Saturday, 31 May 2014

Self Publishing in Canada

I went to a panel at Anime North 2014 called "Self-publishing & Marketing", because the former is something people are suggesting to me, and the latter is something I'm terrible at. Here's a rundown of what took place, with a bunch of embedded links. (A more in depth report of AN2014 will come... well, after the in depth report about OAME...)

This was a one woman panel by JF Garrard, president of Dark Helix Press (more on that below) and multicultural fantasy author. Her first book ("The Undead Sorceress") came out in April, and coming soon is "The Literary Elephant" (subtitle: A beginner's guide to indie publishing). She handed out some info and book codes at the panel. She's also blogged a few times at AHA: Authors Helping Authors, so if you want more information about her publishing journey, go have a look there.


JF mentioned that there are three ways to publish - Traditional, Vanity, or Self-Publishing. The traditional route involves Query Letters to publishers, and may necessitate you getting an agent. If you end up selling your product for $1, publishers would take 70 cents and the agent 15 cents, leaving you with the remaining 15 cents. Of course, publishers often won't often take big risks and the market is ever changing.

Vanity publishing gives up a lot of your control, and will cost money, but the trade off is you have less to do. They'll handle things like copy editing and marketing... while potentially taking some rights to the work, and summing things up in monthly reports (ie- you may not know how many copies you've sold at any given time). Then there's Self-Publishing. It's entrepreneurial, and like building a house, there's a lot of overhead - the publishing step itself is actually easy.

FIRST: Editing. Probably the most costly step, if you want to do it well, because editors charge per word. This isn't "proofreading", this is looking at the plot and the continuity of characters and setting. A few websites tossed out were "" (cheaper but more amateur) and "Preditors & Editors".

SECOND: Formatting. Make sure your gutters/margins/page numbers are done properly, particularly if you're going with a print book. (The digital route makes things easier to take it down, reformat, then put back up - though I imagine that will cost money and readers.) There are online templates (see "Smashwords"). Also so many FONTS! Notably an eReader audience can change fonts after the fact if they want, and there's a reason Times New Roman and Ariel have remained popular through the years.

Or do your own art! ... Maybe not.
THIRD: Cover art. If you get someone else to do the art for you, they retain the copyright. That means if you want to use the image for anything other than your book cover (bookmarks, postcards, basically anything in terms of marketing) you'll need the artist's permission... unless you buy the copyright from them. This was recommended, as it then becomes a one-time fee, you won't have to constantly check back with the artist, and you won't have to worry about a possible veto. The artist for JF's book even asked her straight out if she wanted the copyright. Make it legal, draw up a contract, agree on a cost that isn't prohibitive (maybe $25), and let the artist keep the work in their own portfolio.

As far as the art itself goes - try to be very specific. Provide references to the artist for what you have in mind, using multiple visual sources if necessary. (Wouldn't you be annoyed if you got a vague description, then sunk hours into something only to be told "no... something's not quite right"?) If you're creating your own fantasy setting, you might also want to consider having a map made, and included inside as a reference.

Now, the business side. At this point, we'll be getting into some more uniquely Canadian issues.


FOUR: Picking a publisher. A lot of self-publishing sites are owned by US companies (and the exceptions are International companies). They'll take 30% off the top of your proceeds to go to the IRS (Internal Revenue Service), unless you have an exemption number. So you'll have to deal with getting that. There also aren't any Canadian platforms (except Kobo which JF didn't have any info about), and there's bandwidth charges depending on the country where your book is bought (eg. between Canada and Europe). If you're creating a big novel, you may want to go with a flat rate on bandwidth.

The good news: In Canada, your ISBN (International Standard Book Number) is free. And if you own the ISBN, you are the publisher, not "Amazon". (Apparently in the US an ISBN costs something like $100?) However, you do have to register for the number, and there's a lot of forms and waiting periods involved. Begin by setting up an account with Library & Archives Canada (even that has a waiting period of a week as they verify you're a real person). Different ISBNs are then needed for hardcover, paperback, and electronic versions of the book, so get some "en bloc" (seemed like they give you 10, then you have to use all of those before you get more). Once you have the number, you can generate your own bar code and add it into the book.

You may also want to consider incorporating yourself as a company in order to publish. An audience member pointed out that there are tax benefits if writing isn't your primary job - the increase in income can be held within the company, and corporate taxes are going down. JF was originally going to publish within her husband's company, but decided to create her own ("Dark Helix Press") instead, as her husband's company is technology based. But wait, there's more!

You can be a Federal or Provincial Corporation - and it's best to go with the former. With the latter, you would need to re-register your company in the other provinces in order to sell your book there... and you may not be able to if your company name is already taken out-of-province. Which leads into the problem of name generation. JF: "All animal names are taken." She figures she lucked out with "Dark Helix" because "Dark" might have been seen by others as negative. Don't have your heart set on a name is what I'm implying here. You may also need to look into your "author name" if there's a lot of other "John Smith"s out there.

Okay! You now have an edited, formatted book with a cover and the ability to publish. At this point, publishing itself is EASY. Twelve hours after you upload it, it will be live. But there's still STEP FIVE to consider before you tap the 'Enter' key...


Marketing is a black hole. Do we even know what works? Who looks at billboards and ads?? If you take the book personally to places, between the trip, hotel, and meals, one hopes you can break even. One thing for certain: You'll need a WEBSITE. People will want to know more, like have you written anything else. You can get a free website with blogging software. (I've also learned that a domain name is pretty simple, I registered "mathtans" with "".) Personalize your site. "If someone is going to do an interview, they're not going to interview your book." Be a person online. You also cannot be an 'introvert writer' here, you have to get the word out, or at least get other people to help you do that.

A word about Kickstarter campaigns. It's a good way to test the market and raise interest while getting funds, but be careful what you promise. If you're pre-selling your book as an incentive, you're committed to following through. You'll also need to do constant campaigning not only during the run, but also provide updates after the fact so people know you're making progress. Rob Barba has a good set of articles about setting up a Kickstarter over at MuseHack, just do a search on that site.

Consider also online forums within your genre of book - both Goodreads and LinkedIn were commented on. Online radio shows are often looking for guests, and if it goes well, you might even be invited back. By the way, all of this stuff should be looked into before the actual publishing date. For more information on Marketing and things like "Blog Tours", I recommend reading my summary of Linda Poitevin's session at CanCon 2013. In the end, don't expect to earn $50,000 from self publishing, that sort of income is likely reserved for an author who was already known after going the traditional route.

There were questions all through this session, a lot of which I've incorporated; one that came up at the end was the idea of a serial novel. (Wasn't me.) If you're planning to publish "chapter by chapter", how does that work with ISBNs? Each book needs a different ISBN, but the ISBN allows people to look up the work as a whole... so it was thought that you could use the same ISBN for each chapter, then again to publish as a whole. Anyone else know about that? There was also a media group present, "" who were recording this session (and a number of others at AN), so you can check out their site in about a week's time.

Also going to throw in a plug here for my friend Andrea Milne's set of posts about self publishing. And her book that resulted, if you like dystopian novels with female protagonists.


I am not the sort of person to jump into things without considering all the angles - and this session helped me to do some of that. In the end, could I self publish? Well, no - not and be a teacher too. I know other teachers have, but I always seem to have too much on the go. Which isn't to say I'm ruling it out (and I am planning on taking some leave) but I've already sunk tons of time and energy into one failed project. I need time to fully analyze that one first.

That said, if you're willing and able to self-publish, all the best to you! Hope this panel summary was of some use.

Friday, 16 May 2014

Teaching Paralysis

So far this month I've attended two math conferences, plus I've been part of a lesson study that involved collaboration with teachers from other schools in my district. Much of the discussion has involved what are (to me) radical shifts in pedagogy. Randomized groups. Unsupervised learning. Moving from abstract to concrete. Vertical surfaces. Experimentation.

There is a scene from the "Star Trek: The Next Generation" episode "Ethics" that often plays in my mind. (It's actually a pretty mediocre episode in my opinion, save for this debate.) I've found a copy of the scene online... Picard and Crusher discussing whether to allow Worf to undergo an experimental treatment.


Here's the two lines that I'm going to pick apart:

Picard: He can't make the journey you're asking of him. You want him to go from contemplating suicide to accepting his condition and living with a disability, but it's too far! And the road between covers a lifetime of values... beliefs... he can't do it. But perhaps he can come part of the way.

Crusher: The first tenant of good medicine is never make the patient any worse. Right now, Worf is alive and functioning. If he goes into that operation, he could come out a corpse.

Here's the thing. Part of the way no longer feels sufficient. So if I can't make a full conversion, maybe I end up leaving the teaching profession. I've seen the research, I know where we're headed, and I know the benefits of applied math and group work, but right now it's still too far from the core of who I am. And the road between... you know the rest.

Some teachers are able to pivot and try new things right out of the gate. Others feel energized by the learning that occurs in an unstructured environment. There are also those who are very good at coming up with tasks that involve "real world" mathematics. I am working at all of this, but it feels harder with every passing day. I used to be alive and functioning. Now, going though this shift, I feel like I'm going to come out a corpse... or at the very least, as only a ghost of my former self.


Part of the problem is that I am very much all-or-nothing. But the all (at once) is too much, while the nothing is unfathomable, which leaves me spinning like a top, trying to implement pieces of the whole. I get all the exhaustion of the change, but with none of the exhilaration. I am constantly reinventing, while knowing that it's insufficient. The worst cut is how I see my practical traits, and my meticulous and detail oriented nature becoming a hinderance rather than something of any use. But I can't shake off that part of me... nor do I even want to.

It's all internal, of course. No one else is (directly) telling me that I don't measure up. I am my own judge, jury, and if necessary, executioner. The jury is still out. A couple remarks from Mawi Asgedom (who spoke at OAME 2014) ring true at this point. The first is with respect to pushing beyond your circle of mastery (can do) into your circle of growth (can't do). Even if you don't make it all the way, as long as you are pushing the boundaries, you are succeeding. I passed that message on to my classes.

I now ask: Is succeeding enough? More troubling, do I like what I'm growing into?

His other remark, which I tweeted, was "You can never forget the larger story [of why you became an educator] or you've lost a lot of your power." I've previously blogged about "Yi Teach", effectively boiling it down to "to be able to push others forwards, to places beyond my reach". Also a reason why I write. I want to use what I know to spark something in other people.

But now the game has changed. What I know seems to be of limited use. I question whether I would be hired today.


Like politics, it's as if there's two extremes, and I'm somewhere in the middle. I'm not happy with either side, I'm not happy with where I am, I'm not happy with the route I'm taking, and I don't know how to make peace with myself on the journey. It's left me rather paralyzed.

If this really is a linear continuum, perhaps I should take a step off, moving into a third dimension. But I'm not sure where that would lead either, and (as I've said) I'm not a risk taker. So I'm simply going to toss two questions out into the internet:

1) Is it just me? I know I'm not the only one having difficulty with the shifts in education, but am I the only one feeling actual paralysis as I attempt to "better myself"?

2) How can I change what I do, in order to function in my profession, without sacrificing the quirks that make me who I am?

Tuesday, 13 May 2014

OAME 2014 Ignite

Hope to have time to blog in full about the OAME (Ontario Association for Mathematics Education) 2014 conference this coming weekend.  If you really can't wait, you can always read my OAME 2013 posts... in the meantime, here's a teaser. It's the "Ignite!" session I went to on Friday.

Image pinched from Paul Alves
The "Ignite" session was explained to the audience first, in the following way: Presenters have 20 slides, which automatically advance every 15 seconds. The topic can be anything from a love, a hate, a learning tip, whatever - and it was pointed out that practice is useful, as being ahead of yourself on the first slide could put you behind by the third. This conference style began in Seattle in 2006. In brief: "Enlighten us, but make it quick."

It tested my shorthand. Thoughts on that at the end.


1) Chris Suurtamm. (She also spoke at CMEF)
Topic: "Developing math thinking within communities of inquiry"

She used fractals as a metaphor. The idea is to create nested communities of learners which have "self similar" characteristics, the communities also being "dynamic" and "iterative". Mathematical thinking is at the centre of the learning. Noted that this is not easy (assigning homework is easier), but helps in adopting a stance of inquiry.

The same conditions for students can apply to teachers. Create nested communities of educators and value each others' stances of inquiry.

2) Marian Small. (She also spoke at our Regional PD)
Topic: "Developing a mathematical voice"

Our question styles reflect on us. Identify your questioning style, as this is what we sound like to students. Many of her slides presented a situation with two possible questions. For instance, given a number of shapes one could ask "How would you sort these shapes?" or "Which shape doesn't belong?". The first is more a DO IT question, the other more THINK ABOUT IT. (I rather liked the question 'A spinner has a few more reds than blues but a lot fewer greens, what does it look like?')

After many contrasting questions, we had a follow-up sheet to do ourselves and return to her. The idea is to develop a teacher voice that is NOT a textbook. To create a positive voice, be less directed, leaving room for interpretation/discussion/perspectives.

3) Dan Meyer. (I went to his OAME talk last year)
Topic: "Teaching the Boring Bits"

Any piece of knowledge is an outcome of the resolution of a problematic situation: Agree or No? A student starts class with a still mind (like standing water), then there's botherment (ripples), before a return to stillness. If something is boring (like vocabulary) see if you can first create that botherment, and activate a need for it.

For instance, copying a line/curve drawing may activate the need for a coordinate grid. Slides were shown to see if a student explanation could be matched with the resulting picture. (In one case, no.) Boring or not, there are ways to teach concepts using ripples in the water.

4) Dr Cathy Bruce. (See also
Topic: "Engage Learning that is: Interesting, Relevant, Deep, Creative, Lasting"

She hit us with 6 key ideas about learning...
1. Math is important.
2. Young children have tremendous capacity to learn math (and play with complex ideas).
3. Teacher efficacy in math is central to student learning (and leads to positive student efficacy).
4. Slow down to speed up. (Careful selection and observation matter.)
5. Concepts and procedures go hand in hand.
6. Spatial reasoning needs more attention.

5) Amy Lin. (she organized the Ignite session)
Topic: "The Element of Surprise & Wonderment"

Consider what's expected of us (memorizing?), then get creative instead. What happens when you're surprised? You pause. You wonder as to the cause. It gets you thinking. A possible surprising question: "Use one ball to demonstrate a linear relationship." Student quotes were also shown in the slides as to 'What surprised you the most about math class?' (Some responses may have been surprising to the audience?)

Surprises are also challenging to us as adults. It sparks curiosity. People also enjoy surprise endings.


6) George Hart. ( - father of Vi Hart)
Topic: "Geometry Ascending a Staircase"

The topic is the name of a sculpture he designed at Duke University. He walked us through the process/plan of how it was created. It started with a drawing, a "four orb" plan with diameters of 4 ft, 5 ft, 6 ft & 7ft, slight changes between them. Designs were taken to a laser cutter, and a prototype was made. Then, 60 planes of identical pieces which had to fit precisely.

A "sculpture barn raising" was performed on campus, George providing instructions. It created community - a mathematical analogue to a ballet or opera - where appreciation comes from participation. The canvas being a geometric space also meant seeing things like where planes meet is a line. There were also engineering aspects like tensile strength and weight as the sculpture went up, see his site (above) for more.

7) Ruth Beatty. (I was shown some of her work last year)
Topic: "Rethinking 'Concrete' and 'Abstract' in Math Education"

In terms of representations along a continuum, the goal seems to be to move students from concrete ('specific/limited/immature') towards abstract ('general/more mathematical'). But this alienates many students. Time to rethink "concrete": All objects/concepts are constructed by us, and our understandings. The concreteness of an object DOESN'T come from the object, but from our understanding of it. (Eg. we define a "table" from our multiple experiences and interactions.)

Conversely, abstractness is tenuous and remote, and with no deep understanding, is not meaningful to us. (Slides included actual quotes from students on the subject.) Therefore, we should create multiple opportunities and engage in idiosyncratic ways to personalize what is otherwise abstract. Abstract concepts can BECOME mathematical objects, when we move from the abstract to the concrete.

8) Ron Lancaster. (Was at two of his sessions last OAME)
Topic: "Put on a pair of math glasses and go for a walk"

This is Ron's 32nd OAME, he's done over a thousand talks and clocked 1.5 million miles in flights. When he gets somewhere new, he goes for a walk, and his camera is his diary. Advice: Slow your pace. Stop, linger, be curious, wonder. Look with a math lens. Photos/videos can introduce a topic (and contain a story!). He showed many pictures. You don't even have to travel far (or can use the internet, but "we all need to walk more").

Ron has created 'Math Trails' many places in the world, and has a "Math Lens" column in the Gazette and with NCTM. Which others submit to. Images are a universal message. Slow down.

9) George Couros. (New for me!)
Topic: "Your Digital Footprint"

He started with a camera picture from the days when it took time for film to develop. He moved along to a video (unfortunately the sound didn't work) and asked what we're leaving online... as a teacher, as a person. Don't be blogging about whiny students (can lead to suspension); at the same time, "" puts our identity into the hands of students. What's part of your identity? He has #GeorgeTunes.

On the flip side, how do we empower students who are just being kids? "Facebook has rendered every 20-Year-Old Unelectable". Can we give kids a better footprint? #DigitalLeadership Because when you do great stuff, opportunities come to YOU, and he gave some examples (like a 9 yr old running a daily food blog to raise money). "As educators, you're doing amazing things with connections, help kids do it too." There's more on his blog.

ASIDE: Today's decision in a European court that people have the "right to be forgotten" will have some impact here...

10) David Petro. (I follow his Ontario Math Links)
Topic: "Recreational Reading for Math Teachers"

He prefaced his talk by warning "I'll talk so fast you can't understand", and noted how his page was on all his slides: True to his word, every 15 seconds was a new book recommendation (or in one case "if you read only one book, make it these three"). Notably for me, the book "How to Lie with Statistics" from 1954 is still relevant today. As he said, check his website for the full set.


I rather liked it. Of note, each speaker introduced the next one, which was neat. There were also some clever conventions used, like Dan Meyer repeating a slide over 30 seconds, but with a lighter shading to warn that the answer was coming soon. The talks were also short enough that I could put my secretary "shorthand" to use, getting the majority of it down. Which itself led me to realize a couple of things... 1) squeezing in extra words during a lull is easier when writing than on a computer, and 2) I tend to slant up the page if I'm not looking as I write.

Possible improvements... well, the timing was such that there was an hour between the 5th and 6th talks, as the one slot section wrapped up early and the next started late (a presenter had to arrive). Since time was built in, I would have preferred more of it between each session, to digest or chat with a colleague, rather than having it all at the end. I feel it could also work as two single sessions, rather than a double, though I guess not knowing who will speak when makes that tricky. Relatively minor things overall.

Tips for future Ignite Presenters... sometimes it was awkward to have a wordy slide up, because my brain wants to read it, so I end up tuning out for a bit. Some of the best slide choices (for me) were more image focused. The fact that the slides were changing frequently meant I also tended to focus more on them, rather than on the presenters. (For instance, a colleague said David was very animated, moving around a lot. Totally missed that.) But that's all me - your mileage may vary.

Actual takeaways from the talks... since there isn't much time to pull you into the topic at hand, I suspect what will resonate the most with an individual is the things they are already thinking about. As such, I feel the math lens (8), the questioning (2), and the digital footprint (9) had the most staying power with me. But as I wrote this up, a lot of the other stuff did come flooding back (and little things, like Dan's image of ripples in the water, had tenacity). The other thing you take away is how passionate the speakers are about their subject, regardless of whether it's expressed in a more animated or subdued manner. That alone creates great atmosphere.

So there you have it! Hopefully you feel you've gained something from the second hand experience too. Feel free to post a follow-up comment!

Sunday, 4 May 2014

CMEF 2014 Digest

The Canadian Mathematics Education Forum (Forum Canadien sur l'Enseignement des Mathamatics) 2014 was held in my hometown of Ottawa this past weekend (actually from May 1-4). The CMEF meets every few years, it was previously in 2009 (Vancouver). It brings together university professors, public school teachers, and educators from the private sector, from all across Canada.

I'm going to give a quick summary of sessions in this post. It may be expanded on in the future, when I find the time, but my sporadic blogging about November has taught me that waiting is a bad plan.


1) Plenary Lecture: Reconnecting the Curriculum - beyond tensions, myths and paradoxes. (France Caron)

There is a Double Discontinuity: School math doesn't necessarily reflect on University math, either as an undergraduate, or as a teacher returning to the system. ("University studies become a pleasant memory.") Meanwhile, math in the rest of the world seems to exist outside this closed system.

I believe Jim Pai found these images himself
MYTH 1: Math is constructed like a building, one story at a time.
MYTH 2: Math is hard; as it should be, it's learning.
MYTH 3: Working in the abstract develops abstraction and reasoning.
MYTH 4: Calculus is not particularly useful.
MYTH 5: Calculus is a great [student] filter.
MYTH 6: Proofs are boring; students are not interested in proofs.

There is a Dangerous Paradox: Math has never been so present, yet never so hidden (inside black boxes). Can we recognize programming and algorithm development as mathematics? Are black boxes unavoidable with "technology"?

-Three goals for math. Modeling, Computation, Proof.
-Applied math is messy. Instead of applying mathematics, involve mathematics. (Appliquer v. Impliquer)
-The integral of the square root of 'tan x' is fiendishly difficult.


2) Plenary Lecture: Assessment that elicits and supports mathematical thinking (Chris Suurtamm)

There's a shift occurring from mathematical rules and procedures towards the social practice of investigating ideas. This session looked at some of NCTM's 6 standards for School Math. A question posed of Grade 8s was analyzed, as well as videos of students explaining how they solved problems. See

-Assessment should reflect what students need to know and do, not what is most easily measured.

3) Vignette: Adrift in a Sea of Video Tutorials (Patrick Reynolds)

What makes for a good video? A bad one? The "Mystery Teacher Theatre 2000" competition was referenced, as well as this Veritasium video: "Khan Academy and the Effectiveness of Science Videos". In that one, we see that videos must tackle misconceptions, otherwise students will not change their ideas, so incorrect beliefs remain - and worse, students will feel more confident despite their misconceptions!

If students "know" the answer, they won't search for a video, but if they don't know, they won't know what to search FOR. ("What is this called?" really means "How can I google this?") Coming to a video with questions is valid. Watching it to "learn" is not; we must spark a question first, possibly one about the viewer's preconceptions. Question: Is hundreds of math educators creating 'Chain Rule Example' videos an effective use of our time and talents? A five minute video can take hours to put together.

-Ideally, connect new material with something familiar. (This may be a familiar concept, or a familiar mistake?)
-Time delay answers, perhaps don't even give the answers in the same video.

ASIDE: The Four Points vignette was also during this slot, I spoke to Al Overwijk about it. Can you create four points such that there are only two different distances between them when they are all connected? A square is one way, what are others?

4) Vignette: Students and their Instructor Co-Developing the Final Exam (Tina Rapke)

There is a mismatch between classroom practices and closed book exams. To allow for student input: Six groups are made (4 ppl per group) and given 6 hours to create "practice" exams, including a solution key. (Course expectations are provided.) Groups then write each others' exams and assess themselves. All practice exam keys are posted online. At least 60% of the exam is taken from these questions, merely modifying the numbers.

Observations: If there is no set number of questions, students will make the exam too long. Doing this does not inflate marks to 100%, there will always be some things students "don't get". It's assessment OF learning... but does it lead to memorization? Who decides the legitimacy of a piece of math? This also may work best when problems are posed in class throughout the term, to breed familiarity.

-A good way to see what students see as high priority, and have them claim ownership of the material.

5) Vignette A: Sometimes the best high tech is low tech (Michael Pruner)

Research has shown the following methods to be ineffective:
-"Now You Try". Can lead to over 50% of people mimicking, rather than actually checking their understanding.
-"Note taking". Only a little over 33% of a class kept up with note taking, after which only 10% actually used notes to study.
-"Homework". The only visible difference between graded and ungraded homework is that in the former, more cheating/copying occurs.

A way to change your practice:
Game Changers
-Visibly random groups, changed daily. Students have to see this is visibly random, or may circumvent (eg. trade numbers). Improves engagement, breaks down social barriers, can be a problem if (like me) teacher is bad at names.
-Vertical non-permanent surfaces, to improve visibility. Non-permanent removes fear of writing until things are right.
-Don't give notes. Have one pen per group, can take pictures to track evidence. Put them in a PDF and place online as notes.
-Change how we answer questions. Don't answer proximity questions.
-Change homework to be more individualized.

-There was more (see image); for me this would be a radical shift. More discussion occurred in plenary for Saturday (see #9).

6) Vignette B: Problem Posing in Consumer Mathematics Classes (Jeff Irvine)

The resource for a College level class shouldn't be a text. Use the Newspaper. Every article in the Metro (free paper) can be the basis for a math problem. Allow students to choose the link they will study from an article. Promotes self-efficacy. Also watch language - don't give "word problems" give "missing information questions" (eg. blanking out part of an ad that could be reconstructed).

Do need to have flexibility in curriculum, as never know where/when the elements will come from (through problem solving is in curriculum!). Also may need to go beyond curriculum (like intersection of exponentials). Usually manage 90-95% coverage.

-Students engage. Basis of a problem should be proportional to students' level.

7) Vignette: Beautiful Math Moves, Dancing the Transformations (Susan Robinson)

Being the functions creates a character viewpoint, as opposed to an external view. One student who returned from post secondary said moving in math class helped to create a sense of 3D space. Setting down a grid can also help create notion of scale (vertical may not be equal to horizontal, depending on room). Teacher moving between students can highlight patterns.

Particular uses: Expansions and Compressions. Help to see the stretch is not from a "vertex" but from your "core". More: When part of a class as a group is "y=x" and the other part is "y=1/x", students can add themselves to reach the same point, and you have now graphed "y=x+1/x".

-There is more to this than moving arms: has applications even in limits and vectors. Also, teachers themselves have trouble with common language when it comes to compression factors.
-y=x^(2/3) looks neat.

8) Vignette: Incorporating inquiry based learning in assessments (Jimmy Pai)

Inquiry-based as defined means: Learning through design; Project based; Problem based. The last is the most common. Given results can be unpredictable, not a conditioned response, how to assess and evaluate?

Begin with the Task/Problem/Activity, as decided by students. Can be more structured when first doing this, or a video may be used to narrow the focus. From a prompt, design something based on ministry expectations. Have groups on day 1, individuals on day 2, possibly add an extra element that day. Use an evidence record to evaluate more than just what is written, as math gets discussed.

-Difficult to see everything at once, but can focus on the individuals for which evidence is previously lacking.


9) Plenary Lecture: Environments to Occasion Problem Solving (Peter Liljedahl)

You can't just give a "problem to solve" to students... OR a "method to do it" to teachers. It gets filtered through existing norms. The results will accentuate/amplify what is already occurring in the classroom environment. The environment itself needs to be one that creates problem solving. Adjust with the BIG tool first, then fine tune.

Filtered through existing norms
What works is good tasks (see 11, below), visibly random groups and vertical non-permanent surfaces (see 5, above). There was comparison data shown on vertical/horizontal and permanent/non. Ironically, while non-permanent allows faster starts, students usually don't end up erasing anything anyway. The vertical aspect is better because no one has to look at it upside-down, you can see other groups easier, and standing engages the body. Related, you also need to de-front the room.

There will be chaos. But it's a good chaos. It can remove social/cultural barriers, engagement and enthusiasm increases, knowledge mobilizes, and the kid who simply covers himself with chalk doesn't find that as interesting after a while. Elementary, where you do all subjects, should change up groups a couple times per day (as opposed to per month), and secondary subjects should change groups per day (as opposed to never). Groupings of less than 6 (5 is dangerous). It takes about two Mondays for students to realize that this is going to persist.

Fine tuning involves looking at how you ask questions, handle questions, handle groups (eg. the person with the marker can only write ideas of others, or switch it every few minutes), etc. When everyone in the class has noticed something, you can level the class to the bottom, rather than dragging knowledge up to where you want.

The "Hawthorne effect" (improvement is due to change, rather than the nature of the change) doesn't seem to be a large factor. In fact, thinking too much about the multitude of other factors can create a "move to paralysis" and so it's best to intentionally ignore them. Also noted that when you impose artificial constructs (eg. roles) on a dynamic process like this, you hold back progress.

-Everything. But key for me is that you need to buy into this, and for me that's going to take time.

10) Vignette: Climate Change in the mathematics classroom (Richard Barwell)

Measuring our climate requires math. It may not be that people don't understand the process - they may not understand any math was involved! How does one average the surface temperature for an entire planet? How are predictions made? There's also an element of democracy, as a societal response is needed. Can present unbiased facts in a math class, and data where YOU are may be more personal.


From the data, have students generate questions to pursue. Need to try and strike a balance between "what do we do with all this?" and "here's the step by step process".

-There is relevant data available and a multitude of related questions.

11) Vignette: Bootstrapping Thinking: Role of Engaging Tasks (Peter Liljedahl)

Bootstrapping: "Starting from nothing". The only way to make everyone comfortable is to make everyone uncomfortable. A self-differentiating task was presented involving ordering of playing cards. Noted that to achieve flow, you need to vary the challenge as skill level increases. Too fast leads to anxiety. Too slow leads to boredom. This is impossible to balance in a class of 30, but is achievable with 8 separate groups.

First 3 are external
From research by Csikszentmihalyi, there are 9 items that help people to experience flow. Six are internal, but 3 are external, and teachers can do something about those. With a "thinking classroom", any task is possible, (even factoring a polynomial) but you must build to that classroom state. "All problems are good when you bring the right mindset to them." Change the student's thinking, not the question. "You have to go slow to go fast."

MYTH: There is a resource somewhere, indexed with tasks to use. No. Moreover, you cannot create an engaging task that hits AN expectation, because to hit that point removes the possibility of solving using all other options. You can merely create a problem that goes in the right direction. Assessment must also look like what happens in the classroom.

"Everything I've just told you is guaranteed to fail." It's all in how you approach it, none of this is "teacher proof", and there will be resistance. What do you do next?

-Chaos is necessary for learning, but this is not something to jump into blindly. More thought is necessary (for me).

12) Crowdmark Luncheon

Sponsored lunch, but worthy of an entry for a couple reasons. First, it was the founder and CEO of @Crowdmark himself who came out. Kudos. Second, it is an interesting technology - you scan in tests, each page with a QR code, grade online (with the ability to enter links/graphics!) and can email results to students. Can also flag entries for others to look at. Pointed out that at 2 hours of grading per week, with 28 million teachers in the world that's 2 billion hours of grading per year... a lot of which is paper shuffling and entry. Current pilot project at Universities, hoping for feedback from schools. Seems really good for contests or boardwide assessments, but if you need to look at multiple pages at once, that technology isn't available until summer.

13) Panel: Statistical Thinking in Schools

Individual teachers spoke, after which there was to be a panel discussion. Owing to time constraints, the panel was shunted to a vignette, but here's what each presentation entailed:

A) Michael Campbell
Spoke about the huge mix of people in the 4U Data course, and how it can be taught with limited computer time. Namely a lot of experimental work (even for confidence intervals) and individual data cards which had been made for sampling. A student said the concrete work here helped with later abstraction.

B) John Braun
A plug for "R", an online statistical tool with origins in "S". It's open source, see Quotable: "Things are hard if you don't have the time, energy and inclination", be that math or teaching itself. Also, in 2013 the minting of two dollar coins equalled the original 1996 minting, meaning a 50% chance of that date.

C) Georges Monette
Looking at the news, something not taught post-secondary. Notably the idea of "predictive" associations versus "causal" associations, and how statistical solutions usually involve asking questions, not finding answers. The difficult questions come when Causal Questions are answered (in media) using Observational Data, shown in a "Fundamental 2x2 table of statistics".

D) Len Rak
What is "Real Life" for college students? When categorizing data from an open ended question about 'cell phones' or 'technology', only 10% gave a robust response, trying to explain a large $0 occurrence. When the same data was framed as 'housing', over 50% gave such a robust response. Discovered by trial and error. They also are motivated by "knowing their mark", so he's reported it as a z-value, which increases engagement for that unit.

-Data is interesting for the reasons given. More insights like this need to be shared.

14) Vignette: Une serie qui chante (Anik Souliere & Melisande Fortin-Boivert)

I was hoping to get to at least one french talk, particularly after the opening plenary was bilingual. Here, the slides were (mostly) english and the talk was (mostly) french. Notably they had the audience vote at times for options using a sheet of paper which could be folded in half to show A/B/C/D. But no two papers were alike, so if you saw a "D" in front of you, that didn't mean "A" was necessarily on the other side. That was kind of brilliant.

Looked at music from a mathematical perspective - any complex pitch that is periodic will be seen as musical. Any unperiodic "noise" (clapping of hands) will not be heard that way. A voice is closer to an actual sine wave when graphed, owing to having fewer harmonics. The equation of a single harmonic of frequency was presented, fourier series was referenced. The openness of an assignment being "invent a complex note" threw the students off. I had to leave this one early... look for more here en francais:

-Mathematics can and does explain our perception of music.

15) Vignette: Ad hoc - Song Parody for Concept Retention

Over the weekend, two people said to me that I should consider doing my "Song Parody" bit that I've presented before. I had my laptop, so I decided I might as well sign up... if no one came, no one came. No one came. Well, until about 20 minutes into the time slot, so I gave a quick 15 minute overview to three people, half of that time being videos. I think they enjoyed it. A couple people also asked me about it outside of the session itself.

16) Plenary Lecture: Ontario's Stifling Mathematics Curriculum (Peter Harrison)

Saturday closed off with this. Point P(1,3) is transformed according to (y, (y+1)/x). There were many places to go with this problem:
a) Calculate coordinates until something "interesting" happens. (SPOILER: It cycles. Students can then be told to try the transformation on other points.)
b) Repeat the process with P(x, y), using algebra. Noted that some steps require factoring on two variables, and restrictions pop up.
c) Some seed points won't work, describe what's happening. (SPOILER: See restrictions, above.)
d) Find the point for which P0=P1 (ie - maps to itself). There's more than one, and it turns out to be interesting.

But wait! There's more...
At this point we were taken to a graphical representation, and shown that the cycle actually had some symmetry. Which gets more interesting considering the transformation (y, (y+C)/x) where C is some value other than 1. You end up with a symmetrical curve of (maybe 500) DISCRETE points, technically not continuous. Unless C=0, when VERY weird stuff happens (try it yourself). From a formula, you can then develop a process of induction, in proving how you move from point to point.

The kicker is that NONE of that interesting mathematics can be found in the Ontario Curriculum anymore. Unless perhaps you look in the first 30 pages of the document, relating to problem solving and such. Instead, these days topics seem to have been selected to gear us towards an IB model - why?

There was some pushback from the audience in that if we don't have expectations, creating them ourselves is more work/more time, that people in the same course might end up with different approaches, and that parents would have trouble not knowing what's going on. Peter agreed that these were valid issues, but that "good PD" could help remove the conflict aspect while improving collaboration, and that the result would be beneficial.

-There is more to curriculum than specific courses we are teaching. Be aware of good problems, even if (like in 11 above) they can't be targeted to an expectation.


In the morning there was another Panel listed for "Does the curriculum need some fresh air?" and then Looking Towards CMEF 2018. But when all is said and done, I still need to teach this week, and I'm so behind in my marking that I could mark for 48 hours straight and probably still not be done. So I didn't go.

Oh well, hopefully you found reading this to be worthwhile! Feel free to indicate the most interesting thing in the comments below.