Wednesday, 30 September 2015

TANDQ 05: The Education Game

In 2014-2015 I wrote an education column called "There Are No Dumb Questions" for the website "MuseHack". As that site has evolved, I have decided to republish those columns here (updating the index page as I go) every Wednesday. This fifth column originally appeared on Thursday, July 31, 2014.

How is teaching like a role-play game?

The students are the characters, the teacher is the GM (game master)… and everyone who’s ever participated in a session thinks they’re justified in telling a GM how to do their job. Whether you agree with that sentiment or not, let’s at least explore the analogy a little more.

First, put yourself in the role of a teacher/GM.  (I choose GM rather than “Dungeon Master” for obvious reasons.)  Your classroom is a gaming session, your term a full campaign.  You’ll have up to 30 participants at once (because supposedly class size doesn’t matter), several times over a day.  Some of them mages, some bards, some fighters - some chaotic, some lawful - some elves, some dwarves - all different skill sets, but regardless, ALL of them will be exploring a world (subject) where you are the expert. Together. No party member left behind. Then again, a few party members may be absent today, but they’ll catch up by tomorrow, right? Right.

Now, after everyone’s met each other, your first job as GM is to make sure the party overcomes inertia, so they’re not sitting around in the Inn all day. Experiencing things is key. You need to provide a hook to explore the world. Or ideally, the students/players will provide the hook, and you can craft the adventure around their interests! Then, despite all your careful plans, the majority of people will be keen on investigating the forest, rather than going to the temple. So you’ll have to adapt. Or split the party - no problem doing that, right? You then present the class with your first challenge. Take care that it isn’t too formidable, at least not too soon, because throwing a lich (eg. complex numbers) at the party before they’re ready for one is liable to result in a TPK (total party kill). That would turn every member off of that subject/setting for the foreseeable future. You don’t want that!

Got that? Great, just continue, day in and day out, making sure everyone in the campaign has a chance to be successful. (I’ve actually blogged about this before over on my personal blog.) Now, here’s where the analogy gets painful for me.

System Malfunction

Almost everyone has been in a classroom. Yet I claim you can’t know what it’s like to be a teacher by being a student, any more than you can know what it’s like to be the Game Master by participating in a bunch of gaming sessions. Even adults who do later research into teaching, and then observe a number of classes to move beyond their own childhood experience, may not be able to prevent their own biases from creeping in.

EdGuru: “Mr. GM, I notice your wizards aren’t being successful. I believe it’s because they’re not casting any ‘Ray of Frost’. That’s an easy cantrip which they should all know by now.”
GM: “Actually, that ray is now a fully ranked spell, so what we do to —”
EdGuru: “The heck?! That makes NO sense! We must change the system back!”

(Teaching translation: EdGuru says “I notice your math students aren’t being successful because they haven’t memorized their times tables. Like I did. We must change the system back to memorization of times tables!”)

Now, I can deal with people thinking they know my job. Sort of. Not really. Anyway, what’s actually painful for me is the shift people are now making. Moving away from looking at the role-play (classroom) itself, and onto the underlying systems. Consider, if you want to play D&D Next instead of first edition - or even just play Shadowrun - surely we can still get along? We can acknowledge the strengths and weaknesses of the various RPG systems without trying to change each other’s opinions? Yet as soon as I say “common core”, people are eagerly awaiting my stance, so that I can be properly classified as one of THOSE teachers. (Thus I’m not taking a stance in this post, so there.)

The fact is, education (and role-play) should be about learning in a caring environment. Instead, it’s becoming about structure. And politics. If you’re not teaching under the rules of classic D&D, you’re a bad teacher! Or maybe a good one! How do we know? System testing! To finish the analogy, I now want you to picture a role-play system that gets evaluated by giving every player a standardized test after a campaign. That test is then used to classify the player, and evaluate the effectiveness of each GM. (Your mage can’t shoot a bow? Science fail! What have you been teaching these people?!) I ask you, is this what we want?

Okay, maybe that’s not how we’re currently evaluating education - though I worry it is a possibility.  I do think that people need to take a step back.  Start asking questions of themselves, rather than making demands of others. (Remember, there are are no dumb questions!)  Rifts are forming, even within the education community itself, and the media certainly isn’t helping.  We’ve moved from demonizing D&D for it's influence on our youth (a couple decades back) to demonizing the education systems.  And while everyone is (presumably) trying to do what’s right, I wonder - is it instead that people are trying to BE right?

I’ll end with full disclosure: I’ve done a lot of gaming, but I’ve never run my own campaign. I think it would be really hard.

For further viewing:

1. Teaching Isn’t Rocket Science. It’s Harder.

2. 12 Nutty Dungeons & Dragons Media Mentions from the 1980s

3. John Hunter uses an RPG to teach World Issues (TED video)

Got an idea or a question for a future TANDQ column? Let me know in the comments, or through email!

Sunday, 27 September 2015

A Math Writing Journey

If you’re going to put something out on the internet, be it a serial story, videos you scripted, an opinion column, whatever, you should know the reason you’re doing it. Is it to educate? To entertain? To make people think? Some combination of those? (If it’s to be famous, um, sure, good luck with that.)

For me, I am pretty sure my intention is to entertain, even though it trends to the combination. Heck, I have blogged about that fact before. That said, this post may not be so entertaining - it’s going to look at a writing journey from joy, down to misery, and back up to what I am currently calling a “Good Creative Place”. Featuring personified mathematics.

See, when you have a blog/website, you can totally do this sort of mental archive dive, because there’s a permanent record - the internet never forgets.


I wrote a lot in University. Mostly for mathNEWS, the student run publication out of the University of Waterloo. I had a non-fiction column, “Cynic’s Corner”, and I even published serials - “General l’Hopital” (the pun serial) and “Quantum Loop” (the Quantum Leap parody). For that matter, I drew covers too! I was “published” early, I guess is what I’m saying.

"Quantum Loop" had Sham Breakit & Hal Callalily
Outside of mathNEWS, there was fanfic, which I put online. In 2000, the year before graduating post-secondary, I won “Best Comedy” at the Anime North fan fiction contest (the second time I’d entered anything). That was followed by two years of not even placing in the finalists, a better 2003, and in 2004... I won the Grand Prize. Apparently, people thought I could write! Or at least write fanfic.

At the time, I said “six years later, I guess I’m a decent writer! Just takes practice.” That would be our high water mark. And then... the public writing petered out. I played around with making videos instead - I used to do mix tapes - and entered this short AMV into AC-Cubed 2006. But I was also trying to get a full time teaching job, and finish work on my (unreleased) time travel serial too.


“Taylor’s Polynomials”, personified mathematics, started July 2011. It updated twice per week, initially each part maybe 200 words. I thought it was pretty good, and it’s what sparked the song parodies (popular at my school). After SIX MONTHS of continuous updates - during a move, no less - I was getting five hits. Well, ten in a week, given the update schedule.

Disappointing, but not unexpected. So, the whole reason I started a blog, and joined Twitter, was to find a bigger audience for my math story. And I threw everything I had into Update #100, linking the plot back to my video work, with a theme tune, and entering it in MTT2K (Mystery Teacher Theatre 2000).

No one seemed to stick with me. This blog started shortly after, in August of 2012. We’ll now move to the 27 posts where I’ve mused on writing. You’re welcome to skip to the conclusion at the bottom.

1) If You Build It... So What? (Aug 2012)
In brief: If you’re looking for an audience, you’ve already lost. Everyone’s busy with something else. For the first time since starting (14 months ago), I have no buffer, thus am writing on the fly for... me, I guess.

2) The Pass in Passion (Oct 2012)
In brief: What if doing it for yourself is not enough? After 66 straight weeks, I’m only getting ten views per update (20 in a week). I’m taking a break. Any thoughts? *crickets*

3) Week as Math Educator Roundup (Nov 2012)
In brief: I wrote about a week of teaching, from the perspective of my math characters. With different narrative perspectives. Here’s some topics you can comment on? Maybe?

I would end up restarting the serial in January 2013, with a new buffer.


4) Drawing for a Webcomic (Jan 2013)
In brief: This is how I illustrate my mathematics, with screenshots. I need to improve; any tips? (This post was followed by another on how I mashed up song parodies.)

5) Writers Make Poor Teachers (Feb 2013)
In brief: I pay attention to detail. And I’m GOOD at that. So how the hell am I supposed to grade these tests on vague LEVELS, not POINTS? (I got some comments, but this was less about writing itself.)

6) Writing for Your Gender (Feb 2013)
In brief: Consider both a male and female lead in your story - is the less dynamic one the same gender as yourself? My females are more engaging, every time. Why? Is that me?

7) Seeking New Personifications (Mar 2013)
In brief: I’ve personified math for 20 months! Got any cool math relations I can use? Want a link shout-out? I don’t get much traffic, but I’ll do what I can! Thoughts?? *crickets*

8) Publicity Hows (Mar 2013)
In brief: Not strictly about writing, more a question of how do you get the word out on the internet? How do you stand out without seeming like a jerk?

9) The Web Serial (Mar 2013)
In brief: OMG I’M WRITING A *SERIAL*! I thought it was a weird text webcomic with math! It’s more than that! Let’s talk about serials (in 4 parts), and how it connects to teaching.

10) Why Do You Blog? (Mar 2013)
In brief: Who is my audience? Yeah, I still don’t know. I don’t think I’d even recommend this blog. But maybe you’ll say something to make me do better at this?

I’d posted a chapter of my Time Travel story in there as well. At this point, “Education Realist” became the first educator I knew on Twitter to actually comment on a writing post (previous writing post comments were by writers). There was a temporary blog redesign (of about 9 months) to try and “flag” the topics of my posts.


11) Mind The Gap (Apr 2013)
In brief: Report cards, school play AND my web serial buffer ran out. But here’s how I handled it without needing a posting hiatus! Here’s more ideas you might use!

12) Why I Write Series 5 (Jun 2013)
In brief: How can one personify mathematics and NOT have it become suicidal? Also, I think I’ve determined my audience is NOT students, or math teachers, or writers. I have low self esteem.


13) Being The Outlier (Jun 2013)
In brief: You’re in a group, and the awesomeness is happening around you, and somehow you’re not quite a part of it. This post is either profound or inane.

14) Draw Your Story (Jul 2013)
In brief: Are you a writer? Then you should be drawing. It helps for many reasons, here’s why.

15) Character Diversity Problem (Aug 2013)
In brief: This is a cry for help. I’m a white male, but my story is evolving, and I see a few options for diversifying my mathematical cast - what do you think? Anyone?

16) Writers Make Good Teachers (Aug 2013)
In brief: Counterpoint to the earlier post #4. Curriculum is writing, and there are crossover skills like observation, communication... perseverance...

17) Serial Rewrite Recap (Sep 2013)
In brief: The plot for Series 5 changed from the initial plans. I have recap videos. Here’s my preferences in the years I’ve done so far. Your thoughts? *crickets*

Yeah, this has only been a large part of my life for over two years, I can see how you might not want to chat with me about it... at least tell me why it’s not interesting? I want math to be a thiiiiing!


18) On Building an Audience (Nov 2013)
In brief: DEAR GOD, WHAT AM I DOING WRONG?! (That’s a direct quote.) I was here before Daily Desmos graphs, I did VERSINE before it got big, I want my story to be a fun math thing too, so WHY AM I INVISIBLE?

19) Putting My Serial Together (Dec 2013)
In brief: How I sink time and love and thought into this fiction writing thing that gets no comments. *crickets* (Is no comments irony?)

20) Writing at the Intersection (Jan 2014)
In brief: A regular schedule, original drawings, story arcs, they’re apparently useless - “fantasy” and “math” are DISJOINT SETS. What, AM I NOT INCENTIVE ENOUGH FOR YOU?

I cut my publishing here from twice every week down to once every week. (At a low estimate of 200 words per post, twice weekly, for around 120 weeks, we’re looking at over 24,000 words posted already. Twenty views per post a year ago, not even double that after weekly tweets/FBs.)

21) No Comments (Feb 2014)
In brief: Here are reasons people don’t comment on posts, now I feel better about why I seem to be invisible, except not really, whatever, who cares. (This post got comments!)

22) On Seeking Validation (Jun 2014)
In brief: Internal motivation can only get you so far. Ten years after winning a fanfiction contest, and three years after my lovely math serial began, it’s now OVER, and I stopped writing it ON MY BIRTHDAY, and YOU DON’T EVEN CARE and is my fiction writing even WORTHWHILE?! I’m stepping back from this cliff before I leap off it.

23) Why I Post (Jul 2014)
In brief: I write lots of recaps. My non-fiction gets views. But I want to be an entertainer, and random, and here’s more of my Time Travel story, and WHY YOU PEOPLE ON THIS BLOG NO READ FICTION? Sigh. (People did answer that question.)

Okay, so I’ve started highlighting the worst bits of my posts there. I swear, that wasn’t all about me whining. (The mark of a good writer is that he can try to spin his true feelings out into something a bit more worthwhile for others.) We are STILL on a down slide though.

In November, we hit Yi Can’t Even, which is when teaching imploded as a follow-up to the math serial implosion six months earlier. I was a mess. The kicker is, I’d started a new writing project in September too (2,000 words per week, based on votes). I have to write. It’s a thing.


24) Delayed Gratification (Jan 2015)
In brief: Every week, I’m teaching. Every week, I’m writing. Are people GETTING anything out of those things? I’m feeling micro-invalidated over here. Should I keep screaming?

25) Product of: It’s Time (Mar 2015)
In brief: What you write needs to get out there, because what was acceptable even ten years ago might not be acceptable now. Just do it. I’m releasing my time travel story.

This is also when I decided that I would reboot and/or resume “Taylor’s Polynomials”, at no specified date.

26) Guessed Writing 2015 (Apr 2015)
In brief: How I wrote an April Fools post for a guy who’s had a serial running SINCE 2007. Perspective!

That post got over 1,500 views here (seeing as I posted the link up in the comments on Jim’s site). That more than doubles the next most popular post. And here I thought the traffic was impressive when Dan Meyer tweeted out my post about the CMEF 2014 conference! (Okay, and it was impressive, but even now that’s still only at 600 views.)

27) ConBravo: Making It Online (Aug 2015)
In brief: If you think this isn’t going to grind you into the dust, you’re WRONG. It’s a huge amount of work. But if you love doing it, it pays for itself.

I may be a masochist, but I did love doing it. Summer 2015 is when I restarted my math serial - as a math webcomic. Now, here’s the reasons why I feel like I’m back in a “good creative place”:


a) For two months, each math comic has seen views of 100+. (Okay, last Monday’s is still at 68, I’m gonna call outlier.) In comparison, for the math serial, a few parts got to as high as 80 views, but most were lower. During the run itself, 40 views after posting was typical. One part (“Cliff Notes”) remains under 50 even now, which for a serial is effectively like purchasing a fiction book, then deciding not to read Chapter 7. You’re not really invested.

b) I’ve had TWO COMMENTS on the first eight posts - from different people! In comparison, Series 6 of the serial, which had almost 40 posts over 7 months, only saw two comments in ALL that time (by the same person - hi Scott!). Granted, I’m not counting the Author Asides, or my own comments.

c) Archive binges are a thing. In April 2015, when I wasn’t even publishing, I had 2,500 page views for the serial, and some remarks on the story’s Facebook page. There is something to be said for putting it out there, and hoping that years (and years) later, people will see the light.

Here’s what kills me. What I’m doing now, with the comic? THE. SAME. DAMN. THING. I. DID. FOR. THREE. YEARS. (ALMOST.)

I’ve simply trimmed the 200-500 words down to about 40 words, and have added figuring out word balloons, lettering (damn you, crossbar I’s!) and thumbnails to what I was previously doing. SAME characters, SAME content, SAME style... FEWER words, MORE pictures. Am I missing something? Apparently packaging is everything?!

Oh, sure, you could say my writing has improved, or that I’m more well known - EXCEPT. My Fiction Blog is on track for the WORST MONTH EVER. Seriously, it has been going for over a year, story posts EVERY week, and it has NEVER had a month with less than 100 hits... until, it seems, September 2015. (I may yet break 90.) Which breaks THAT theory.

I suppose you could say my writing has gotten worse, and people are pleased to finally have a format featuring less of it. But for the record, it’s actually damn hard to try and say in 40 words what I’d rather do in 100, plus my drawing is weak sauce, so I don’t really buy it.

The only other thing that occurs is it takes you maybe 20 seconds to read my webcomic, whereas it would have taken you 3 minutes to read my serial. (Or 15 minutes, in the case of my fiction blog.) Are people THAT busy, as I said way back in #1 up there? ... I guess I only read Justin Aion’s blog a couple times out of the week, so I shouldn’t judge.

TL;DR (Too Long; Didn't Read)

If you jumped down here, I don’t blame you. In summary? I want to entertain people. For three years, I tried doing it. I only sold a few tickets. Getting ever more desperate, I tried everything from requesting new personification ideas, to screaming into the wind for an audience, only to learn now that apparently the problem wasn't WHAT I was doing, only HOW I was doing it.

Webcomics sell, serials don’t?? (I miss the straightforward days of fanfiction.)

I’ve always known I can write. For years, it’s been a question of is my writing WORTHWHILE? Beyond the non-fiction recaps, that is. For the moment, I have an answer, and it’s apparently, YES. Hence why I’m in a “Good Creative Place”.

But more than that, things haven’t tipped over into “crazy” territory (yet?), where I’m so popular that people actually want my opinion on anything. (Sometimes I give it anyway, like when I embarrass myself by tweeting at Dan Meyer “Hey, I write too!” when he's talking to non-fiction authors.) Right now, I can keep up with my posts, and my job, and people are at least clicking on the comic links at a rate I’ve never seen before.

It’s been said, you never know what you had until it’s gone? I think I know what I have. For right now, I’m going to appreciate it. The way I appreciate you reading this. Peace out.

Wednesday, 23 September 2015

TANDQ 04: Riffing On Khan

In 2014-2015 I wrote an education column called "There Are No Dumb Questions" for the website "MuseHack". As that site has evolved, I have decided to republish those columns here (updating the index page as I go) every Wednesday. This fourth column originally appeared on Thursday, July 3, 2014.

How can you tell when criticism is justified?

Look for certain telltale signs. I’ll expand on that below, after I tell you what Khan Academy has in common with old movies. Specifically, about something called “Mystery Teacher Theatre 2000”.

Odds are good that you’ve heard about Khan Academy. But let me quickly recap the history. Ten years ago, in 2004, Salman Khan posted videos on YouTube to help his cousin with seventh grade math. YouTube being a public forum, he got positive feedback not just from relatives, but from many people. Thus the not-for-profit “Khan Academy” was created, and in 2009, Khan decided to turn this hobby of making videos into his profession, quitting his job as a hedge fund analyst. In 2010, Bill Gates advocated for Khan at the Aspen Ideas Festival. That same year, “Khan Academy” won one of 5 two million dollar prizes from Google. In 2011, Salman Khan gave a TED Talk about using his videos to reinvent education. In 2012, he was featured on “60 Minutes” and he was listed (as an educator) among “The World’s 100 Most Influential People: 2012” in Time Magazine. But something else also happened in 2012.

The “Mystery Teacher Theatre 2000” (MTT2K) videos began in June 2012. Two professors (Dave Coffey and John Golden) watched a Khan video, commenting in the style of “Mystery Science Theatre 3000” to “get a conversation started”. Justin Reich and Dan Meyer picked up on this idea, sponsoring an MTT2K prize for video critiques. (Incidentally, Meyer also has the credentials of a TED Talk, in 2010.) And conversation did occur. The media reported on the issue. Khan himself responded to one critic in The Washington Post. Many teachers made MTT2K videos (mine among them), the winning video looking at “What if Khan Academy was made in Japan?” And in fact, the very idea of videos being used for instruction had been critiqued a year earlier, in 2011 - here’s Veritasium’s look at “Effectiveness of Science Videos”. Increasing confidence in the wrong answers? That can’t be good!

Haters Gonna... Wait

Hopefully you’ve noticed that at least some of the criticism levelled at video instruction is valid. Don’t get me wrong - I’m not saying all criticism is valid, or that you should let a few people talk you out of pursuing your dreams. But I do think that this story illustrates how easy it can be for any of us to dismiss criticism of our work as “THEY don’t understand”. (Particularly when, as in Khan’s case, you have people in high places who are on your side.) So, to return to the original question, what are the signs that your critics may have a point, as opposed to just “haters gonna hate”?

First, look at their qualifications. When asked about why teachers were upset, Khan responded “It’d piss me off too, if I had been teaching for 30 years and suddenly this ex-hedge-fund guy is hailed as the world’s teacher”. But if “they” actually have qualifications you do not, it might not be that they are simply nitpicking. It may be that they have some understanding or experience that you lack. Just because you’re an innovator doesn’t mean you should disregard the history.  Secondly, look at the research. I’ve already mentioned confirmation bias, whereby we tend to find exactly what we’re looking for - whether it’s wrong or right. So is all your data anecdotal? Should we dismiss the Veritasium experiment above as a single incident, or is it worth doing further research? Finally, look at your goals. If they align with the goals of those people who are criticizing you, then perhaps it’s more beneficial that you all work together to get results. Granted, there are always those people who will be trying to tear you down so that they can “get the credit”, or have less competition. But if that’s their goal, presumably it doesn’t align with yours any more.

In all cases, you shouldn’t lose heart - you can upgrade your qualifications, you can track down new research in order to counter any future claims, and you can build a network of people with different perspectives to help you make more progress. Granted, it’s easier to simply dismiss those critics and keep walking down the same path - but you should at least ask yourself if that is in your best interests.

As far as Khan Academy goes, two years later, it has been piloted in many schools. EdSurge summarized an in-depth implementation report, adding the caveat “No single implementation model was used across all the sites”. Khan has also partnered with other institutions to promote blended learning, and with NASA to promote STEM opportunities - good on them for that. The Academy has even moved to become “Common Core aligned”… which invites a host of new critics who are against that educational model. Through it all, Khan has spoken of changing “the traditional classroom”. Because we all know what “a classroom” looks like, right? It’s a bunch of geek teachers coming up with crazy ideas, trying their best to educate people… people who have a tendency to simply tune them out. Then again, the classroom might be a bunch of students watching five year old instructional videos, wondering if a remake might look any better. No, that’s silly - why would anyone want to update a classic?

For further viewing:

1. Summary of Funding to Khan Academy

2. An open letter to Sal Khan (2013)

3. Educators Meta Parody their own MTT2K video (video)

Wednesday, 16 September 2015

TANDQ 03: Popular Misconception

In 2014-2015 I wrote an education column called "There Are No Dumb Questions" for the website "MuseHack". As that site has evolved, I have decided to republish those columns here (updating the index page as I go) every Wednesday. This third column originally appeared on Thursday, May 29, 2014.

Why is my network below average, compared to all my friends?

It likely isn't - instead, a couple well-connected individuals are skewing our perceptions. Your friends may even be wondering the same thing! The “Friendship Paradox” was first observed by Scott L. Feld in 1991, but it has been gaining more notoriety lately, since it has been found to apply to online social networks too. Not only directed networks (like Twitter, where I can follow you without you doing the same) but also undirected ones (like LinkedIn, where you must confirm me as a connection). How about that, an application of directed graphs!

The paradox boils down to the fact that “on average, most people have fewer friends than their friends”. For instance, consider this set of follower numbers: {2, 4, 6, 8, 100} . Add them, divide by 5, you get 24. Meaning all but one of those people is BELOW average in followers. When George Carlin said “Think of how stupid the average person is, and realize half of them are stupider than that”… he’s assumed a uniform, or perhaps normal distribution. Not a skewed one, as we have here. This outlier issue is also why fully 99% of a population has the potential to be below an average salary, but I digress.

Something a little different is happening with our social networks - after all, the most popular person (let’s call him/her Pop) can’t have a connection of 100 unless there’s 100 other people to connect with in the first place. Two things are going on now. First, if someone has a lot of friends, you are more likely to be friends with them too… that’s simple probability. In other words, if Pop is connected with 90% of the internet, you’re more likely to be connected to Pop, and thus have your perception thrown off. Second, it’s a problem of averages.

Mathematical Means

Imagine a network of “n+1” people where everyone is connected to everyone else. You have “n” friends - you don’t friend yourself - and Pop has “n” friends, and Goofy has “n” friends too. In this network, what is the average number of friend connections? Well, if everyone you know has “n” friends, and we add this up (n+n+n+…) to get n-squared, then divide by the total “n”… average connections is “n”. Makes sense; everyone has this number. Still with me?

Now, what if you and Goofy break your connection? You’ll have “n-1” friends - and so will Goofy, not that you can tell - but everyone you’re connected to still has “n” friends! So from your perspective, the average is STILL “n”. You are now below average. (More rigorously: When we sum again (n+n+n+n…) we’ll only have (n-1) n’s. Divide by your (n-1) friends - to get “n”.) Yet amusingly, from Pop’s perspective, the average becomes (n-squared minus two)/(n), a value LESS than “n” - he’s above average! Balance is preserved.

As we keep chopping out connections (to create something more like an actual network), everyone less connected will - from their perspective - find themselves sinking below average, while a few popular people like Pop will become the big above-average benefactors. Thus while you may believe that everyone else you know is more popular and more connected, guess what? They’re experiencing the same effect. It doesn’t help that you’ll probably see updates from Pop more often than anyone else - the guy had to get popular somehow. (For a slightly more rigorous mathematical proof of why the average connection for friends MUST be less than or equal to the average connect for friends of friends, check out the Mind Your Decisions blog here.)

It turns out this actually has repercussions beyond our own self-esteem. The blog post I just referenced points out a connection to vaccinations (target the more popular individuals), and there’s also a link with the spread of infectious diseases (finding who is most likely to be exposed). Moreover, published this year (the MIT Tech link below) is how this paradox can even apply beyond the numbers - your friends don’t only seem more connected, but also richer! And happier! Yikes! Granted, our own “negativity bias” can also be a factor in how we see the world… but that’s a whole other topic. For the moment, your best bet is simply to stop comparing yourself to whatever you perceive as being "average".

For further viewing:

1. Steven Strogatz in the New York Times

2. MIT Technology Review (2014)

3. “Apple Daily English” Video (< 2 min)

Wednesday, 9 September 2015

TANDQ 02: Getting Graphic

In 2014-2015 I wrote an education column called "There Are No Dumb Questions" for the website "MuseHack". As that site has evolved, I have decided to republish those columns here (updating the index page as I go) every Wednesday. This second column originally appeared on Tuesday, April 29, 2014.

How is graphing technology changing in schools?

Short answer: Fairly rapidly. To see why, let’s quickly look at the past, aka what you may remember from your own high school math and science courses.

For many years, the TI (Texas Instruments) graphing calculators (specifically TI-83s) were the standard for graphing polynomials. But as xkcd points out, that calculator still costs over $100, has a poor display (comparatively speaking these days), and is not allowed on most standardized tests. So not many students buy them. Hence, class sets for schools - along with associated maintenance costs, like replacing the AAA batteries whenever students would steal them to power their MP3 players - was the result. (Okay, the stealing doesn’t happen quite so much these days, but tells you they’ve been around for a while!)

Here’s the thing: Once the TI-83 began seeing use, replacing that entire calculator empire became seriously impractical, given how public schools are (in my opinion) chronically underfunded. I’ll tell you right now: if the latest thing is not backwards compatible, forget about it. Schools have no money for new power adaptors. An overhaul would also require teachers to buy in, leading to training, which requires money for substitutes. There’s also the nightmare issue for superintendents of potentially spending a bunch of money for something that doesn’t turn out to be any better than what was already there. Thus, for many decades: the TI-83.

But with the rapid evolution of portable technology, there are now alternatives. Have a product? Do you know how to market it? Hint: It’s not through the school boards. It’s through individual teachers. Wolfram alpha was one of the first websites I knew of to provide online graphing capabilities. More recently, a colleague of mine is using the “Free Graphing Calculator” app with her class. And then there’s the Desmos website. If you haven’t heard of this company yet, I suspect it’s only a matter of time. They have a tool with dynamic capabilities that has increased what I can do with graphing in my class by a factor of about a thousand. Oh, and it’s affordable. Because it’s free.

Next Big Thing?

Their website says, “Desmos supports the development of our calculator through select partnerships with organizations that can benefit from our powerful and intuitive HTML5 technology.” The founder and CEO, Eli Luberoff (who graduated from Yale in 2009), even came out to personally present at a mathematics conference that I went to. That’s what brought me on board. They’ve got a twitter account, and respond to tweets, listening to what educators want, and then delivering. They post student work (artwork!) right on their front page. I see Desmos as being a key part in the future of math education. They don’t need a big name spokesman like Bill Gates to get people to listen - me, and other teachers like me, are now their advocates.

All well and good, but what can we take away from this story? A few things. First, the field of education is changing. But ignore the big names waving their magic wands: change doesn’t happen overnight. Look for the little (inexpensive!) smaller things that are being incorporated (like radian protractors, perhaps?). Those have more staying power. More to the point, if you’re marketing to education, don’t plan on public schools being your primary source of revenue.

Second, marketing itself doesn’t have to be about competition. That may work in high tech, but telling an educator how your product “is so much better than the current standard” is merely a good way to annoy them. For one thing, it’s not news - huge technology upgrades are only possible in a school every six or seven years, if that. Even then, it’s often only done because there’s really no choice - a prime example being a recent switch away from (the now unsupported) Windows XP. For another reason, it’s not enough to be better, or even to be good - to get use in a school, your product has to be dynamic and scalable over time.

Finally, this story goes beyond education. I’m not just speaking of the Desmos platform itself, but consider that Eli started out as a tutor who was looking for a way to accomplish that over the internet. This is another of those success stories involving someone with a passion, who found a way of bringing his vision to others… and in the process, he discovered ways that his software could be used beyond his expectations. Plus he has also helped to bring art back into mathematics. Something that’s incredibly important in our increasingly math-phobic culture.

Oh, by the way, Desmos is hiring. (They’re based out of San Francisco).

For further viewing:

1. 2011 Finalists: America’s Best Young Entrepreneurs

2. Eli Interviewed on TechCrunch Disrupt (video)

Saturday, 5 September 2015

Summer's End 2015

As I said back in 2013, I shouldn’t be so focused on teaching that I neglect other achievements. As the end of August is more of a conclusion to a year than the end of December could ever hope to be, here we go. I think this summer went better than the last two. I’m not going to break it down chronologically either, let’s split it another way.


Less than the last two years (could be a correlation with my mood?) in part because no “Twitter Math Camp”. I finished reading “Our Days Are Numbered” (by Jason Brown) which has been on my shelves since 2013. I started reading “Fooled by Randomness” (by Nassim Taleb) a more recent acquisition. It’s heavier reading, I don’t expect to finish it this year.

I also got through “Avoiding Teacher Burnout”, a small book put out by the Educator’s Room. For writing, I blogged about COMA and OAME conferences, and put some news articles into my stats website. That’s about it, unless you count the TweetUp in Carp (which was really for fun).


Depends on the fans.
The faucet in my kitchen has been without water pressure for at least 16 months - no more! It has been replaced. The water filter in my fridge has needed to be replaced longer than that - done! My back deck has been growing algae or something - cleaned! Related, the old barbecue out there was hauled away, and me and my wife bought a new one and assembled it. The air filters hadn’t been cleaned since 2013 - done! Washed a number of the exterior windows too, and replaced a toilet arm.

Last winter, our soffit and eavestrough were damaged somehow - work has started! (I hope they finish soon...) And though I’m still not sure what’s harming my trees, mini-ones are not growing in the eavestrough corners any more. On a more personal side, I booked myself a physical for the first time in four years. (Amazing how some things slide. Should do my eyes as well at some point.) I also signed up for a clinic to track exercise and diet over the next 12+ months. And I’ve continued to see my social worker to try and handle my depression, including maintaining a journal.


Math Webcomic!
I went to ConBravo in June, and blogged extensively about it. It inspired me to charge ahead with my personified math, and I’ve now published five comics (I update there EVERY MONDAY). My time travel serial has continued, in fact I’ve edited ahead into 2016 (end of Book 2). Re-edits for the serial take longer than I thought; at least an hour or so per part, assuming no major rewrites (and there have been some!). Book 2 will start soon.

I’ve also written a completely new bridging episode for the story (before Book 3), and completed 10,000 words on *Book 5*, the one I started roughing out last summer but didn’t get too far with. Honestly, the drawing is what’s holding the current story up, as I’m more familiar with writing/editing. I tend to draw in chunks. But I’ve still been able to update every FRIDAY. Commentary every second Sunday. My 200th post here was also a short time travel story.

I finished reading “Shadows Over Sheradan” (by Scott Barker, a teacher in my district); I hadn’t really wanted to start Part III without the time to enjoy it. I read “The Beautiful Land” (Alan Averill) which my wife bought me for my birthday. I read “Starship Titanic” (Terry Jones), on my shelves for a while. I caught up in some online serials: “TwiceBound” and “Unruly” including leaving some commentary there. Also more commentary on “Legion of Nothing” (nearly caught up!).

Subliminal message?
I did an anime marathon of “A Certain Scientific Railgun” (first season), which I’ve owned and have been meaning to do for a couple years. I streamed “Nanoha Vivid” and the show remains cool (though ‘Adult Mode’ is a bit creepy). I also marathoned “Attack on Titan” (first season) and watched a couple episodes of “Steven Universe”, to keep up with popular culture. I’ve read some manga. With my “There Are No Dumb Questions” education column having wrapped up in May, I have the XML from Steve, and intend to re-run it on this blog, on WEDNESDAYS.

Web Videos: I watched “Radio Dead Air” live for their 10th anniversary show, and 3 times since. I caught up on Nash’s WTFIWWY. I’ve stayed current on Linkara’s show (not Longbox, granted, the guy’s a powerhouse of content) and saw the SF Debris Comic History among other online shows. I caught up in NCIS: New Orleans with my wife, as well as Sherlock Season 3. Bought ’Chvrches’ and ‘Carly Rae Jepsen’ CDs. Am trying tumblr.

I started reading “Outlander”, but I think that goes on autopilot next week... along with everything else. (Sound like a lot? For contrast: The other 10 months of last year I was able to stream “Sailor Moon Crystal” and keep up with “Doctor Who” and “Agents of SHIELD”. For reading, I got through “Shada”. And I wrote 2,000 words per week, Sept to March. That’s basically it on hobbies.)


Bach, to the future
Went to France (in laws) and Germany (cousin’s wedding). Airlines did not lose our luggage! This is friggin’ huge after the airline mess around Christmas. Air France is awesome, just saying. Honestly, I’m more pleased about the webcomic than going to Germany, but it’s a close second, in part because the Bach Museum was in Leipzig. I got a tie. There was also a pretty cool writing museum (which was free).

Back in Ottawa, I went to the Governor General’s movie night, and a couple other movies in there. Celebrated our anniversary, checked out the new restaurant down the street. Went to the Alex Colville exhibit at the National Gallery. (I do get to some NAC shows the other 10 months of the year too.) Figured out how to get pictures off my new camera.


So, with all that... what did I NOT get to? Song parodies. I’ve had one in my mind for a few months, but haven’t set aside the time to work on it. Videos. I’d thought of doing one for a parody, or to close off Series 6 of the math serial, but no. Improving my marketing is still from nowhere, my name is out, but it’s not a draw.

There are other anime I didn’t get to, like Durarara and “Certain Magical Index”. I have a one week buffer in my blogs; more would have been good. And more T&T would have been good to write. There are also some books I still did not get to, including “Thinking in Numbers” (bought last year) and “Buffy Season 8” (had it for a while).

Still, those are all things that would take an investment of more than a couple days. I’m at the point where I’m spinning my wheels a bit, unable to find something to do that’s a short term investment. To that end, I guess I’m ready to go back. I need to figure out Desmos Regressions for my Data Course, and I should incorporate more “what do students already know” in my plans.

Which basically wraps up this post. I have now posted 10 straight days across 3 blogs, so taking tomorrow off, then Webcomic Monday. Hope to see you there! In the meantime, feel free to read the Summer 2014 Wrapup or Summer 2013 Wrapup.

Wednesday, 2 September 2015

TANDQ 01: Bias Confirmed

In 2014-2015 I wrote an education column called "There Are No Dumb Questions" for the website "MuseHack". As that site has evolved, I have decided to republish those columns here (updating the index page as I go) every Wednesday. This first column originally appeared on Wednesday, March 26, 2014.

How can we ask good questions?

In brief, start by not knowing the answer, not knowing where to find the answer - and perhaps not even knowing if there IS an answer. For more depth, read below. For context, it may help you to know who I am. Which would be Gregory Taylor (@mathtans) a high school mathematics teacher from Ontario, Canada who knows a thing or two about education and statistical curiosities. As a geek, I’ve written a fair bit of fan fiction, as well as my own serial (ongoing), “Taylor’s Polynomials”, which personifies mathematical relationships in the same way the anime “Hetalia” personifies countries. I hope to bring a different perspective to things, along with a sense of who’s going to be heading out into the workforce in 4-5 years time.

Now, back to the problem of questions. Many questions that we ask ourselves today are not very good, simply because they end up being answered using a search engine. Yet in doing that, we often bias our own results! For instance, if you believe Asimov wrote the Foundation series of books, you will likely include the term “Asimov” as part of your search. Or if you believe health care is unaffordable, you will include the term “unaffordable” in your search. In both cases, there will be some results that confirm that you were right all along… and so you will not ask any more questions. (Questions like: Is it just me, or is Asimov’s “psychohistory” becoming reality?) This problem is known as Confirmation Bias.

Confirmation Bias is the tendency for an individual to seek out information that confirms what they believe already. We have all become guilty of it, in large part because (if you’re logged into an account) web searches remember the sort of pages you like to visit - ensuring that you will constantly cycle back to the same sorts of pages, reinforcing your beliefs. By the same token, we also don’t tend to follow people on Twitter who disagree with us, or initiate online chats with people who have dissenting viewpoints. In short, the internet is a terrible place for discovering new information - unless we are first able to reject our own preconceived ideas. (Could there be a connection here with Steven’s thoughts on Deep Geeks last week?)

Highlighting the Problem

Watch the following to see what I’m talking about. The Veritasium video “Can You Solve This?” elegantly demonstrates how our initial beliefs can lead to asking the wrong questions. In this other video, Numberphile summarizes the experiment behind a recent newspaper article: “Politics wrecks your ability to do math”. Basically, people stop questioning as soon as their liberal or conservative beliefs are confirmed - even if there is a different interpretation. But it gets worse: being presented with facts to the contrary merely has a tendency to strengthen our initial (flawed?) preconceptions! It’s something called the backfire effect.

So what are we to do? Now, that’s a good question. I know I try to include a few people in my Twitter feed with dissenting viewpoints. I also try to make a point of checking out page 6 in my Google searches, rather than always going with it’s top choices. And, of course, I consider the sort of questions I ask - a topic that is becoming big in education these days. (At least in MY circles - oops, bias is creeping in!) In particular, it’s more important that students learn to question WHY things are the way they are, rather than simply accepting “facts” like “a negative times a negative equals a positive” on blind faith.

To conclude, while I (obviously) believe that there are no stupid questions, this is largely because I don’t want you, my students, or the public in general to ever stop questioning things. There’s more problems out there than just confirmation bias… like the fear that asking a question will brand you as ignorant, or argumentative, or subversive. But who cares? Ask anyway. It sure beats the alternative. Feel free to ask me questions in the comments below too!

For further reading:

1. The 12 cognitive biases that prevent you from being rational

2. The importance of questions

3. Eli Pariser video: Beware online “filter bubbles”

Tuesday, 1 September 2015

About the 42nd Cdn Election

My previous post here involved a timeline of events leading up to this October's 2015 Canadian Election. At the end of it, I predicted a Conservative minority government. Here, I'll explain my reasoning.

Let me make a few things clear right off the bat:
1) I do not like Harper. (He killed the long form census, and I teach statistics.) But that doesn't mean all conservatives. I have good friends who are conservatives who might be reading this, so keep it classy in the comments. Also, don’t comment until after you’ve read the whole post.
2) I am not a political expert. As a general rule, I don’t like wading into politics, but I fear that someone has to. (Read this article about “getting ones head around politics” for some reasons why. Yes, I am aware that’s an American source.)
3) I am a teacher, I am in a union. If you now think I’m hopelessly biased, fine - personally I think we all are to some degree - but remember, I teach statistics, so it’s also possible that I know a few things you don’t. Also, these views are personal, not professional.

The reason I’m predicting the conservative minority is threefold:
1) The Backfire Effect
2) Status Quo is God
3) People Don’t Care Enough


The effect is easy to state: When your beliefs are challenged by contradictory evidence, those beliefs get stronger. As I said in my post “Ask a Scientist”: Something Aunt Wendy asserted when drunk will need to be disproved by a panel of experts before you change your mind. Because she was FIRST, and you have emotional TIES to her, and it makes SENSE in your world view.

Ergo (to pick a topic at random), if you believe Harper didn't know about Duffy, no news article spewing testimony is going to alter that opinion. Similarly, if you believe Harper did know, same argument. And if supposed facts won’t alter your beliefs, they sure as hell won’t change because someone with a different political belief system says so! I venture that the only thing that might change your belief is personal experience.

One of the more well known adages in writing is “show, don’t tell”. (That’s a TV tropes link, be careful.) And there’s a very good reason for it’s existence, as humans have a tendency to be skeptical of things we’re merely told about. (Bella Swan’s all that and a bag of crisps, eh? Okay then.) One can pair the saying off with “seeing is believing”, except it’s worse: in this digital age, we tend to “see” more of what already conforms to our world view. (I see you liked those TV Tropes links - would you also enjoy these Top 5 Hated Character Tropes?)

This digital masking cuts both ways, by the way. I saw a message on social media the other day saying “If you are going to vote for Stephen Harper please unfriend me”. That’s horrifying. At best, this person is building a little echo chamber (if they didn’t already have one) and at worst, they’re turning more people off politics. Not conservative people, I’m talking about the majority of undecided people who now WILL NOT vote (or will spoil ballots), because screw this noise.

In other words, for every “10 reasons to Vote for Anyone but Harper” post you’ve also got “100 Reasons to Vote for Harper Conservatives”. You’re not convincing anybody with facts, not if they have already formed an opinion.

Granted, I’m not sure if there’s a case to be made if enough people who ALSO share your belief start to have doubts. I’m no expert - feel free to read this on The Backfire Effect if you want to explore more on your own. (By my own logic, anything I say won’t change your mind!) My point is, the more you attack the beliefs of ANY party, the more entrenched those views become... which pretty much assures the Conservatives of, say, at least 20% of the vote. Moving on.


“People can be very frightened of change.” (Kirk, Star Trek VI) I believe this is partly to blame for TWO DEAD MEN GETTING ELECTED in the US, after one Democrat and one Republican died during their 2012 election campaign. And you have only to look at the Canadian Government’s targeted advertising to see the Conservatives believe this too, with their insistence that “Being Prime Minister isn’t an entry level job”.

Wait, sorry, that’s actually an NDP quote from 2014. (See? You're learning.) Still, the Conservatives are also claiming this isn’t the time for change. (Don’t interpret those attacks as me voting Liberal, Trudeau is simply getting attacked more.)

This dislike of the “unknown” means two things: First, even people who disagree with Harper’s politics might still vote Conservative (or Liberal, Bloc, etc) in their riding. Because that’s the local guy, and while things may be going to hell federally, at least where WE are, things are okay, right? (Granted there are 30 additional seats this election, and some key ministers aren’t running, but party lines are party lines.)

Second, people who did not vote in the last election aren’t going to vote in this one either. Why? Well, they don't know the process from back then, plus maybe they’ve heard it’s even more difficult this time, and what’s the big deal about politics anyway? Related, there has been a Declining Voter Turnout noted in the younger electors. Which brings me to my last point.


If you read my last post about the last 10+ years of elections, you’ll know that we elected a Conservative Majority Government after they were found to be in Contempt of Parliament (in 2011). Basically, all the other parties got together and told Harper “You need to be held accountable” and Canadian voters turned around and said “Nah”. (Yes that link is intended to be “Ironic”.)

Seriously, if that wasn’t the nail in the coffin, I don’t know what else could be bigger.

Now, I’m not saying EVERYONE doesn’t care enough. (In fact, some people seem to care too much, see my earlier remark about echo chambers.) But not enough people do - even the Americans have noticed how little we’re talking about things: see “The Closing of the Canadian Mind” (NY Times). We are uninformed. You are uninformed.

Yes, I’m calling you uninformed. That’s the only weapon left, really - not to attack your political beliefs, which cannot be shaken, but to say you are making an uninformed decision. You are blind to the other side (or blind to the idea that voting matters). And with the media mostly going after things you already have set beliefs on (the Duffy Trial, the Economy...), perhaps we need to look elsewhere for inspiration.

For instance, were you aware of the following 10 points?

1-The longer election campaign will cost more to taxpayers.
2-The City of Ottawa (and other groups) have asked the federal government to move their “Victims of Communism Memorial” (and they won’t).
3-The claim “2.5 million protected lakes and rivers is down to 159” is NOT true in an environmental sense, only a navigational one.
4-It’s been over 2 years since Harper last appointed a senator; this has led to him being sued by a BC lawyer. Ten of Harper’s 59 appointed senators have left the upper chamber (some of natural causes).
5-Data on Canada is drying up since the nation scrapped the mandatory long form census. And even if we get a new government, there won’t be time to fix this by 2016.
6-Proposed changes to the “Tax Free Savings Account” were said to be a problem for people in 2080. (Implication: not our problem)
7-The union for federal scientists broke their traditional neutrality in 2014, saying they will campaign against Harper. Seemingly more for his war on unions than his muzzling of scientists.
8-The federal government has retroactively rewritten laws (at least that one about guns) to suit itself. Omnibus bills!
9-The United Nations Human Rights Committee said the recent “Anti Terror Bill” (C-51, passed in June) may not contain enough legal safeguards. The Liberals supported this bill.
10-Less than 5% of Conservative candidates agree to interviews (unless they get the questions in advance).

If I’m incorrect on those, then I’M uninformed. Correct me. I don't know if that even makes a difference to you; maybe the Backfire Effect is still in full force, as it is with the media.


One final word for people who decide to point to “polls” - ooh, look the NDP is ahead! And they did well in Alberta! Well, the prediction in the United Kingdom for the May 2015 election was for a close race. The Conservatives took an easy majority there. There has been a bunch of later analysis. Rick Mercer’s had something to say about Canadian polls (in 2012) too.
"Obligatory" Mercer reference accomplished again.

If you’re still on “Backfire Effect” for your poll beliefs, here’s one predicting Conservatives as the favourites, and here’s a whole article about How Harper Will Win. (TL;DR: The Conservative plan is working if at any point you’ve thought “Trudeau is too inexperienced”.) Oh, but you've got a viral “HarperMan” song? Yeah, there was a song in 2011 too. And there was a website back then. And we still got a majority government, "in contempt of Parliament".

So yeah, I call conservative minority. A cynic might add: Followed by a prorogation, and as soon as oil prices go back up, another election. The nail went into this coffin back in 2011.

I believe the only one who can change that outcome now (assuming there is any interest in doing so) is you. Get informed, and vote.