong.)

You: "There's this great blog you might enjoy."
Me: (It's great but I don't have time for it, why do you taunt me, and why is everyone so much cooler than me, sob.)
Me: (It's not great at all, why don't you understand what makes me tick, you're hopeless, I'm never talking to you again.)

I'm exaggerating for dramatic effect. But here's a personality consideration: when you're on the OUTSIDE of a community, and someone keeps talking to you about it, which of the following are you more inclined to say? "Bring me along next time" or "If you like them so much, why not go talk to them instead of bothering me"?

I feel like it's MORE difficult to talk to someone externally than internally, which seemed to be required here. Am I the only one with that problem?


A lot of the things I see online, I couldn't hope to pull off. (At least not at my current ability level.) So if someone came to me saying "try this 3-act in your class!" my knee jerk reaction would be "why must you add so much more stress to my life?!" I do not think like you. I know where my strengths are, and while I may be working on my weaknesses, jumping into the deep end is not the way I deal with them.

In other words, in my world, I'll approach YOU, not the other way around. In the end, if the lesson screws up, I only want to have MYSELF to blame, not to have you as a scapegoat. I want to be thinking "This went badly, what did I do wrong", not "Stupid Mario, it's all his fault for saying this would work in my class". Because if the roles were reversed... can you say that NO part of you would be thinking "that stupid Greg, bringing me this lesson"?

So I guess this mission doesn't feel like a random act of kindness so much as a targeted act of kindness, and I'm not good at targeting.

Meaning that, while I'm self aware, I am not good at judging the strengths and weaknesses of others. Of course, if you're one of those people who can look at a task and go "Justin would be able to do GREAT things with this!", kudos to you. But I think that even if I DID have a sense, I am not confident enough to say "here's something!" to someone - unless, again, a request is directly made of me.

Yes, I'm absolving myself of responsibility. But that's because, frankly, I don't feel like I'm enough of an expert to be diagnosing in the first place... therefore you'd have every right to use me as a scapegoat.


Consider that one student (or group of students) in your class who are spoiling the learning for everyone else. If you got rid of them, then not only would the whole class be easier to control, the other students would probably feel a sense of relief as well. I... am not able to kick them out. Not yet. Maybe they go in the hall. Maybe not even that.

Yes, I'm saying I would rather run around and try to teach 19 students individually, than to kick out student number 20 and talk to the 19 students as a whole. I am the authority figure in the room with a bunch of teenagers, and yet I hesitate to exert maximum power. Now, do you think this is going to be any better with a bunch of educators?

Don't get me wrong, I see the big picture. Would everyone be better off if I took action? Probably. Logically, should I do/say something? Probably. Emotionally, am I there? Hell no. Because I don't know your story. Because maybe there's emotional or spiritual reasons for your hesitation that I'll trigger, because maybe there's things happening at your home and my speaking up will make you think I don't care, or that I only care about your work life, or perhaps my attempt to help will only make things worse for you, and I - can't - deal - with - doing - that - to - you.

I don't deny that sometimes, we simply have to dish it out. The same way this mission was asking me to dish it out. But I can't. Because even if this dish is a decadent chocolate layer cake, maybe I'm being insensitive to your gluten allergy that I should have known about if not for my inability to see what's apparently bleeding obvious to everyone else.

Of course, this is coming from someone who has delivered Professional Development before. So perhaps the problem is that I'm not as passionate about the MTBoS as I am about Music or Personification. Making me think, was passion a requirement to be able to fulfill this mission?


To finish up, let me rephrase. My problem isn't so much that Mission 8 involved "telling people that I know better". It's more that it involved telling people "I know something you don't", which automatically elevates me to a position of authority I don't want, in a conversation I'd rather not have, over values that I may not even share. ... Of course, I do tend to overanalyze things.

This just feels too unnatural.

But nothing's impossible. Twitter did happen to come up in conversation with someone on our Mathematics Council, at an informal holiday dinner. I mentioned the MTBoS, because it fit neatly into an already ongoing conversation, and thus there was less chance of me being seen as making any kind of judgmental observation.

Does that count? I suppose I have the authority to say that counts, the same way I tweaked things to complete Mission 3. So let's say it does.

That will put to rest what was, for me, the absolute hardest of the eight missions... even though for many of you, I imagine it was all too easy.

Sunday, 1 December 2013

MAT: Estimation Isn't Math

At a professional development session Saturday, keynote speaker Marion Small (@marian_small) remarked that she had a "new rant" of sorts: Most of the calculations we do are a waste of time. We should be doing estimating.

Then, in the secondary breakout session, Robin McAteer (@robintg) and Anne Holness asked what we value in our mathematics classes. One of my items was PRECISION, and I think I was the only person to list that.

So, yes. I already know it's me against the world with this post. Still, maybe you can stick around for my four point case for why ESTIMATION ISN'T MATH.

My reality involves precise calculations


Part of the reason I like math so much (and value precision) is the nature of numbers. Draw an isosceles right triangle. Measure the hypotenuse. Surprise - you CAN'T! No matter how hard you try, you will always be able to go another decimal place, you will always be able to get a result that is more precise... UNLESS you invoke mathematical notation. Unless you use root(2).

From the "Matching Fraction" song parody

Think about that. You have drawn a finite length that is NOT MEASURABLE. This is awesome. Mind blowing, even.

The counterpoint, of course, is something Marion Small herself mentioned. Define a number line, and where is 10? We find it - but wait. Did you use a ruler? Couldn't it be a millimetre to the right? Doesn't your pencil mark have a thickness that "10" doesn't really have? We're estimating where 10 is. We're estimating all the time. So that hypotenuse probably isn't really a length of root(2). How could it be?

Irrelevant, I say! ESTIMATING IS NOT MATH. Estimating is the HUMAN REPRESENTATION of math. Which certainly has it's uses. But why can't we appreciate the theoretical beauty of numbers? Simply because "you'll never use it in real life"?

The math curriculum seems to be swinging the pendulum over to the point where everything has to connect to students' daily existence. I don't know whether that's because teaching is now more student centred (and they're demanding "when will I ever use this"), whether it's due to the stigma math is getting in the public that is forcing math to "always be relevant", whether it's a prioritizing issue on the volume of mathematical material that now exists, or whether it's something else.

Question: When was the last time you estimated something as root(2)?


So, you're given a problem, and you estimate the answer. Now what? Well, naturally, you want to know if you were right. You need the EXACT answer, and so you invoke MATH to figure that out. When was the last time you went into a store, looked at your cart at checkout, said "I think this will cost about $30. So here's $30. Bye!" That only happens if you're on the barter system.

Without an exact value to compare against, we have no idea what makes one person's estimate any more, less, or equally valid than another person's estimate. Now, am I saying don't estimate? Heck no! Estimation is an important step! Am I then saying you're never using math AS you estimate? No! What I AM saying is that a PRECISE answer requires the mathematics - the estimate does not.

The problem here is that people aren't very good at this estimating skill. This estimating skill... which generally involves numbers. So, hey, numbers - it's math! Right? "Sure it is," cries the public. And so they demand, "Study more estimation in math! Estimation is the goal! Who cares about that root(2) nonsense, 1.41 is good enough for an engineer!" And that makes me sad.


I mentioned this before, after taking the Triangleman Decimal Institute Course - decimals belong in science, not math. They are a product of scientific calculators. They imply some number of significant digits - just like estimation. I claim that this is science because math has the potential for an INFINITE NUMBER of significant digits! A potential that lately seems woefully untapped.

At our PD Day earlier this month, teacher Andrew Cumberland asked whether 1 = 1.00000; I would say of course that's true. So is 1.0 m = 1.00000 m? I would say of course not. There's measurement involved in the second example, and thus an element of extra precision. On the right side, we can now carry more decimals around for our science calculations. (Another teacher posed whether 'm' is actually a variable - a discussion for another post.)

Scaling is important.

Here's the thing. At it's core, math has AS MUCH PRECISION AS WE WANT. Fractions. Ratios and proportions. Root(2). Meanwhile, estimates trend towards rounding off, towards using some number of decimals or significant digits, and - forgive me - that nonsense isn't mathematics. It's science. It's VALUABLE science, and it's a tool for VERIFYING mathematics, but it's NOT the infinite precision OF mathematics.

Granted, there are cases where we must sacrifice precision. If you solve a proportion and get an answer of "buy 13.458 apples", we likely need to round that off to 14. But that's not estimation. That's discrete math. Which brings me to my last point.


I know what you're thinking. If estimation isn't mathematics, but statistics uses estimation, is he saying statistics isn't really mathematics? No.

Let's first talk statistics. It's randomness, sampling, and making predictions - based on scientific data. Thus it is inherently flawed, because you can only be as precise as your instruments are calibrated, and only as accurate as your survey allows. This is why you can analyze down to an almost sure thing, only to have the unexpected occur. In fact, in it's own way, statistics has as much mind blowing power as the concept of drawing a length of root(2).

An I-Q-R is not bizarre,
If you know medians... you know medians!
But while the data is flawed, the mathematics is sound. So yes, statistics is mathematics.

When you read in an article that "this survey is accurate plus or minus 3 percent, 19 times out of 20"... there's CALCULATIONS that went into that. Margin of error. Degrees of freedom. And while the statistics may only be generating a "best guess" prediction, this is NOT the same thing as being in your grocery store saying "I think this will cost about $30." (Or in my experience, they're not taught the same way.)

So here's the caveat: Estimating is not math, so long as you can look up the answer and see "oh, I was 0.5 off". Estimating is ONLY mathematical if you are comparing against an UNKNOWN quantity, using calculations to determine HOW PRECISE your estimate is. (Again with the precision!)

Now, does hiding the answer from your students (or yourself) make it unknown? Does that now make estimating it a mathematical process? Perhaps it's the theoretical mathematician in me, but I'd say no. Not unless you are mathematically analyzing your estimate without EVER knowing that "true" answer.


In case I haven't been clear, here is what I am NOT saying:

Perhaps you've misinterpreted...
- I am NOT saying that estimation doesn't INVOLVE math. You may do math as you estimate, the same way you may fiddle with html tags when you assemble a blog post. Doing so may even help you to understand what's really going on. But it's NOT math, in the same way blogging doesn't make you an HTML coder.

- I am NOT saying that we shouldn't estimate in math class. We do word problems in math even though we don't teach English, and in Geography class they look at graphs. Crossing curriculums is good. Just because estimating is not math, that doesn't mean it isn't handy.

- I am NOT saying we should teach infinite precision in the younger grades. A certain amount of precision is sufficient for understanding daily life. That said, we should call rounding out for what it really is - science - and there should come a point in high school when we nix the decimals, in favour of fractions and ratios.

- I am NOT saying that we should nix the real world applications. Applied mathematics is as valid as pure math, and rounding off is tied into that. But at the same time, not EVERY exploration has to be a hands-on relevant experience, does it? Because that's all I'm seeing. (If math is moving to only hands-on... I'm screwed.)

So that's what I'm NOT saying. What I AM saying is... well, ESTIMATION ISN'T MATH. It's humans attempting to represent math, imperfectly. You're welcome to argue with me in the comments.

Wednesday, 20 November 2013

TCH: Stretched, Taught

Pic by Errol of Debs and Errol
Intro: Back in September, I signed up for "Explore MTBoS", an eight week event connecting math educators online. This is the seventh post connected to that event. If this is your first time on my blog, welcome! For the record, I post about writing in addition to math teaching. I also have a second blog, "Taylor's Polynomials", a story about personified math. Find it here:

This week's mission came from Tina Cardone (@crstn85). It asked us to participate in "Day in the Life of an Educator", similar to what happened last year (archives here). Called it.


WARNING: As a writer, this is completely up my alley. Last year, I did "Day in the Life" every day for a full week, each in a different narrative perspective. (Check out the wrapup here.) This year, for whatever reason, I'm much more stressed out - so you're getting one LONG post rather than... well, a bunch of long posts.

Incidentally, being a teacher is why I cannot do NaNoWriMo.

If any teacher CAN, I applaud them. Don't know where they find the time. Of course, NaNoWriMo isn't my style anyway, and this day is a BIT more action packed than the norm. On a scale of 1 to 10, where 1 is clear sailing, 10 is high stress, and 5 is typical, I'd rate this day a 7. (aka "Stretched Taut") If you think it's relevant, I'm basing that on teaching for over five years, but less than ten.

Catch the pun there?
Oh, and I'm going to have Dr. Elizabeth Weierstrass (from my web serial) tag along for the ride. But since I'll be in third person, and her comments will be interjected continuously, I doubt you'll be able to differentiate Weierstrass at any point.


12am: He's still awake. He wants to finish this one piece of marking. Then he answers an email. He's in bed before 12:30, but with thoughts running through his head, so it takes a half hour to fall asleep.

6:45am: The tradition of waking up before the alarm on a "Day in the Life" day continues from last year. This is a stupid tradition. His body needs to get with the program.

7:00: Alarm goes off. He's out of bed and into the shower within five minutes.

7:20: He's at the computer, with a bowl of cereal. Tweets out the latest episode of "Taylor's Polynomials" - it auto-published at 7am. (Find it here - race is suddenly a factor!)

7:50: Leaving home. A little bit earlier than normal, for two reasons: He was away Tuesday, so wants to allow time to catch up, and he wants to drop off his shirts.

8:00: CBC News on the radio. Mention it because they talk about the Federal Government's bill against Cyber Bullying, and this happens to be Bullying Prevention Week in Ontario. (There's a talk on Thursday. He doubts he'll have time to attend.)

8:10: He's at the shirt place. Seems they've changed their hours in the last month or so, don't open until 8:30am. Close at 7pm. What are the chances of getting back before 7pm? (Hint: He almost never drops off the shirts early, so the fact he was trying....)

8:15: At school. He starts by catching up on the missing day; all seems in order. Falls into the rabbit hole of email for a bit. Ensures first period is okay to go. Copies some files off his laptop that he'll want over next 24 hrs.

Having first period Prep SUCKS. Especially on Wednesdays and Fridays. He spends the first five minutes watching the student announcements; one of his last period students is a co-anchor. Today they're spoofing "Big Bang Theory"; student remarks that those writing the Math Contest tomorrow should give Mr. Taylor 1,000 pennies, or ten dollars. Har har. (It's funny because Canada doesn't use pennies anymore, y'see.)

8:45: Notices that courses on the board since Sept 6th have been erased, likely by substitute teacher. Thrown off stride. Recreates. Then he needs to create a quiz for MAP 4C this afternoon. Slams something together based on previous one, with an eye to the test he still needs to generate for Friday. He's normally got those ready a day in advance, so he's even more out of sorts.

Doesn't sound so great on the outside.
9:05: He heads to the office to pick up mailbox items and photocopy items for the day. He's lucky - last time, the photocopier jammed and led to a 20 minute struggle that made him late for his duty. Speaking of...

9:15-9:55: Library Duty. The librarian gets a prep period just like any other teacher, so teachers have duty slots to keep the library open on those periods. Can't complain about this duty - can actually mark sometimes, unlike lunch duty.

There's also a presentation going on here for a class (about depression), so less need to wander the library. He sifts through his mailbox items. Finds a guidance slip for a student -- from yesterday. Sub didn't check the mailbox. Fair enough, but now need to drop by the office again. Manages to do a bit of marking, as well as scan the Serial currently running in the Metro newspaper.

9:53: Librarian lets him go a bit early. Hurries to guidance to explain the missed appointment, to office to check on if can hand out report cards, runs into student in hall who was sick last week and is wondering about missed assignment. He talks to the student and is still on time for...

Two people still need to write a test from last Thursday. Neither are present. (One arrives late, and should write tomorrow.) A number of students still need to give in their summative topics! He gives a handout, then makes the rounds. At end of period, still not everyone has their topic, which was due Monday.

10:35: At this point, he remembers the schoolwide fundraiser about Typhoon Haiyan, which affects this period in the rotation. Reminds students. Then instructs about Correlation Coefficient and r^2 measures, based off handout.

11:15: Class ends, two students donate to Typhoon relief on the way out.

11:15-12:05 LUNCH: MATH CLUB
Wednesday is math club day. With tomorrow being the Waterloo Math Contest, our blogging teacher goes to make a schoolwide announcement. Despite that, only person to come is one of the two actual club members. (Small club.) Students gets a puzzle to work on, as teacher remembers he still has to reassemble slides for period right after lunch - 3U is being taught in a different order from last year (experiment that he should really blog about...).

11:30: A couple more students arrive.

11:40: Afternoon is set, but now students have some questions about last year's math contest - and money to pay. He deals with those aspects, can't remember everything about one of the questions on the fly, checks on the internet.

When in doubt, check the internet.
11:55: Students heading out, teacher decides food might be an option before lunch ends. He apologizes to the math club member for getting totally distracted. Response is "it's fine, having lunch in this room is relaxing".

11:56-12:01pm: Lunch (5 min)

12:01: Head back to office to photocopy a sheet that had been forgotten.

12:08: In class, students show a calculator spelling out something... slips his mind at this point, y0l0 ("yolo") was involved.

12:10-1:25: PERIOD 3: GR 11 FUNCTIONS
Happens to be the intro day of "TrigGate r=1", the most popular post by far on this blog. (Now over 400 views!) He's doing it earlier than usual this year though, and trying to integrate it into previous day, despite not being there previous day. And before that...

12:12: Student reminds him that she needs to write a test from two weeks ago when she was out with surgery. Realization the test variation (since that test was returned) hasn't been printed off. Go to print that from prep room. Get student set up to write in hall.

12:15: Start working through material, but student borrowed teacher textbook last week. We never got it back. Not sure where it is. Run to the book room to get one temporarily. Field trig questions from previous day, then into the unit circle.

Ultimately make Trig connections which seem to resonate with a number of them, hopefully everyone's on board by tomorrow. Only five minutes in the end to try questions. He's not pleased with how this went on his part, but supposes it could be worse.

1:30-2:45: PERIOD 4: GR 12 COLLEGE MATH
Seventeen of eighteen students are here. No, no, you don't understand. Don't think there's been more than 15 students present at once since mid-October. Not a slam on this class either - the last time there was perfect attendance for ANY class was likely over a month ago. This is going to be a bit hectic. Oh, and no textbook for this course... we're running two sections, and only have enough texts for one section.

Everyone in the room is on task, right?
Hit the highlights of yesterday's work for those who were away. Then a quiz, before the test on Friday. Unit is regressions, and identifying linear v. quadratic v. exponential models. They're still kind of freaking out about this. Some get to work, others he has to encourage. One girl's working on science but assures she'll do math before end of period. (She does.) Why do they still put the FIRST table column on the VERTICAL axis? This has NEVER been a thing!!

Oh! And there's a cake auction now on Friday for this period. Football team won locally and is going to OFSSA in Toronto, but that costs money. SO. In light of this auction now coinciding with the test, and losing tomorrow's period to an assembly, and student concerns, teacher is convinced to change test to Monday. Will find more regressions to do Friday, maybe. Whee.

2:45: Period ends. Time to enter attendance.

2:50: More math students come wondering about the contest tomorrow. @MathFitton comes by and helps field some questions, which is good.

3pm: First chance to visit washroom since 7am that morning.

3:10: He leaves students in class talking math, changes for Yoga session. (It's in the school, meant to help with stress relief. Not free.) Finds $20 in pocket (from lunch), puts it with rest of math contest money.

3:15: Drop by office to leave report card for absent student. He runs into fellow teacher organizing a trip for them, agreement they really need to talk about Edinburgh issues. Where to find the time.

3:17: First chance to drink anything all day, at water fountain. (There was milk in the morning cereal.)

3:20: Arrive at 3:15pm Yoga session, already underway. Not the last to arrive, a fifth person comes in a bit later.

 Ordinary Day, by Great Big Sea

Wait, shavasana is supposed to be done on the back...

4:15: Yoga session ends. It's taking place in the same room as the Math Contest next morning, so he starts to set up the room. Others assist, which is great, goes faster.

4:25: Change, head back downstairs.

4:35: Back in classroom; students are gone, piles of paper need to be sorted. Hey, screw that.

4:37: Back in prep room. Finish lunch while listening to @MathFitton and @JPBrichta talking about the PD session from the other day. (Something else that needs to be blogged about.) Difference between ACCURACY and PRECISION is brought up -- level marking is Accurate, but not necessarily Precise to a percent.

5:00: He shows a video to @JPBrichta. Takes the opportunity to tweet out about his web serial again. Also discovers he's still signed into the prep room computer from printing the test at 12:15 earlier. Derp. Is signed out.

5:05: Discussion about issues with simple interest and compound interest in @JPBrichta's class. This helps to put things into perspective for the day.

5:20: Enough stalling. He's back to the classroom. Organize piles of paper. Clean out desks (someones left candy bag, handouts). Discover calculator is missing... recall lending it to someone. They'd better return it. He then uploads lessons of the day to course website. Also updates website, and plans topics to end of current unit.

6:15: Back to office to do photocopying for next few days - student is away next week, needs materials early.

6:30: Principal pops head into photocopy room to say goodbye. Scares the daylights out of our overly focussed teacher. Brief conversation. ("Long day?" "Maybe slightly." aka 7 on scale of 1-10.)

Heads you win, tails I lose...
6:35: Back to classroom. Need to do so much more marking, SO behind it's NOT even funny.

7:10: Email break. Discover pep rally will be next week. Plans of one hour ago now already obsolete. Will need to tweak going forwards to accommodate. Also, United Way drive wrapping up soon.

7:15: Back to prep room to search for United Way form. Chat with @JPBrichta again about Level 4 exponentials question.

7:40: Phone wife. She's on her way home. Suggest just picking up food tonight, she's in agreement.

7:45: Back to classroom to do a bit more marking. Decide will call it before 8pm.

7:58: Check school voicemail on communal phone for first time since last Thursday, due to long weekend and being away. No messages. (Wise people do not rely on voicemail to reach teachers.)

8:00pm: Pause on the way out to chat with custodian. Topics range from the unpaid workday on Dec 20, to VLAP, to tow trucks that were clearing the parking lot early this morning.

8:10: Actually drive out of school parking lot, just shy of 12 hours after arrival. Actual work time, were this being recorded: About 10.5 hours.

Yes, I did plan to be leaving work around this time.
Granted, I had hoped to have accomplished more.

8:15: Stop in at Wendy's for Mushroom Melt. Former student asks if I recognize her! Says I taught her Grade 9 and 11 -- I *do* know she looks familiar, I'm lousy with names. I go with Kira, which is right! But I've likely spelled it wrong.

8:25: Orleans Traffic Circle. (Only hit it going home these days.) Wanted to stop by the bank, that didn't happen. Obviously didn't get my shirts, may never see them again.

8:40: Arrive at home. Brief chat with wife. Start working on this blog over dinner.

11:00pm: Finish blog. Start watching Jon Stewart while editing and getting images for this post. Multitasking slows things down.

Final post at 11:50pm. Final note about NaNoWriMo: This post is about 2,400 words, so more than 1,670 per day, but doing this every day would probably kill me. Didn't get to finishing task corrections as it is. I just hope the math contest goes well tomorrow. Oh, and me and Weier hope you enjoyed this slice of non-fiction! Feel free to comment below on whether you would rate this day a '7' or not.