Saturday, 6 February 2016

Order the Fruit Salad

January is the worst month. No question. It’s three weeks until exams, everyone has forgotten everything, and you have ZERO turnaround time to prepare for Semester Two, let alone generate report cards. Yet it’s also the start of the MTBoS “Blogging Initiative”... maybe that will make it better.

The Week 4 (and final) blogging challenge is “Share a Lesson”. (For my previous weeks, see “Questioning” here, “Favourite” here and “Day in the Life” here.) We were warned about this one in advance, since depending on where you work, there might not have been teaching this past week. So I had something in the back of my mind.

That said, I did teach - namely the startup of semester two, with new classes and students, while still finalizing marks for semester one. (I did mention January was the worst month...) But with the startup, I realized I should probably blog here about how I start off my Data Management class (aka Statistics) every year. Namely by making a run to the store to get an apple.


I’ve been doing my fruit lesson for at least four years. Probably longer, though I didn’t always start the semester this way. Mainly because I didn’t always start with the counting unit. I’m also cheating a bit, because this “lesson” actually spans three days.

Day One, I don’t immediately start with the fruit. My first example is the probability of getting the correct combination for a standard locker lock. Then definitions, some other simple probability examples, and THEN the fruit comes out. A grapefruit, a lemon and an orange.

With the objects, we can no longer repeat our choice (versus having a password of all ‘a’s). Once the grapefruit is down, I only have two options left. 3x2x1 = Six options total, the students are on board. That’s when I pull out the lime, as seen below. The total arrangements is easy. The number of arrangements where the lime is first requires a bit more thought.

From there, it’s into factorials, and we call it a day. The BAD news from this year, is that this intro was on a day when the busses weren’t running. And even though only 10% of our school uses busses, the bad weather means lower attendance. (Schools are never closed. Ever. We could get 20 feet of snow and they’d still be open.) So I had to do a little rerun the following day.

Day Two, we move from factorials to permutations. Here’s where the apple is added, to make things interesting. Normally I’d get all the way through my “how many ways with lemon and lime together” example - seen below. But with the “ice day”, I had to leave it with them to think about. This picture was actually taken to start off Day Three.

Oh, I physically move the fruit around too, to emphasize. (This arrangement is fine. Not this one, not this one, but this one... *I switch the position of the lemon and lime only* ...and this is fine. *groans are heard*) And normally the apple is green, to match the lime, but my wife happened to have an apple at home, so I took that one. I don’t like apples much, this is the only time I buy them.


Once the lemon/lime example is done, I don’t advance the next slide. I pull out a second orange. And they know what’s about to happen, and someone says “Sir, why would you do that to us?” THEN I advance the next slide. And sometimes someone will try to argue that the two oranges are different enough, and so I have other examples with letters and words, and they will grudgingly capitulate.

Thus the first part of Day Three is finalizing this permutations knowledge, but of course, I have one more trick up my sleeve. I pull out the grocery bag, and announce that I’m going to take three of these home for the weekend. And I grab the grapefruit, the apple and the lime, tossing them in the bag. But wait!

Does it matter that I selected the grapefruit first? It’s coming home with me, the same way as the lime is, even though I picked it last. Of course now order doesn’t matter, and so now we have combinations, to round things out. Factorials, Permutations, and Combinations, all taught with fruit.

The inspiration was in part due to the “Shad Valley” program I went to at University of Waterloo in 1993 (when I was in high school). Ed Jernigan used fruit in his math lecture, as a way of trying to categorize “fruit” for artificial intelligence. This is, by the way, the closest I get to a "3 act" lesson.

Things to watch for: Students tend to like the visual/physical presence of the fruit - two of them remarked on that aspect this time. Students also tend to ask if they can take the fruit home with them. (Someone wanted the grapefruit this time.) I’m more leery of that, in case bad things happen. Also, I like grapefruit; if they want the apple, meh. Along the same lines, one guy wanted to be in my picture (above) but while I applauded his enthusiasm, I said I probably shouldn’t do that.

Fun fact: At one point, some of them were talking about salad. I’m not sure why (this period was right before lunch), but it was easy enough to steer that conversation back to permutations and combinations. Fruit salad, anyone?


Quick bonus, the lesson I likely would have written up if I hadn’t been buying fruit this past week is the “painted cube” problem. You paint a cube, then disassemble it - how many of the component blocks have no sides with paint? One side? Two? Three? It’s a rather elegant way of having linear, quadratic and cubic patterning in a single activity. But it’s also one that educators are liable to find more familiar - maybe you’d already heard of it?

The plan is now to have lime tilapia at some point for dinner this week. But before Monday, I need to get my personified math comic coloured and uploaded! (I hit entry #250 last week.) Thanks for reading here, if you enjoyed, know that I’m all about the writing. Feel free to check out some other posts:

-Check out the Bola Fruit in the Conic Household with “Tea Leaves”
-The math song parody “Permute” is the one I use for this Data unit
-Here’s my reminder that, even in the face of other creative ideas out there, “You’re a Good Teacher” (too)

Saturday, 30 January 2016

The Quest in Question

January is the worst month. No question. It’s three weeks until exams, everyone has forgotten everything, and you have ZERO turnaround time to prepare for Semester Two, let alone generate report cards. Yet it’s also the start of the MTBoS “Blogging Initiative”... maybe that will make it better.

The Week 3 blogging challenge is “Questioning”. (My Week 1 post at this link; My Week 2 post at this other link.) Nearly didn’t post this week, for reasons I go into below. But I’m an MTBoS mentor for three other math educators, so I decided I should set a good example. In no small part because my more “hands off” approach to mentoring has a tie in with this particular subject.

So, why did I nearly opt myself out of Week 3? And what did I come up with for a question in the end?


I am not very good at asking questions of others - I’m much better at giving responses. In fact, I’m really lousy at approaching others in general, even people I know (or teach). There’s this default mode in my brain, where I tend to assume people are just fine without me, so why should I interfere and possibly make things less clear or more complicated.

It’s probably the introvert in me. Coupled with the depressive.

The paradox is that I want people to approach me with questions - mostly about my recreational writing - yet perhaps they’re assuming I’m just fine without them too. It’s the same sort of thing with teaching and mentoring, I’ll sit here waiting for the questions, so that I can respond to them. Not always to give an answer, mind you, but to give options, start research, or to turn the question back on the poser. And sometimes I interpret body language as being a question. Point being, I rarely initiate.

Given that, I don’t believe I’m someone people should look up to. In fact, I can be quite self-deprecating. It occurs to me that this could be the reason why I’m reticent to take on any sort of student teacher. Is MTBoS mentoring even a thing I should be doing? ... I don't think that's a question I can answer myself.

Let’s focus back on the classroom.

What are you thinking about?
Breaking down the MTBoS assignment options: A question to get kids thinking about something? I tend to improvise off the cuff, or ask lame questions to give them processing time. An awesome/sucky test question? I feel pretty middle of the road. A student asked a question that sparked something? This happens a lot, but it’s pretty ‘in the moment’. And while I have a great memory in that I can remember details of the story I wrote 5 years ago, I rarely retain a memory of social interactions. Plus I’m SO bad with names.

In the vein of “a question I didn’t know how to answer”, I suppose I could get into the “why is it a greater than 5 check?” in statistics. (It’s a threshold for the normal and binomial approximations, it’s referenced as the lowest indicator for the coefficient of determination, and then there’s p values. Why 5?) It’s a question that almost always comes up, yet I never really have an answer aside from “let me know if you find out”.

But if I only put that out there, this would be a really short post, and as you may have noticed, I’m bad at those.


I haven’t been teaching this past week. It’s been four days of exams, and while there was class on Monday, that was fielding final review questions. Standard form stuff. (Or factored and vertex form stuff.) I did get an interesting email from a student on Wednesday afternoon though. It cycles right back to the idea of a problematic textbook question.

For anyone in Ontario with the Nelson 3M “Functions and Applications” text, follow along on Page 188. It’s a multiple choice in the cumulative review. Question 14 gives a quadratic area formula, asking what width option gives an area of 130. The student solved the equation, ending up with two answers of 5 and 13. And BOTH were listed as options.

She dutifully subbed both answers back into the equation - and they still worked. This was when she emailed me with a snapshot, stating “I’m a bit confused” and “I might not be doing it right”. I reassured her that she was correct... but I wasn’t content to leave it there. How could the text have misfired like that?

We take many words for granted.
Not content to leave it at “textbooks are stupid, yo”, I generated the lengths for the rectangles as well. This gave me a hint, producing 5 by 26 and 13 by 10. Which suggests to me that they had rejected the 13 because this would make “width” longer than “length”. After all, properly speaking, the English definition of “length” is “the measurement of something along its greatest dimension”. Did you know that?

It’s mathematics which muddies the waters, tending to use ‘length’ and ‘width’ interchangeably, depending on which way your page is oriented in front of you - and here we had no page, only a formula. There was a rather interesting discussion of the meaning of “length” with a sixth grade class on Ask Dr. Math from 1999. This is not a new problem!

So the textbook listed “5” as the correct answer for width. Since “13”, despite being a “width” that solves the formula, is technically a length. (And “10”, also given as a possible answer, would be a valid width but doesn’t solve their formula.) Now, do I think that was the INTENT of the text? No. And it’s needlessly confusing. But wasn't that journey interesting?

All this to say, I rarely initiate questions. I respond.

Thought from a prior post.

I also respond to every comment on my blog, if you’re so inclined. Both here, and on “Any Q-Bars”, my math webcomic which is a play on words for the popular “Any Qs” mixed in with “Q bars” denoting the irrational number set. I’ll also throw in a quick plug: If you’re an educator in Ottawa, Canada, check out #OttSlowChat on Twitter!

For now, I should get back to marking exams. Wheeee. If you enjoyed reading this, I’m all about the writing. Feel free to check out some other posts:
-There’s some fun math questions in this COMA Recap Post
-The Big Question: Me blogging about my depression
-And in the vein of better questioning, “Hinge Questions” by Nik Doran.

Saturday, 23 January 2016

Lattice Puzzle

 January is the worst month. No question. It’s three weeks until exams, everyone has forgotten everything, and you have ZERO turnaround time to prepare for Semester Two, let alone generate report cards. Yet it’s also the start of the MTBoS “Blogging Initiative”... maybe that will make it better.

The Week 2 blogging challenge is “My Favourite”. (You can find my Week 1 blog post here.) Now, I presented a “My Favourite” back at ‘Twitter Math Camp 2013’ - namely Unit Circle Estimations (for Trig). I’ve also droned on a bit about teaching the Sine Law. Those are more traditional topic centred posts, but I’m still feeling subversive, so let’s use this one to talk about this number puzzle I got at OAME 2013 instead.

I'll pause to give you a moment to scroll though all those other lessons and recaps I threw at you. Do I link too much? I probably link too much.

Here is the puzzle.

The premise is simple enough. Fit all the numbers flat into the box provided. Note that the conference was in Toronto, hence the CN Tower in the logo. I don’t recall if everyone who attended that PD conference got one of these, or if it was something related to the fact that I presented there (Musical Mathematics - I’ve parodied 30 songs). But the puzzle has been surprisingly popular this semester! Does it fit into the curriculum? I don’t know.

Presumably, it’s got some spatial reasoning associated with it. After all, the only way to make the pieces fit is to create a full lattice, with no gaps or spaces. (In the image below, look in the lower right corner.) Now, if you think about it a bit longer, you might realize that symmetry is a useful tool. (For instance, lock the ‘7’ in with the ‘1’ - looks a bit like a ‘4’...)

What it looks like on my desk this week.

I simply keep the puzzle on my desk at the back of the room, and students (Grade 11 students) who are finished work early or want a bit of a break can play around with it. I have sets of puzzle cards on my desk too, but for whatever reason, this is the popular thing. It started the semester fully assembled, when a couple guys would time each other for the fastest to assemble it.

Eventually, it spent well over a month fully disassembled, as people toyed with it and couldn't put it back together. One student wondered if there was a way to get/make her own. I had a teacher in my room for an on-call ask me about it the following day. I even played around with it a bit once, while catching up on “Supergirl” (while procrastinating from catching up on marking). There’s only been one casualty, the tip of the ‘5’ (2?) fell off - a student glued it back on.

"How does it work? I MUST KNOW!"

So there you go - the favourite thing that has nothing to do with instruction. Though "a game your students love to play" was an option, so maybe I'm not as subversive as I think. Related, perhaps I should bring in a tangram next semester.

If you enjoyed reading this, I’m all about the writing. Feel free to check out some of my other posts:
-How Teaching Is Different
-Meet Lissa Jous, over at my math webcomic.

Monday, 11 January 2016

Busy Not Teaching Day

January is the worst month. No question. It’s three weeks until exams, everyone has forgotten everything, and you have ZERO turnaround time to prepare for Semester Two, let alone generate report cards. Yet it’s also the start of the MTBoS “Blogging Initiative”... maybe that will make it better.

The Week 1 blogging challenge is “One Good Thing” OR “Day in The Life”. If you know me, you KNOW which one we’re going for. The question is how will I subvert it? In 2012 I blogged every day for a week. In 2013 I had Weierstrass talk, but you couldn’t differentiate her at any point. This time? Monday Jan 11th? You get a quiz!

The background info: I did NO teaching today - it was all evaluations of some sort. I tend to forget to eat and drink. So far in January I’ve managed at least 7,000 steps per day. I’ve been posting personified math at least once per week for over 5 months. I WILL lose my mind at one point here, which I like to think isn’t is a typical thing.


If you know me, or know teaching, let’s see how you do here:
1. My first drink (of water) today was: (a) At lunch; (b) After school; (c) After 6pm.
2. My loss of mental control occurred: (a) morning class; (b) afternoon class; (c) after school.
3. My step count was: (a) Under 7,000; (b) Average (7000-8000); (c) Above 8,000
4. Views for today's math webcomic: (a) Under 50; (b) Average (50-70); (c) Above 70
5. My meeting 1.5 hrs after school: (a) Arrived early; (b) On time; (c) Arrived late

Answers follow:

6:30am: Woke up for no reason. Weird dream. Sort of back to sleep.
Expona talks to Sine
7:00: Alarm goes off. To the computer to tweet out my new math comic, post it to Facebook, and update the index links.
7:10: Breakfast (cereal), catching up on social media, prepare for day.
7:45: Left house. Cop cars all around; apparently the city’s first murder of the year took place two blocks from my house. Okay then.
8:15: Arrive at school, a bit later than expected, terrible icy road conditions.
8:16: Answer questions from 3 students. (There's always more questions on evaluation days.)
8:29: Get to math office.
8:30: “O Canada”, and announcements start. I keep an eye out in the hall.

8:30-9:45 PERIOD 1 (PREP PERIOD)

I really hate starting the day with prep. It means I wasn’t so productive on the weekend, in anticipation. It means I have little chance to react to email or things once the day does start. I’m much more likely to be exhausted at the end, as you'll see.

I check email; I answered students at 11pm the prior night, not much new. Need to download a new agenda for my math committee meeting at 4:15pm. I double-check solutions for the Finance Task I’m giving today, then go to copy it. Check office mailbox. Photocopier runs out of paper; the fairies didn’t pay a visit over the weekend. I refill all trays.

It’s 9:10am. There’s a funny 4min video about 'how to powerpoint' that I want to show my afternoon class, put it on my jump drive, realize I need to photocopy something else. Now need to wait for photocopier. Run into a former VP in the hall. It’s 9:30am. Now I can get to finalizing my exams, which I need to have finished before end of day tomorrow. Obviously not enough time now.

9:50-11:05 PERIOD 2 (GR 11 3M #1)

Finance Task all period. One person out with a concussion, another is AWOL, so 20 students. Since I wasn’t here first period, I didn’t get to set the date, so it’s (2x+1, x=5) which is cool. Finance means they can use their devices for the TVM Solver, as long as it’s airplane mode, or the TI calculators. Also, open notes.

I get some remarks about the task names I used (Stu Dent and Penny Savour). I’d wanted to take time this period to verify some trig questions for tomorrow and write the derivation of the Cosine Law on the board - latter didn’t happen, spent the majority of this time running around and answering students. One calculator ran out of battery power, grabbed the spares from my desk, put the dead ones in my pocket. (Also, TI calcs refuse to treat a negative and a subtraction as the same. Because they’re annoying.)
My classroom setup. It was a process I blogged about.

End of period, I give them 5-10 minutes to finish up, stapling up the ones done. It being lunch, a student from my afternoon class comes with questions. He’s missing a handout. I go to print it, and I have the chance to grab my lunch (macaroni and turkey), then start eating it while answering questions.

Lunch is 11:05-11:55. The first 20 minutes was getting all my tasks in, the rest was helping students. I didn’t finish eating, I forgot to drink anything.

12:00-1:15 PERIOD 3 (GR 11 3M #2)

Task Repeat. One student AWOL, so 19 students. Still didn’t get the cosine law on the board, because when I went to enter my attendance, I saw I had an email about the student from the morning. Answering it could make my life easier in terms of phone calls, so I try to respond between answering questions in class. With five minutes left in class, I started to lose my mind.

1:11pm: Student with an IEP for extra time can’t stay after school, wants to continue writing in our school’s “blue room”. This is okay, but unanticipated (I try to build the time in).
1:12: More questions about task.
1:13: Question about if I have a stapler. Yes, somewhere, next?
1:14: Question about marks. Go away. (I didn’t say that.)
1:15: Bell goes. I tell students, hand in, tell me if they’re coming for 15 minutes at end of day, or if they can’t, I’ll give a note to be a bit late next period.
1:16: Collecting tasks while phoning blue room, they can accommodate the guy.
1:17: Stapler is found by student, sign on door is directing my next class to computer lab.
1:18: Phoning blue room back because guy needs to use his phone in airplane mode, right.
1:19: Two other students heard call, also have IEPs, want blue room. I’m writing notes for a couple other students here.
1:19:30: Paper cut.
1:20: Five students here, I have to dash to unlock lab for Per4 and dash back.
1:20:40: Blue room is full now, fine, other IEP students can write here, others give me tasks now or come back at end of day!
1:20:50: Student comments that I seem stressed. *YUP!*
1:22: Office calls my classroom asking a question about earlier attendance.
1:30: I have all students’ tasks and notes for lateness are written. One IEP student left, plus blue room upstairs. Run back to lab to actually start my class, already in progress.

1:20-2:35 PERIOD 4 (GR 12 STATS)

1:31pm: Chance to finish Summative Report (due today) and start on Summative Presentation (due next week), I give handout on the latter, answer a couple questions on the former.
1:40: Back to class for last IEP student.
1:42: Back to lab. Call blue room to confirm other student finished.

Breathe? Breathe. Okay. This class is 12 students, down from 23 to start in September (long story). At 2pm I show the little video about 'how to ppt', which I’d intended to show at the start. No other questions. Make the mistake of checking my email. No info on earlier student, need to deal with some Cappies information. One student needs to leave at 2:15. Another student finds a good website for making graphs:

2:25: No questions! Nothing for me to do! I’d check Twitter, since I didn’t get to at lunch, but I think that would be frowned upon. Wait, question. And there’s no markers for the whiteboard in the lab to sketch something. I hate whiteboards. What’s wrong with chalkboards? Or slates? You can at least draw with your finger in the dust on those.

2:35pm: Period done, back to class for P3 students who need 10-15 more minutes. Also a chance to finish my lunch. Also a chance to write Cosine Law on board. And to finish stapling, and double-check counts to ensure I have all tasks. Except stapler runs out of staples. And I have dead batteries in my pocket, why do I have dead... OH, right.


By 3pm, students are all gone, I have found staples, prepared things for tomorrow (will be singing the Sine Law Song!), put away dead batteries, and printed a report I’ll need for my meeting at 4:15pm. There’s some discussion in the prep room, including about a student with a concussion who will need breaks/extra time for the board wide summative and how does that work given the regulations in place?

I need to log back in to check my email before phoning parents about the AWOL students today. Then I phone, in both cases I end up talking to the students themselves, so followup call to work in order. Then need to drop back by office to get the task from the blue room student.

Able to leave at 3:45pm, need to get from Orleans to Downtown Ottawa in half an hour. A reminder that I did NO TEACHING today, yet I’m tired. My step count is 5282, which is higher than average for a school day. Of note, CBC Radio is talking about the local company that makes pants for dogs. Because of the meme this year, they have reached the equivalent of over 3 years of orders in 11 days. Did you know I parodied that meme in my webcomic?
Post with mouse rollover here... this post is liable to do better.

The traffic is in my favour, I make it to my math committee meeting on time. There are snacks. No water yet today. I do secretary stuff for over an hour. We’re done about 5:45pm. For the first time since 7:30am, I check Twitter. My comic has had one RT, I’m at 24 views. Sad. Fire off another tweet, also end up responding to another student related email, and chatting about the Data Course with someone else on committee.

6:05pm: Everyone’s leaving/left. I’m thirsty. I search for a water fountain - find one! First drink of the day!

At this point, I’m meeting some friends at 7:30pm, there’s no point going home. I hang around the meeting room, returning to finalizing exams, like I was doing back at 9:30am. Except listening to Chvrches.

Realize at 6:30 that my step count isn’t going anywhere this way, so start walking in circles as I solve and adjust questions. Yes, this is a thing I do. I get to a point where I should be able to finish before leaving work on Tuesday.

At 7pm, another quick check of Twitter. Discover there is now an MTBoS bot, and Kari has a piano version of “Being Watson”. Even if you're not a Sherlock fan, do yourself a favour and check out Kari's song here, it's one of my favourites. (“I got it wrong, of course. I always do. I’m not sure why I even try. I’m not stupid, but I’m not you.”)

I head out at 7:15pm, step count 7652. Arrive at pub a bit early, pace for a bit to get more steps. Dinner with friends from 7:30-9pm; get to use the washroom for the first time since 7am. Then drive home, put out recycling and take my tie off. My step count is 8654. I have 35 views on my webcomic. I'll need to catch up on "Supergirl".

This is from RDA last week.
And it’s 9:30pm, so I type this whole thing up while listening to “Radio Dead Air” (RDA) with Nash Bozzard. (Who has to do legal homework to run his show, because apparently now small time music streamers are charged as if they’re Pandora. Why??) Lots of David Bowie played, natch. And if I wasn't typing this up, I wouldn't be marking, I'd probably be drawing for my serial, so no time lost. Marking tomorrow.

And now it’s midnight, and I'm done but need to find images for this post. So how did you do on the quiz? How well do you know me? I’m all about the writing. Feel free to come back for another MTBoS challenge next week, find me on Twitter @mathtans, and check out some of my other posts:
-There Are No Dumb Questions: Text Me Never (on textbooks)
-A recap of the OAME Ignite Sessions 2015

Friday, 1 January 2016

Five Webpages, One Post

Last year, I started off 2015 with “Four Webpages, One Post”, summarizing 2014's statistics across all my blogs, etc. So, what the heck, let’s do a round up for 2015 as well! I state five webpages this time, not because I started a new website, but rather because I decided to include my personal NCF site. (I also maintain a website for the courses I teach, but why include that?)

I’m pretty sure this post will make you feel better about yourself. According to what I see on web fiction guide, my serial stats are abysmal, and I’m pretty sure most four-year-old teaching blogs out there also do way better than my math comic. I’ll try for a positive spin though.


Freenet Site. Began: 90s? Info pages only. Didn’t update at all this year.
I had 2,586 hits on that site this year. I'm using this as a benchmark, given it’s a site that may register in searches or archives, but it’s doing basically zilch.


Google Site. Began: July 2011. Posts in 2015: 5. (Up 3)
Contained my math web serial until August 2012, by which point I’d migrated to the blog. Still stores my math song parodies, hence the five new posts.

Total of 1,093 sessions for all of 2015 (and 4,810 sessions all time). Also total of 2,023 page views for all of 2015 (and 14,044 page views all time). This is a change from last year when there were only 617 sessions; there were a few more parodies posted.

FINAL THOUGHTS: Well, it’s an increase. Worse than the benchmark, but I don’t post here much, so it’s fine.


Blogger Site. Began: June 2012. Posts in 2015: 27. (Up 5)
Contained my math serial from July 2012 to May 2014. Resurrected in August 2015 as a webcomic, with a comic every Monday, plus some extras.

12,410 page views in 2015, bringing the all time total to 32,425. Over A THIRD of my views were this year. The massive spike in April 2015 (2,690 views) was someone doing an archive dive, while the lowest month was July 2015 (421 views). Tangentially, the Facebook page had 18 likes in December 2014, and it’s now at 25 likes (which allowed me to get a bookmark, mathstans).

With now 187 total posts, we’re looking at 173 views per post, higher than last year. Views HAVE been on the decline though - new posts in August regularly got over 100 views, which is now down to ~70. Which has me wondering and sighing a bit. The post “Ahead of the Curve” (from March, forecasting a return) was the most viewed at 857. I have no listed “followers” here (unlike my other blogs).

FINAL THOUGHTS: I do this page more to amuse others. It is doing better than I thought - way over the benchmark. I must remember the higher month view counts (like August) are outliers, and we then regress back down to the mean/average. I still wish I had any sort of brand recognition whatsoever, but for now, I think I can live with this.


Blogger Site. Began: August 2012. Posts in 2015: 53 (Down 3)
Post total is slightly artificial, in that 15 of the posts were reruns of my “There Are No Dumb Questions” column, the majority of which were written for MuseHack in 2014. But even without them, there has still never been a month without a posting.

The (new) huge spike in April 2015 at 4,113 views was due to me writing an April Fool edition for someone else's piece of serial fiction. “Legion of Nothing” had been going for over six years at the time, so my post “Guessed Writing 2015” garnered 1567 views.

The prior year (2014) no month was below 2,250 views; this year (2015) February, March, May, June and September were all below 2,000 (the worst being Feb). Total of 28,747 page views for 2015, and all time total of 84,087 views. This is worse than 2014 (which had over 30k views even without January), but I did post less. I have five listed “followers” here.

FINAL THOUGHTS: Most of what I post here is for me, with maybe tips or recaps for others, so I’m fine with those numbers. Though the knowledge I will likely never again have a post as popular as “Guessed Writing” is a bit depressing.


Wordpress Site. Began: August 2014. Posts in 2015: 76 (Up 51)
I posted every week - even over Christmas this year. Plus bonus material. Granted, “Time & Tied” (which began in April) is more an exercise in editing and drawing than writing, but that still takes time.

What estimate would be too low for hits here? Brace yourself.

I discovered that Wordpress does an “Annual Report”: There were 2,208 page views (to a total of 2,707), with the top day being April 1st (58 views) - see my April Fool guest post remarks above. This is BAD... total views per visitor in 2015 was a mere 2.85 pages.

The posts with the most views were “The Gathering” (first epsilon proj), “Timely Discovery” (first time & tied) and Time & Tied’s “Awareness Index” - start pages, which implies no one kept reading. The only people to comment more than once were Scott D, John Golden and Education Realist. Random aside, the Time & Tied Facebook page has 6 likes.

I saw hits from 44 countries, though mostly the US (1,000+), Canada (500+) and the UK (170+). Best month was May (359 views) the month Billy Higgins wrote me a review at 'Web Fiction Guide' (WFG). Worst was September (91 views) the first time I dropped below 100 since the blog began. November was on par to be worse, but there was a surge from 'WFG' in the last week to offer advice on my site design (not the writing itself). I have 4 listed WP “followers”.

FINAL THOUGHTS: OW. I posted the MOST here and got the LEAST to show for it. Why the hell am I still writing fiction? (Because I enjoy it, natch.) SOME people out there read it... right? It’s the pictures or navigation that’s a turnoff, maybe??

Alternatively... what if WordPress simply has a more aggressive spam filter? What if these numbers are the only TRUE ones, as they remove all the hits from bots and the like, which Blogger includes? What if my whole online life is a lie?! ... Surely not.


My best Tweet was Oct 20th, it got 43 RTs and 56 Faves (not likes) because it was ReTweeted by “FiveThirtyEight”. It wasn’t for my stuff (it was on “World Statistics Day”), but I even got my tweet on their site, brought to my attention by David Petro, so that was neat.

A week ago, I used one of the Twitter Apps that determines who mentioned me the most in 2015. (Might have been only the latter half of 2015, it was a bit unclear.) Here were those results:

Not quite 600 mentions overall, so between that and the small number of likes on Facebook, it would seem social media is not working for me.

So, that’s where we’re at! In total, I posted OVER 150 TIMES THIS YEAR. If we're searching for positives, that’s not bad. If the webcomic site continues alongside the serial site this year, it may end up being about the same for 2016, so hopefully I can at the least maintain the viewing numbers too? What do you think?

Farewell to 2015, all the best to you in 2016.

Wednesday, 23 December 2015

Drawing my Math Webcomic

Almost three years ago, I wrote a post I called "Drawing for a Webcomic". Back then, what I was really doing was illustrating a serial. Now, it's a legit comic. So I thought I would update the post, in part because I feel like I'm terribly inefficient. Let me know if you agree.
I'd ask Koch, but he only speaks in riddles.

STEP ONE: The script

I write the script in TextEdit on my Mac. Usually about four comics worth at once (roughly a mini-arc), which tides me through a month (I publish every Monday). That said, episode titles and mouse rollover comments tend to be put in the week I thumbnail, unless a really good idea strikes me sooner. The script is also extremely flexible, as you'll see.

STEP TWO: Refining the mental image

This step involves thumbnails, effectively a tiny version of the finished page. I learned about the technique at Anime North 2015, and it makes lots of sense. My thumbnails are set up in columns, even though my final panels are a 2x2 square, in part because I hadn't decided on that format when I started, and in part because I find it easier to fit 8 on a page this way.

You can see strip #22's thumbnail pictured on the right. After drawing it out, I realized I'd put Expona on the wrong end of the bar - she'd be looking off the page in Panel 4, hence my arrows and remark "look left" (to have her face the prior panel). This is where I try to vary the character sizes between close ups and long shots.

STEP THREE: Refining the actual image

I jot down the script (more or less), then fit in word balloons before sketching. This step usually takes a couple of passes, one for the overall setting/character location and one for the detail. Sometimes I will do that on a panel-by-panel basis. Here, still with strip #22, I made two overall passes so you can see the difference.
First pass - words and positions

Backgrounds are a pain in the ass. First, because although this step alone takes about two hours (half an hour per panel), it's somewhat mindless work. Unless I have to account for the position of things in the background - that needs thinking! And I cannot simply drop in a prearranged background, because of how my perspectives zoom in and out.

I had no idea how annoying backgrounds would be when I wrote my "Xeno: Paradox Princess" parody, which required objects for the protractor/chakram to hit. I now hope to avoid objects wherever possible. There's also the fact that I will usually need to do a web image search for a frame of reference with a new item, like the exterior of the "Bowditch" here.
Second pass - Faces and detail

Above, you'll see the second pass. I added a shot glass onto the bar, to try and fill the otherwise empty space. The 'Hmm' in Expona's thought bubble (Panel 1) was an addition for the same reason... and while that word will be at the start of the sentence, the lettering itself is a full step later on.


Essentially a third pass, using black ink. Sometimes I catch minor mistakes here, like the fact that I missed drawing Expona's watch in Panel 2. Basically, this step is exactly the same as it was three years ago. There's merely more ink needed.
Third pass - Refinements

You may notice, I don't ink the panel boxes themselves. That's because they're merely guidelines for me when drawing. Ditto for the words, in fact they'll get erased out (see lettering, below). This is the point when I would ACTUALLY scan the thing in. On the same printer I had three years ago, which only my old computer has drivers for.
Pencils erased, scanned in now

STEP FIVE: Panel Template

At this point, I take the scanned image and grab it, panel by panel, dropping it into my panel template file. The "Any Qs" and copyright are already on there. Aside from those, the template is a 2x2 grid, all panels the same size, and it is layered such that I can put the image under the lines. I grab my squares (as square as possible), then shrink the panel layer down to about 300 by 300 pixels (so roughly 25%). The title also gets grabbed. This is the simplest step, but if I drew outside the guidelines, sometimes I'll need to resize and regrab.
Dropped into the template

STEP SIX: Lettering and Cleanup

I'm getting better at judging the spacing for word bubbles. But sometimes I misjudge, or need to rearrange words in a sentence so they don't escape. This time, I decided to have Expona say 'Trigonometry' rather than 'Trig' in the last panel, thus had to pull her word bubble further apart (rather than pushing it closer together). The text is inserted line by line (line breaks are never positioned properly).

The font I decided on back in August was Candara, size 18. Why? Well, it's free. Also, it has a boldface option that's basically the same size as regular text. (When everything is in all caps, you need boldfacing to imply capitals. With this font, I can simply type over an old word with a boldface version.) It doesn't do "Crossbar I's" though, so I have to adjust those manually.

If you don't know what those are, have a look at Expona's last dialogue bubble: "I MEANT IS THERE..." The first 'I' is on it's own, and thus needs top/bottom bars, whereas the 'I' in 'IS' is merely a stick. Incidentally, the 'LISSA' tag in Panel 3 is a different font, Optima. I don't recall why I decided to change it for character intros.

Once the words are in (and script readjusted), with their bubbles being digitally fixed, I tidy up any other pencil markings I see; areas where I extended a line too long, etc. Then I flatten the whole thing (removing layers), resave it as a PNG, and get ready for the next step.

STEP SEVEN: Colouring

I do this the same way I did three years ago as well - basically reach into the prior file, grab the last image of the character, put it (temporarily) on a new layer, grab the colours with the eyedrop tool, and use them on the new strip. If there's objects being introduced (like the Bowditch here) I mix colours up a bit and see how they work out. The pinkish (on the sign and the stool) was to coordinate with Lissa's hair.
You can read this comic in context too

Sometimes final touch-ups are needed. For instance, I noticed that the shelves looked a bit like sequential bars stretching backwards, so cut and pasted a new line for more dimensionality.


I now transfer everything to my current computer. I have the "Next/Previous Page" table in a file that I can cut and paste into the HTML (exactly like my time travel serial). The comic script can then be pasted underneath that, though sometimes I'll simply retype it. The mouse rollover comment is added through the HTML. After the post has gone live, I can finally add it to the table of contents.

And that's it! The whole process likely takes between 4 and 5 hours, but it's rarely done continuously; I take breaks before the image is inked, then sometimes after scanning and/or before colouring. Three years ago, it apparently took less time, but I was doing less of it.

Now, is that process terribly inefficient? Is it even worth it? I suppose that's for you to answer. Let me know below. Thanks for reading!

Wednesday, 9 December 2015

TANDQ 15: Animated Discussion

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 fifteenth column marks the last in the series. It originally appeared on Thursday, June 2, 2015.

Should TANDQ be resurrected in 2016? Well, if so, what would you want to read about?

What animation is acceptable at your workplace?

There’s my question to you. As I’m not at your workplace, YOU tell ME (in the comments, or email if you prefer) - what is your workplace, and what is the threshold of acceptance there? Would you be allowed to have, say, “Despicable Me” minion figurines at your desk? A “My Little Pony” poster? Could you wear a “Sailor Moon” brooch on the job? Yes, I’m trying something a bit different here, turning this last question back to you. I’ll explain why the subject came up, then provide my own answer too.

This particular idea came out of a panel at an anime convention regarding “Fans in the Professional Workplace”. On the panel were a lawyer, a banker, a teacher, a graphic designer and a librarian. (I’m simplifying the job descriptions slightly.) Now, obviously there are lots of fandoms out there… and on a related note, I recommend checking out the recent “Fan I Am” series of postings by Steve Savage. (Have you considered politics as a fandom?) But I’ve decided to target animation. Partly because it was the primary topic at the panel, but also because there’s a lot of conflicting information about it on the internet, and out in society.

There’s this notion, particularly in America, that animated films are “children’s entertainment”. But are those attitudes changing? Or are we merely expanding the demographic? What about outside the US? The more I look, the more I feel like animation has lots of misconceptions tied to it, perhaps because it bridges so many different genres. Even Ben Zauzmer, who used data and statistics to predict almost all of the 2015 Oscar winners, missed out on his prediction for “Animated Feature”. (For that matter, why didn’t “Lego Movie” even qualify?) So when an audience member in that panel I attended indicated that she was soon graduating from post secondary, and essentially asked how much one could or should put anime out there, I was intrigued. It felt like something relevant for this website [MuseHack]. But there was no clear answer - as often happens with good questions.


To be clear, I’m not talking about whether it’s proper to engage in your hobbies while on the clock. Nor am I suggesting fandom should be completely excluded from a resume, given the lessons it provides that may be relevant to your career. What I’m looking for is the middle ground. Can one person name drop “My Little Pony” in a workplace with the same ease as someone else drops “Game of Thrones”? Remember, one of those shows involves rather more violence and death! Well, it turns out the answer is likely no, as “FiredBrony” found out in 2013. (See my “You Can Be Fired for This” link below. Though let’s not pretend the issue is specific to gender.) So I ask again, in an age where new graduates are worried about simply getting entry level jobs, which workplaces are more accepting of one’s interest in things like anime and animation? My suspicion is “Your Mileage May Vary” (YMMV).

I’ve done some online searching, but figure it’s better to hear from those with actual experience. To that end, let’s first consider the people on that panel. The lawyer had to be totally undercover. The banker was mostly undercover, in part because when she was a summer student, she’d had complaints from older people at work about her reading manga on her lunch break (seen as “unprofessional”). The graphic designer could get away with subtle decorations (like an anime belt on casual Friday), but wouldn’t comment about it randomly. The teacher could potentially say something depending on the audience - for instance, recognizing a Totoro shirt is a safer move than recognizing “Kill la Kill”. And towards the other end of the spectrum, the librarian could discuss anime and manga with coworkers, and even use it to connect with people when done correctly.

While we’re on the subject, some other thoughts that came out of the panel was how the mention of anime (like volunteering at a convention) could make your resume more memorable - but you may also want to look up the hiring manager on LinkedIn to see what the company expects. There was also mention of the fact that, if you type in “The Manga Guide to” into a search engine, you’ll find they’re being used as a learning tool beyond the high school level. Someone’s even doing their PhD as a graphic novel. Is there a generational divide forming? At minimum, I suspect the definition of “professionalism” may be evolving.

Anyway, here’s my answer: I’m a high school mathematics teacher. As the teacher advisor for the anime club at our high school, I have some anime CDs on my desk, and occasionally discuss it with students. I could discuss it with coworkers, but there isn’t much interest. I haven’t thought much about American style animation; I’m no fan of the Simpsons, but I don’t get hassled for that. How about you?

For further viewing:

1. Yes, for the Millionth Time: You Can Be Fired for This

2. Why animated films are the UK’s favourite - and why that’s not likely to change

3. History of Early Animation (video)

Gregory Taylor is a high school mathematics teacher in Ontario, Canada, who does serial writing in his spare time. He can be found on twitter @mathtans, and runs a few blogs including "Mathie x Pensive".