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.


STEP ONE: WRITE


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.


STEP TWO: EDITS


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.


STEP THREE: DRAWING


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.


STEP FOUR: POSTING


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.


IN SUMMARY


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


ELDER SIGN
UNSEEN FORCES EXPANSION

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.

ENDGAME:
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...

AMV FRIDAY


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 www.animemusicvideos.org (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!

AMV FRIDAY ROUNDUP: 1-12


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).
http://www.youtube.com/watch?v=Xu27rAKf-BM
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)
http://www.youtube.com/watch?v=YOfSdThCfKY
Channel: JessieChaos
Views when found (approx): 2,000 (Nov 8/13)

8) Initial D. Song: Give it All (Rise Against)
http://www.youtube.com/watch?v=gFPsAagnM3o
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)
http://www.youtube.com/watch?v=YfGFeTRvf8o
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: http://mathtans.ca

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.


WEEK 8: SHARING IS CARING


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.


TALKING IS A PROBLEM



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?


SUBJECTIVENESS IS A 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.


AUTHORITY IS A PROBLEM



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?


IN CLOSING


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


POINT 1: MATH IS PRECISE


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)?


POINT 2: ESTIMATION ISN'T ENOUGH


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.


POINT 3: ROUNDING BELONGS IN SCIENCE


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.


POINT 4: STATISTICS REQUIRES ESTIMATES


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.


FINAL CAVEATS


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.