Monday, 27 April 2015

Public Math Relations

Back in September (Sep 16, 2014 to be precise), the local Ottawa math association (COMA) had a social event. At this event, Marian Small was invited in to talk about “Our [teacher] relationships with Parents and the Public”. I made a bunch of notes at the time, as I often do, with the plan to post them up later. Welcome to later!

Any errors are my own. In particular, sometimes a remark can be interpreted in multiple ways, so you’re seeing my viewpoint below.


Marian began by acknowledging how teachers can be “caught in the middle” (between policy and the public). The media may or may not end up offering factual arguments about curriculum/implementation, yet that’s what most people see. So, when speaking with others, a teacher must be honest, informative, and professional, yet divorce themselves from professional language - don’t sound like the ministry, sound like a “regular person”. And don’t talk about ‘buts’ (eg. “I do this, but sometimes...") since once an already insecure parent sees a possible weakness, it’s over.

With respect to mathematics education, the same big questions tend to come up.

“Do students have to know their times tables?” YES. There isn’t a debate here, the real issue is whether there is only one way to learn them, and whether that way is best for everybody.

“Is knowing the facts the key to success in math?” While it is extremely important, it is not a KEY to success. (An excellent K-5 resource from Alberta clarifying ‘basic facts’ for parents is at this link. It’s a result of a reporter in Edmonton who published numerous articles.)

“Are students still learning the ‘right ways’ to do mathematics?” Let’s look deeper at that one.


IS THERE a “right way” to learn mathematics? After all, in different countries, different ways are right, who’s to say our convention is any more or less right? One could argue there are “more efficient” ways - but our whole lives are inefficient, why should math be so different? “How many 9 year olds do you know who are efficient?” Besides, is the “standard algorithm” always the most efficient? (NO: Consider 300 - 2. Or using quadratic formula to solve x^2 = 9.)

Does that mean we should force kids to use multiple strategies, or merely expose them to multiple strategies? Consider, if you look at a curriculum document (in Ontario) there are many mentions of “multiple strategies” - it doesn’t mean we always require 3 ways to solve a problem. We can, for instance, differentiate assessment OF learning from assessment FOR learning (show many in an instructional situation, then the student uses one for an evaluation).

Aside: I hate those BEDMAS Qs on Facebook.
Calculators! “What if the calculator fails?” Well, “do you keep a horse in your garage in case your car doesn’t work?”. (It’s not recommended you say that to a parent, but as long as students are able to recognize when the calculator is giving them a bizarre answer, why not use them.) And what if the child encounters “hard” numbers? A better question is why ARE they encountering those numbers - we can choose what we should have them do. (When things are simple, they can do more in their head!) And while authentic problems do involve “hard” numbers, many questions we ask in school are not authentic.

Homework! “Don’t they have to practise?” What does ‘practice’ look like? It could be 30 questions that are very similar, or one question like: “You multiply two numbers and the answer is about 65 less than if you add them. What might the numbers be?” This can engage a student for an extremely long time. (Leading to: How do we get a LESSER product? A fraction, a negative?) Practice is not always obvious. Unfortunately, there is also no way to be RIGHT when a teacher is answering a question about homework - some parents will always love you or hate you, and different places have different rules. One rule of thumb is ‘multiply your Grade number by 10 to get number of homework minutes’.

A key point: If homework is confusing, it might do more harm than good (it should not make things worse, and reinforce errors). Should it be about rote skills? Sometimes, but there can be more conceptual things that aren’t difficult to try. (For instance, “You have two fractions. If you add, subtract, multiply and divide them, what is usually the order from least to greatest?” Exploring that can be lots of practice.) What if you offer homework but don’t require it or mark it? Pro: Homework for marks is a problem anyway, you don’t know who did it, plus no marks makes it low risk, a chance to make (and fix) mistakes. Con: A lot of students/teenagers may not make the right choice in doing it.

“Why are textbooks so wordy and unclear?” In real life, nobody says “Subtract now!” (with the exception of Revenue Canada). People won’t tell you what to do, applying math in life is a different skill than performing calculations. (Besides, how do you describe a problem without words?) While new digital tools can make math more oral (hear instead of read), in books things have to be written down. That said, perhaps oral responses can be an additional option, if it gives a better sense of whether the student understands.


“Why do we have to learn things in a different way?” Lots of people today may know their times tables, but are still anxious about math. Change is needed. Yet “discovery” is not a good word - how can you discover if you don’t know the basics? Well, think about how we learn to do new things. Do we read the manual first? Or explore first, and check later? Some basics do come first, but lots can be learned through investigating and inquiring.

It's not all about that bass.
Marian presented her “music teacher analogy”. If a kid is doing piano lessons, do you want to choose the teacher whose kids are winning competitions? It may be that they play the same pieces over and over, to get the theory perfect first. However, if the kid can also play what they want to (popular music?), won’t they stay with it longer? We need to teach that there IS some tedious stuff, but also some playful stuff, so that there’s more of a sustaining effect. You can also make a sports analogy, the idea of dribbling endlessly before playing in a game... math is a like a game, and you can teach the needed skills in the course of playing it.

“Why is my child always working in a group?” These days, it’s less likely that we work in isolation; even in university/college lots of work is done in groups. Teaching problems can also be talked about with colleagues. More to the point, we need to focus on getting students cognitively ready, not merely structurally, since later structures will be different anyway. (Now, evaluating in groups is a whole OTHER question. We need to find strategies to deal with that.)

“What do you think of [Kumon/Khan/flipped classes/etc]” Nothing is right/wrong or good/bad, it’s more complicated than that. Be respectful. The issue is whether such things are effective as the main event. If you think drill will garner success or cause enjoyment, likely no, but if the student needs skills, then yes. Of note: The goal of math is not solving a problem. Math is learning how to think in mathematical situations.


We used to believe that the best way to learn facts was to sit down and repeat them over and over. We now realize that you are ahead of the game if you have more strategies to fall back on. Even though some kids memorize well, for kids who are anxious about math, having to be quick and use the old strategies dooms them to failure. Moreover, research tells us that effort and persistence account for more variability in scores than native intelligence. “Hard work and good study habits are effective. Bad attitudes are a killer.” Telling a student you believe s/he can do it works - but no guarantee! Similarly, a parent saying they’re bad at math is an invitation for kids to tune out.

Temporal paradox? Seems legit.

What can I do (at home)?  Number play. Avoid saying “That’s hard” just say “Let’s do it”. Marian’s theme is that math classes should be about thinking and not doing. Estimation is important, and there is learning through problem solving. eg. “I bought something for $10. She gave me back one bill and 4 coins. How much might the item have cost?” Counting dots on a piece of paper is hardly exciting, but counting all the spoons that exist in your house, that’s kind of interesting. Or sections in an orange (do they always have the same number?). Consider rolling two dice - you can double one result then add the other, the first player to 100 wins. Consider a strategy. Support involves not showing, but probing.

What is success? Not just a mark. In the last round of EQAO (the Ontario Grade 9 equivalency test), 93% of Grade 9 kids said they hated math. (Aside: Ontario is the only province that makes you report on five strands in elementary, no other province does that.) Enjoying the math is success!!! So you, the teacher, need to show that you enjoy math too. Show confidence, believe that the student can do something if you give them the time. Meet your audience where they ARE and take them somewhere better, rather than starting above them - they may not want to listen/climb.

In the end, you’re the manager of a classroom the way there are managers in a workplace. “Make stuff happen.” Don’t simply stand there.

Marian’s website:

Wednesday, 1 April 2015

Guessed Writing 2015

Back in January, over at the “Web Fiction Guide (WFG) Forums”, Alexander Hollins proposed “an old favourite”: Writing an ‘April Fools’ update for another serial writer. (While they write for someone else, etc.) What I said at the time was, I liked the idea of getting into someone else(s) head, but wasn’t sure that my present serial would work for someone else. After some encouragement, I signed up anyway.

This is what followed. There’s spoilers for the entry I wrote, if you wanted to read that first.


If you know me, you know I like playing with people’s expectations. My thought going in was: Can I write something that mimics the style of the original author closely enough at the start that it won’t be immediately recognized as fake? (Makes the foolishness that much better.)

I was then assigned “Legion of Nothing”, written by Jim Zoetewey. First, I recommend checking it out, in particular if you enjoy “superhero” and “slice of live” kinds of stories. (And while I won’t be revealing plot details below, there are some spoilers about the LoN universe. If you don’t want those, stop here.) Second, WHOA. Good thing I’m not easily intimidated.

On the one hand, I know Jim’s a regular guy, just like anyone else. But on the other, his story had been running continuously since late 2007. It’s got it’s own TV Tropes page, had a successful Kickstarter towards becoming a set of ebooks, Jim himself is a WFG Moderator... and I’m used to writing for a dozen people who rarely comment, whereas a dozen comments seemed like a SLOW day over there. Okay then!

"I'm going to read your thoughts!"
When the assignment came out, I was also in the middle of January exams (I teach), so the weight of this didn’t hit me until early February. It left me with a new question: How does one create a spoof that keeps to the style and characters of a serial with such history?

The simple answer is, you don’t worry, you write something silly and be done with it. Still, while it’s all in fun, for me, that felt too easy. In particular, you have to know the rules in order to subvert them properly, and I didn’t know the rules of Jim’s universe yet (beyond the fact that he seemed to write in first person). I decided that I wanted to learn the rules, and that reading was the best way to do that.


I started reading “Legion of Nothing” sometime around Valentine’s Day, 2015. We were supposed to read at least the last two months of our assigned serial, but I started at the beginning, ambitiously deciding that I would read as much as possible before skipping ahead. (Spoiler: I read all of it. It’s very good.)

I also read (or browsed) every post’s comments. Partly because I’m nuts. Partly because I figured this was the audience I’d be writing for, so I might as well get a sense of their preferences. Partly because Jim would sometimes remark on details that didn’t fit the current narrative. (Ergo I knew about the underwater jet entrance before it got used.) Finally, because the remarks could be funny. For instance, someone commented that “the Shift” is Irish slang for making out; I never did find a good way to incorporate that.

I refrained from commenting on posts myself for two reasons. The first is that it would take precious time away from reading, and I was on a deadline. The second is that Jim would have to approve my first comment, and from then on, constant remarks through an archive dive might spoil the surprise to his readers of who was writing in April.

So instead I, uh, stored about 80 comment flags/assorted typos into a text file. To flesh out into comments for later. I suspect Jim Zoetewey will either like me or hate me when this is all over. (Sorry Jim.)

Any "Natsuiro no Sunadokei" fans out there?
Anyway, in Book 1, Arc 4, part 19, a character named “Future Knight” appeared. Time travel was possible (or at least accepted) in Jim’s universe! That’s when I created the text file to start recording thoughts/comments. If you have no idea why time travel makes me SQUEE, feel free to read this post about “Time & Tied” (formerly “Time Trippers”), the serial I’ll be starting this Friday.

So, “Legion of Nothing”: a universe of superheroes, teenagers, and potential time travel, the last two of which are completely in my wheelhouse. Somewhere in reading Book 2 I decided I would either do whacky time travel, or subvert the story with an “unreliable narrator”. (Tell the story as if it was Nick, but it turns out to be someone else.) I rejected the latter once I realized that Jim had also written parts from the perspective of other characters.

Which gave me pause. What if he’d already written an entire time travel arc too? “Rachel in Infinity City” looked particularly suspicious, but I was only in Book 3, and didn’t want to jump ahead yet.


As it so happens, this is when I ran into the last time an “April Fools Update” was applied to “Legion of Nothing”. Except owing to a miscommunication, it didn’t happen, instead there was a multi-part crossover epic that was ultimately adopted as canon. While it didn’t exactly use time travel... could my idea could be seen as derivative? What would people think? What if they thought I was trying to write something canon too? Was that good or bad? WHAT IF I’M OVERTHINKING THIS?

Ahem. This is for fun. I will keep reading.

By Book 4, my entry was starting to take shape in my head: Nick vs. the Time Bandit, but we never see her, only the fallout at some point in the past. Which I realized would best be served around the present of when I was reading. Sweet. Two ways I could take the ending: A reset, with everyone going ‘WTF?’ or some ‘OMG we’re now trapped in an alternate timeline’ scenario. The former appealed to me more, because I could have Nick himself push against the fourth wall.

Wait, what if the current Arc isn’t from Nick’s POV? I might need a new plan. I jumped ahead for the first time to check out the present. Okay, still Nick. I gotta stop overthinking this.

I got into Book 5. Rejected thoughts by now included Rachel using Nick’s guitar weapon as a real guitar, Nick charging up a time machine attachment by jogging in place, and a time travelling wardrobe falling onto their power impregnator. (Uh, if you haven’t read "Legion", you are likely confused.) Instead, mental time travel felt right, I think because I re-read Alex’s assignment message which offered “Gender swap a character. Switch brains.” Easily done. And I kinda wanted to mess with Daniel’s head (a "Legion" character).

I started writing my “Fool” entry the weekend of March 14th, a month after my first read - I’d only just gotten into Book 6, but figured I wouldn’t see anything new that would cause a serious deviation in Rocket’s personality. (For that matter, the Time Bandit stuff could easily have happened before Book 6.) I finished reading “Legion” up to the present late Sunday evening, showed the entry to my wife for her take, and sent it to Alex before going to bed.


There were only minor revisions after that. If you haven’t read my entry yet, you can do so here. I tried to keep it a length within the realm of Jim’s usual entries. I also recommend you check out Lucy Weaver (or possibly Rachel Flowers?), who wrote this entry for me. (She writes the serial “Tapestry”.) She also found a clever way to use the characters without knowing where the plot line would go in the two weeks leading up to April 1st.

The guy in the back has a story too...
Now, readers for “Legion of Nothing” may notice that, in the end, my entry used the core characters, even though there are many more secondary ones by now. My thought was this particular focus could help boost Jim’s readership (via my blog, or others in the WFG forums who didn’t already read - assuming such people exist). I’ve started second guessing that, because they’re the characters that regular readers already know so well. Did that work?

I’m also not sure about setting the story in the past any more, lest people think I didn’t read the recent stuff, and whether wrapping it up in such a tidy package was a good idea, given that it’s supposed to be silly and non-canon. Not silly enough? Too silly?

Oh well. It is what it is. Thanks for reading about the process! My time travel serial will be starting up this Friday, if you want to read more by me.