Monday, 31 August 2015

History of Five Elections

Back in 2012 (before this blog), I posted a little timeline on Facebook I titled “History of Four Elections”. Seems like it’s time to update that. Follow along to learn a bit more about Canadian federal politics. I’m going to try to avoid bias, and look at this with an eye to democracy, though I have an opinion at the end.
This is Canada. Just to be clear.


It was June 28, 2004, after a 36-day campaign (the minimum required length at the time). Liberal minority government. This was the first election featuring the new Conservative Party (following the merge of the Progressive Conservatives and Reform Party). Of note, Paul Martin (Liberal), Stephen Harper (Conservative) and Jack Layton (NDP) were all new leaders for their parties in that election.

The sponsorship scandal had become a problem for the Liberals even before that. In 2005, Paul Martin went on national television, promising to call an election within 30 days of the final report coming out (scheduled for February 1st, 2006). But after Justice John Gomery’s first report came out on November 1st, 2005, opposition parties united against the Liberals.

On November 28, 2005, Stephen Harper tabled a motion of non-confidence bluntly reading "This House has lost confidence in the government". It passed. This was historic, as being the first time a Canadian government fell on a straight motion of non-confidence, not one attached to a budget or other legislation. (The sponsorship scandal was not part of the motion.)


Was January 23, 2006, after a 55-day campaign to allow for the holidays. Conservative minority government. On May 3, 2007, Parliament passed the Fixed Election Dates Act (“Act to Amend the Canada Elections Act”), which put federal elections every four years, unless the government loses the confidence of the House. (Meaning an election October 19, 2009.) The thought was that Harper was trying to prevent prime ministers from calling elections "on a whim".

In September 2007, Harper delayed the opening of Parliament. This was the first time he would “prorogue” the federal government. I admit that I probably wouldn’t bring this up, if not for the later instances (see below) and what happened one year later. Namely:

On September 7, 2008, Harper called an election "on a whim". Wait, what? (Doesn't this violate the above law? Loopholes?) His reasoning was “Parliament has become dysfunctional” and he needed a “renewed mandate”. September is apparently not his month.


Was October 14, 2008, after a 37-day campaign. This was literally the day after Canadian Thanksgiving, that’s why it wasn’t on a Monday. Conservative minority government. Again. (With a few more seats.) In November 2008, the Conservatives proposed an end to per-vote subsidies. Similar to 2005, opposition parties united, this time against the Conservatives.

On December 4th, 2008, Harper prorogued the government until the end of January. This prevented any vote of non-confidence or challenge from occurring (which could have led to a Liberal-NDP coalition government, rather than another election). For those unaware, all bills in progress DO get killed when this happens, so I feel it's relevant to election history.

On December 30th, 2009, a year later, Harper AGAIN prorogued the government for two months, which delayed hearings into the Afghan detainee scandal - though he cited the Vancouver Winter Olympic Games and economic “recalibration” as his reasons. To be fair, this had some precedent. Jean Chretien did it in November 2003, to avoid the tabling of the Adscam scandal - citing the Liberal leadership turnover to Martin.

Aside: July 2010. Conservative government kills the long form census. The Chief Statistician (himself appointed by Harper in 2008!) resigns over use of the new "voluntary survey". I know this isn’t strictly parliamentary, but it’s a personal pet peeve. Even Rick Mercer ranted about this.
Obligatory Rick Mercer reference made!

On March 25, 2011, Michael Ignatieff (then Liberal leader) tabled a motion expressing non-confidence, finding the government to be in contempt of Parliament. It passed. Harper’s Conservatives became the first government in Canadian history to be found in contempt. “A government that breaks the rules and conceals the facts from the Canadian people does not deserve to remain in office,” Ignatieff said.


Was May 2, 2011, after a 37-day campaign. Conservative majority government. Yes, Canada re-elected the government that had been found in contempt. The NDP (New Democratic Party) formed the Official Opposition, as opposed to the Liberals (Ignatieff lost his own seat). Elizabeth May also won the Green Party their first federal seat.

In September 2013, Harper delayed (“prorogued”) the opening of Parliament. If you’re keeping score, this is his fourth time - which again has precedent, Chretien also did it four times.

Pictured: Elections Canada
In February 2014, the “Fair Elections Act” (Bill C-23) was introduced. It would pass in June. Here’s Everything you need to know about the Fair Elections Act. Paring that down to three points here: 1) Elections Canada can no longer encourage people to cast ballots (no advertising). 2) “Vouching” (voting using your voter information card, among other ways) is out. And 3) donation limits to party campaigns went up, spending also pegged more to the length of election campaigns.

The “Fixed Election Dates Act” (see 2007) had already set the next election for October 19, 2015 (four years after 2011). Traditionally, there are two televised debates prior to the election - one in English, the other in French - arranged by the television consortium of the CBC, Global News, and CTV. The Conservatives rejected this, instead taking debate proposals from other sources. (The NDP has since said they won’t attend debates that don’t include the Prime Minister.)

On August 2nd, 2015, Harper set things in motion, meaning a 78-DAY CAMPAIGN. This is the longest Canadian election campaign in over 100 years. Compared to 2011, there are 15 additional seats in Ontario, 6 in Alberta, 6 in British Columbia and 3 in Quebec. This increases the total number of seats in the House to 338.


Will be October 19, 2015. I am pretty sure we’re looking at a Conservative minority government. (FYI, we've reached the opinion section here.)

I’ve decided to put my reasoning for that into my subsequent post. If you want to shout at me for the opinion, go there. If you have FACTUAL corrections or clarifications, THOSE can go here. 

In the meantime, I'll conclude this post the same way I ended things in 2012: I think everyone needs to vote. If you support what Harper has done (or at least what his local MPP has done), vote Conservative. If, like me, you think this undemocratic nonsense has gone on long enough, vote for someone else. But vote. Don't sit back and "protest" by not voting or spoiling your ballot - because really, in my opinion, that's just condoning Harper's actions.

Saturday, 29 August 2015

OAME 2015: Days 2-3

This is a continuation of the previous Day 1-2 post, regarding the OAME math conference from May 2015.


(2B) Beyond Relevance & Real World: Stronger Strategies.

Friday Keynote Speaker Dan Meyer, basically asking “How do we engage kids in challenging mathematics?” The “When will we use this?” script has never been written down, but we all know it. The question is not ACTUALLY about their future, they’re complaining about their present! They don’t care, and why would they? (To a kid, isn’t unemployment kind of the goal? “Do school for 10-12 years, and we’ll reward you later with work.” Yay?)

There seems to be an attempt to make the covers as interesting as possible: “If math is not real world, it will not be interesting.” But in trying to make math more ‘real’, does math become more real, or more foreign? The real world is unreliable. We don’t think about triangles when looking at whales. “Make math real world” works less often than we’d like, “Make math job world” works even more rarely.

It’s got to be their world, not real world. Actually, not merely their world, it’s got to be RELATABLE. [“Teachers are so eager to get to the answer that we do not devote sufficient time to developing the question” -Daniel Willingham] We often start teaching the way we were taught, it’s hard to free oneself of that. Get creative.

Ideas for jump starting your own creativity: The “math” dial (min -> max). MAX: “Plug it in and get an answer!” How best can we turn the dial backwards, towards MIN: “Ask FOR questions.” Dan showed a graph of animals which had ‘too much’ information on it. Dial this back, so as not to scare people off - subtract the numbers and labels. If you can ask questions about it, it becomes real to you.

NEXT: Ask for wrong answers and best guesses. If you can guess about it, it is in your real world. (The fake world is unguessable.) Numbers brought in only now. NEXT: Start a fight. The effectiveness of constructive controversy - do you agree with what’s been said/shown? If you can fight about it, it is in your real world.

Dan illustrated this by asking for four numbers from 1-25. (17/3/22/8) Which number doesn’t belong, and why? Note there is no “right” answer, and he gave a shoutout to Mary Bourassa’s “@WODBMath (Which One Doesn’t Belong)”. Dan also showed an abstract problem involving circles and squares dynamically changing areas. The big change isn’t stapling a context onto boring math, it’s asking students to do different work with numbers and shapes.

“Barbie Bungee” is a classic problem, we want a fun ride for her but not a fatal one. Dan googled this, and found six different worksheets. The one with an existing table implies rushing to an answer. “There’s lots of dial turning to do before we get to an equation.” And yes, there has to be a Quad 1 grid/graph at some point, but spend time in a less precise land first.

The best move you can make to turn the dial backwards is to take textbook problems and delete things. Not because it’s BAD, but because it’s MIS-TIMED. Cover elements of the problem up, reveal them slowly to ask more interesting questions along the way. “Every new slide is a new dial setting.” Careful, it’s possible to erase too much! “I’m not saying be totally open and ask them where they want to go.” Great formative assessment is possible before revealing more later.

From my session (below): Line Rap
One last piece of advice about engagement: Consider your job, you have lots of them, teachers, explainers, caregivers... how about a salesperson for pain relief? Who is your best customer? Someone who’s feeling a bit of pain - not a migraine. If MATH is the aspirin, then what is the headache? (And how do I create it? If you just give a student a problem, they’re not feeling the headache, so why do they want it?)
[Addendum: Dan got some pushback on his blog here; should we be selling the relief if we’re the ones causing the pain? He counters the pain is there anyway, we’re exposing it.]

Dan likened the pitch to “You gotta take this pill”, so we’ll put some music to it to make it palatable (video shown), but that cheapens what we do. (I take mild offence to this. More on that later.) Instead, create a brief moment of pain, such that the math makes things easier; he did his “choose a point” activity, where labels make that easier. “I’m not here to deny the reality, I’m suggesting that there is other stuff going on, aside from the real world.”

In Summary: Ask yourself, “How can I remove stuff that can always be added back later?”,  “How do I create a constructive controversy?”, in essence, how do I turn the dial down and how do I create a headache? These are harder to answer than changing the context of a question, but often more successful. Also, there are missing places on the dial, because there are missing things we don’t know about student engagement. Find them out, and then come back and talk about them/share them with your students.

I dropped by E303 briefly between the keynote and my next session.

(3B) Growth Mindset in MCR3U

Gordana Rakonjac and Alison Pridham have looked at problem-based lessons in MCR 3U (Grade 11 Functions course). This from a ministry funded but teacher directed Leadership Program; colleagues worked on the Advanced Functions/Calculus course. They basically walked us through their course; it involves a lot of activities and group work.

They start with a hotdog contest commercial, and an apple tree problem, which prompts self-directed linear/quadratic review. The “lesson” is student consolidation, as they tell a scribe what to write. Next a function sort video and classification. Exponential functions in the context of hamburger toppings, paper folding and spreading diseases. (Make sure students mingle for this last one; infected trading with infected also creates realism.) TIPS documents can be used as homework.

From that into Trigonometry, a sorting terms activity, and spaghetti use to model the graphs. (I’ll be honest, I’m not an activity guy, but trying to break spaghetti in a precise manner had my interest.) This is put in the front of the book to refer back to later; then there are trig carousel activities. Of note, the Discrete Functions (sequences and series) is done as an Independent Study in order to free up two weeks, since this instruction method can take longer.

It was noted that you should still take at least 5 days for the Finance component towards the end of the course. There is student interest and it is relevant! There was a handout of the powerpoint, and they had us doing most of the activities. I can see this being good for someone with a different headspace from where I am now.

At this point it was my lunch, but having seen people yesterday walking into session having having picked theirs up, I decided to do the same. I went to OAME Ignite, which I did blog about in May. Because of the double format session, they actually started their second round at the beginning of break, so I stuck around... meaning 20 minutes into the next session... that made me a bit late for:

(5B) MathsJam!

Envelope folding...
This was with Dan Allen and Chad Richard. Because I was late, I missed the introduction, though I was already somewhat aware of it through Twitter. “MathsJam!” meetings started in the UK, and there are now two gatherings in Ontario... effectively people coming together to play math games, do puzzles, etc. That was in full swing when I arrived.

I helped to create a couple Sierpinski triangles from size 8 letter envelopes. I also looked at a few puzzles that had been offered - and created a much more involved solution for the nested circles question than was necessary. (Multiple methods...) Someone else there also proposed one involving nested radicals equaling 6. And while I’ve never been into games, there was one with funny cards that people were playing.


I went to the OAME AGM, because it’s not long and gives me an idea of the inner workings. Finances are still an issue, in that the books close long before the report is presented. Also moving the AGM needs a motion AT the AGM (it’s in the Constitution) which will likely happen next year (to implement for 2017). OAME 2016 announced at Georgian College in Barrie. I chatted briefly with William Lundy and Tim Sibbald; everything was adjourned by 4:18pm.

I’d opted not to go to the Banquet this year; it hadn’t really thrilled me the previous year, and moreover, I felt like I might want time away from people. Which was good, as I’d actually had a complete mental breakdown Wednesday night, upon arrival, when my keycard wouldn’t work. Crying and everything. I needed quiet time here.

I ended up taking a long walk, all the way to the nearest grocery store, where I bought some supper, brought it back, and wrote the post “You’re a Good Teacher”. It relates to people I heard discussing whether it was right that Marian Small was posting up tweets, and my feelings about Dan Meyer slamming music - it begins "There’s nothing quite so simultaneously invigorating and demoralizing as going to a math conference..."

(1C) Problem Solving without Algebra

To start Saturday was Serguei Ianine’s session focussed on ratios and proportions. (He had another for percents, but it was opposite my session below.) He’s a private school teacher teaching 7-9 and 10-12, and his session included a booklet of problems.

Students are introduced to the idea of using “x” really early, and while equations are good, that can be wrongly timed. Technical aspects should go in parallel with problems, we shouldn’t introduce operations, and then the applications, 80% of kids get lost in the transition... for the simple reason they lack experience. The very abstract isn’t tangible, and creating the equation is difficult.

From my session (below): Fraction rap
Do simple solving of equations and simple applications, then something slightly more difficult for both - don’t use equations in your applications. Eventually you reach problems that can’t be solved by inspection or other methods, and can merge then. Also watch for a tendency of students to work from left to right, instead of using order of operations.

Ratio problems: Can be a ratio of three. You’re a lawyer, problem of a man’s last will, his wife is pregnant, “If it is a son, he should get twice as much as his mother. If it’s a girl, the mother should get twice as much as the daughter.” (Sexist challenge? If you reverse it, there are no problems. Interesting.) The wife delivers TWINS, one boy, one girl, so how much should each person get?

There’s always a couple kids saying ‘let’s call this x and this y’, but we don’t need the abstraction - go visual. Son has more than mother, who has more than daughter. Partition out a line. Always start with the smaller part, end up with ratio 4:2:1 and can now solve based on initial amount. Don’t require the kids to remember words, establish concepts, the linking can come later (even at Grade 10 level).

Another problem was presented involving a timeline (not to be confused with a number line), where a difference between two ages stays the same, but the ratio of the numbers CHANGES (always decreasing, for mother and son) - and how old are they? Shift after this into rate problems, the “per one” (e.g. km/h) is not easy for students, and even the word “rate” is an abstraction.

Proportion problems: This is more than setting two fractions equal; there is both Directional Proportionality and Inverse (reciprocal) Proportionality. Again, don’t run to an equation. Classic example: “20 birds eat 20 kg of seed in 20 days. 30 birds eat how much in 30 days?” What does your intuition tell you?

If we kept days the same, and doubled birds, the kg would double. If we kept kg the same and doubled birds, days would cut in half. The first two are directly proportioned, while the outer two are inversely proportioned. But “I don’t need any variables here, only how to multiply fractions”... keep days the same, 1 kg/bird. Now divide down to one day, then pump back up to 30, all using direct reasoning. Now have 3/2, pump that up to 30 birds, and finished.

That problem should not appear too early, but somewhere in the middle of the process. Don’t expect students to go through these questions at your speed either - it WILL take longer, half a school year for sure. But if you try to set an equation for a problem like that, you will never win. Proportions also has applications in Grade 9 applied, more so than Academic. Do things over and over and over again, and remember there are alternatives to using ‘x’ as some unknown number.

(2C) Teaching & Learning Math Using Spatial Thinking

Saturday’s Keynote Speaker was Nora Newcombe. She approached the math from a more psychological viewpoint, noting “I might be right or wrong. I’m eager to get your reactions.”

There’s a starting point back when we’re born: A generalized magnitude system, for both spatial and mathematical thinking. Development occurs even before getting to a formal school system. Then there’s differentiation of space from number, and number for little kids becomes discrete integer values. Which is a different sense of quantity from continuous! Our intuitions about continuous quantities get superseded, even though we need them later, for fractions.

Piaget said metric coding of space appears late - “Children cannot measure, cannot compare heights that aren’t on the same base.” So there’s a confusion between number, length and density. Nora argues it’s not that this observation is WRONG, but what it actually TELLS us about a child’s understanding might have been incorrectly interpreted. Babies do look longer at places where things are “surprising”, like things popping out of a sandbox where they were not originally hidden.

Containers make the difference.
There are TWO TYPES of Quantity. Intensive (Proportional) vs Extensive (Amount). Given two half full containers, remove the context, and one actually has more in amount. It’s that proportional quantity that babies DO come with. They look more when 1/2 isn’t 1/2. Good news! Proportional/Intensive quantities are what we need for scaling, like reading maps. (Three year olds aren’t accurate in such activities, but neither are they random.) The implication is we can build scaling early... but teachers tend to resist this, and cite that Piaget study.

There are more connections. Spatial level ability at age 3 predicts spatial at age 5 (makes sense) but ALSO math at age 5. And spatial at age 5 predicts math (or “approximate symbolic calculation”) again at age 8. The caveat is, spatial is not the only thing that predicts mathematical functioning, there’s other variables (like “jumping around too much”). A number line (age 6) is seen as both spatial and numerical.

But the mapping of abstract numbers onto discrete objects is problematic. There’s interference, it’s harder to measure (3.4 mL) because they don’t know what to COUNT, it’s harder to deal with proportions (3:4) because they look for the COUNT, it’s harder for fractions (3/4) because those exist between the COUNTING values. Piaget’s argument that children do not understand number until the age of 6 or 7 is based on that confounding of density, weight, etc - continuous measures, of which there WAS awareness.

Many paradigms led to the conclusion that infants (and nonhuman animals) know number. It’s probable that small numbers (1-3, maybe 4) are subitized, perceived by a separate system. Though experiments in 2010 showed a sense of “moreness” or “lessness" is present (generalized magnitude system). Children then get hooked on integers, and count numbers on rulers - looking at a length from 2cm to 5cm, there are 4 numbers (2-3-4-5), so it’s 4cm long. (A “hash mark error”.) We must highlight the COUNTABLE units. Can use plastic/unit chips, or show with fingers a unit apart.

On Proportional Reasoning: Unfortunately, many children and adults struggle with this, even though infants and younger children are sensitive to such relationships. We have to get ourselves AWAY from the impulse to count. Proportional reasoning is better with continuous quantities. Don’t draw a picture breaking the drink down into discrete unit chunks, remove that thing that’s deceiving (“seducing”) them.

On Fractions: They’re difficult but important. Strong predictive relations exist between early fraction understanding and later math achievement (controlling for other factors). Kids in preschool (age 3) can add 3/4 and 1/2, with portions of a circle. When they do make errors, it’s based on “count words”... two thirds is really TWO OF THREE, but they fixate on “two something”. Different languages are a factor here! English: “One fourth” VS Korean: “Of four parts, one”. American children did better with fractions when done in the Korean style of terms, and we CAN do that without sounding like idiots. OF is a great word. 

Nora closed off by reminding us that she is not a teacher, but that the research suggests early math teaching should use continuous as well as discrete representations. Use number lines in which whole numbers do not dominate the fractions - and they can help teach negative numbers later too. “Taking away a negative number” means you should be adding to the positive side, not “you give someone five cents, so negative five cents”... five cents is five cents is a DISCRETE object. We need more ways to get across what negative numbers mean, like zero as a fulcrum.

(3C) Musical Mathematics

In the last slot was my session with Michael Lieff. It was kind of a blur; we’d also pitched a double, but only got a single. After some general introduction and pop music word frequency charts, I got into the idea of rap vs. parody, and encouraged people to try writing their own song about a difficult concept, possibly with a partner. I and Mike circulated, and got some people to share afterwards. I took photos, and asked permission to post; they're throughout this post, including here on the right.
From my session (left): Trig Rap

Towards the end, I did my live version of “Polar Plot”, as promised in the blurb. We also took questions. One person asked me about how I marked my Data Management song assignment (it was an option instead of doing a probability project), and I said that from the outset they’d have to have a minimum number of terms included - it wasn’t that different from “Counting Stories”, if you’ve heard of it.

Someone asked about students recording while performing; Mike pointed out that he’d asked for his act to be recorded. Me, I started with “don’t” and have since backed off to “if you like, but don’t post it anywhere”... mainly you need the students’ respect, I guess. One teacher had a horror story of posting something online, then someone (not a student) took her audio rap and made their OWN video, which included profanity! Be sure to click “No Video Response” when you YouTube post so others can’t do that without permission.

I got a couple other sites, updated my Music document (I now have over 60 links) and sent it out after the conference because one person had wanted it and I couldn’t remember who. Someone else responded too, saying thanks because they’d wanted to come, but had to leave early. (There were about 20 people who attended, much better than any previous time it’s been run.) And so that’s basically that!


As I typed/edited this, one theme I’ve noticed running through the conference is the whole “multiple methods” angle. Both in terms of student solutions, and teaching strategies. Diversity is definitely seeing a lot of attention these days (on a number of fronts), I think in part because humans have difficulty with it. I know once I’ve found something that “generally works”, I tend to come back to it. Related to that there’s also the fact that what might be typical for me might be new for someone else, and it’s not always easy to recognize that.

Will I be back again next year? Well, I rarely make decisions on such things so far in advance; I guess we’ll see. Thanks for reading, I hope you found something in this post to interest you.

Thursday, 27 August 2015

OAME 2015: Days 1-2

Every year, the Ontario Association for Mathematics Education (OAME) holds a May conference somewhere in the province. In 2013 I "live blogged" about it. In 2014 I managed to post in June, after exams. This year (“Building Mathematical Mindsets”), we’re looking at August. So, this might be the last year; anyone getting anything out of these?


The day started very meta, as I dreamt about being sleep deprived at a math conference. They were trying to sell bibles at registration? I got nothing.

(1A) Pythagoras, the Man and his Theorem

C. Chan started with some of the background on Pythagoras (lived 570-490 BCE), and his school “All is Number”. In particular, some of the links made between numbers and characteristics; 1: Source of All; 2: Female/Opinion; 3: Male/Harmony; 4: Justice; 5: Marriage. 10 was the Divine, the sum of the four spatial dimensions (1+2+3+4). (Granted, we now see ‘1’ as the ‘0’ dimension.) Johannes Kepler once said “Geometry has two great treasures” (one of those being a^2 + b^2 = c^2).

Looking at the Theorem itself, the Berlin Papyrus 6610 (1300 BCE) was related to Pythagorean Triples much BEFORE Pythagoras. Babylonians (YBC 7289) also tried to calculate the diagonal of a square, and found proportions close to root(2) in their system of Base 60. (The special isosceles right triangle case, approximated: 1 + 24/60 + 51/60^2 + 10/60^3 ) And China had the “Gougu Theorem” (3-4-5) with 1 chih at about 23 cm.

The presentation then looked at the numerous proofs of the theorem over the years, and included a handout illustrating many. Euclid’s proof appears in his “Elements” (~250 BCE), Book 1, proposition 47. Extended in Book 6, Proposition 31 to any figure (not merely squared). A proof from the 3rd century AD is here: Chan also showed how you can also create a fractal tree from the Theorem.

The big question: “Did Pythagoras prove the theorem?” Ancient sources do not say this, and Euclid’s “Elements” did not mention him. There’s a legend saying “Pythagoras sacrificed 100 oxen” upon the discovery, but the guy was a vegetarian so... unlikely? Either way, his name is linked now; I note it is spelt with “A”s there is no “U”.

(2A) There’s Student Mindset, what about Teacher Mindset?

Thursday Keynote Speaker Marian Small: “You’re used to me being all math all the time. ... This will be a bit more philosophical.”

As a teacher, what do you think about most in terms of your teaching?
(1) Covering the curriculum (good, that’s what they pay you for) and keeping kids engaged (given different mindsets: busy/interested/other);
(2) Higher EQAO (provincial test) scores (if you’re practicing they must matter somehow - is it boosting the higher students or bringing up the lower ones?);
(3) Instilling love (or ‘not hate’) for math (which secretly means being successful);
(4) Improvement of your own practice;
(5) Convincing other teachers to try what you do;
(6) Fitting in with current ideology (all teachers like belonging, just like kids).

How do you settle this?
Marian sent out 3 TWEETS including: “The best math class ever is one where..." Responses in ‘Group 1’ were sincere but sounded politically correct. Leaning towards what the class looks like, versus the learning. But even something like “All ideas are valued and many perspectives are explored” can be questioned - should it be ALL ideas? Her ‘Group 2’ classification focused more on something being accomplished, something being learned. She noted how hardly anyone responded to her tweet “I want my students to think that math is..." which itself is interesting.

As teachers, do we not think enough about what math is, or is not?
-VIEW 1: Do nice algebra stuff. That’s all it says to do. VIEW 2: The kid should understand that any relationships can be described in different ways. View 1 teachers bring out different highlights; there’s different mindsets here. That’s not to say one is always better.

As teachers, we have different assessment beliefs too. How do we measure success? A View 1 teacher is happy when a student can add fractions. A View 2 teacher is happy if the student can provide an addition using different denominators, such that the answer is out of 15 parts. Both of you are right, it’s just different perspectives. Don’t fixate on “Growth mindset is good, fixed mindset is bad”, think about your perspective!

Is math about getting answers to problems, or is it about having a deeper understanding of mathematical relationships? Is fun critical? Did you mean fun, or engagement, and is that enough? Marian then provided a number of statements, asking which one people agreed with more. For instance: You are a better math teacher if: (A) You know the math you’re teaching deeply OR (B) If you’ve struggled with math yourself so you better understand potential student struggles. (This isn’t “fixed vs growth”; it seems to be something else.)

Other statements: (A) If you work at your teaching, you improve and student learning improves. OR (B) You can only control some of what kids learn; most of it depends on the attitudes of your students. (I feel like that depends a bit on the day!) When you struggle with a new strategy: (A) You keep trying until you get it OR (B) You try a few times and abandon ship to look for others. (I’m definitely ‘B’, there’s too much out there, move on. It was noted that both are valid as long as you DID try the strategy!)

Wrapping up, is the point of school: to teach expectations? to build problem solvers? to build curiosity? to make learning attractive? More to the point, do you think the “purpose” affects the way you teach, and what do you expect of yourself and your colleagues? Marian says that neither she, nor school boards have the right to tell you what you think about being a teacher. The right to expect you to try something (not reject OR accept out of hand) but not the right to your thinking.

Teachers don’t have time to stop and think. That’s a social-political issue that she has no power over. Still, try to think about what your mindset it, and it may influence you.

(3A) Be More Dog: Enthusiastic and Curious Classrooms

This was Featured Speaker Amy Lin. I’ll be up front: I do not like dogs. I am a cat person. Partly it was delivering newspapers for close to a decade, but dogs also like to get up in your face whereas I wish they’d give me my damn space instead. So I went to this one mainly because it had to be a completely different perspective from me!

Dogs are playful and curious, they like to explore (a dog was first into space). They also have better senses than we do (smell & sound). Useful qualities for investigating mathematics; don’t be scared of adventure. What you didn’t learn from the books on mindsets: Changing mindsets is really hard. “Becoming is better than being.”

Have an element of surprise driving learning, and piquing curiosity. Dogs also live in the moment. They like to make messes - and math can be pretty messy. Big Idea: The same object can be described by people using different measurements and/or levels of precision. (Can we deliberately choose units so that the measurement is more valuable? A puddle is “10 steps wide” vs “12 steps wide” - smaller steps mean you’re right?)

Multiple Methods: “If 24 items are to be handed out to Ann and Ben in a ratio of 3:5, how many would each person get?” Answer via: Intuitive (guess). Additive (keep giving 3 & 5). Equivalent Ratios (9:15 same as 3:5). Finding the Unit: 24 whole, 3 subunits of 8. Try opening questions; instead of “there are 30 children on a bus, five more boys than girls”, there are more than 30, you decide the exact number.

Dogs are visual learners... okay, maybe that’s a lie, but let’s talk about visualization! Follow up questions can get students thinking this way. (“Where do you see 12? Why do you think a subtraction sentence was used?” “Why could you always write a division sentence if you have a multiplication?”) The same algebraic expression can be used to describe two different situations: “5p” could be total amount of money at $5/hr after p hours... or five fingers per hand means work out number of people.

More dog links: “Be dogged” means persistence, not finishing until you’re done. If you want what is buried, dig deep to find it. Dogs are also very social. A final performance task could be questions surrounding a picture; can week out non-mathematical ones by topic sorting, ranking what is a good question. “We are all in this together.”

(At this point, 4A, I had lunch and browsed the displays.)

(5A) They Can Do it! Supporting All Students’ Thinking.

This was Featured Speaker Chris Suurtamm. “All students are able to engage in mathematics. And to extend their mathematical thinking.”

She presented five ways to encourage students’ mathematical thinking:
1) Value prior learning and experience
2) Provide space for students’ own solutions
3) Pay attention to students’ thinking
4) Focus on connections rather than hierarchies of solutions
5) Encourage opportunities for success

#1: Consider “What math looks like at home” vs “What it looks like at school”. We need to connect things to prior learning, as a ‘blank slate’ leads to memorization. What models to students use, what understandings do they have? We were told to partner off (I was near to Jennifer M from St. Catherines) and discuss models for integers. “It doesn’t make sense for me to begin a lesson with a number line if prior knowledge is different.” (Use temperature? Algebra tiles? Money?)

#2: “Research has shown that allowing students to develop their own strategies deepens their own understanding of the problem and processes involved.” Because their method is seen to be valued. Turn off timers, no “mad minutes” use RPM (Reasoning strategies, Practice and Monitoring). We considered a ‘children on a school bus’ example (not unlike in Amy’s session above).

#3: The most important thing! It’s so easy for us to keep talking. She showed a student solving b+b+b-30=12. Of note: Listening to student thinking helps me with what they know, but it DOES NOT tell me what they DON’T know. “Just because someone doesn’t do something, doesn’t mean they don’t know it.” You can solve with one method, but still know others. You can drive through a stop sign, but still know you’re supposed to stop.

#4: Every bus solution (from #2) involved mathematical thinking. Avoid the idea of “I did it but I didn’t do it the math way.” They’re ALL math ways (merely some are more symbolic). What strengthens understanding is not that they can see one representation over the others but that they can make the connections between the different forms. Demonstration here from

#5: Problem: It’s easier for a student to not try and not hand it in and then fail, versus to ACTUALLY try and then fail. Chris mentioned a student who had produced work in class, but when work was due, didn’t have it and said they were willing to ‘take a zero’. We need to be rethinking ability-oriented language. Moving mathematical thinking forward is the goal, and a successful lesson is one that helps to do that. (We shouldn’t throw out success criteria, but don’t narrowly define them, we’re not aiming every kid at the same target.)


After the Thursday sessions, there was the usual Wine and Cheese. I ran into a couple people, but my memory fails me. Then a number of Ottawa teachers got together. I saw Balazs, my former math head, now vice-principal (actually returning to our school this Sept). He proposed oral explanations, for anxious students (about tests or generally). It doesn’t need to be time consuming, you can record one student, then they interview the next as you’re back in the class, and so on. Listen to the recording later, you’ll know if they were prompting each other.

Then we went to “Lone Star”, as we had last year, for a “Tweet Up”. (I got a lift with Tania A and some other teachers.) I remember hearing a bit from Al Overwijk about some class struggles, and there was a fascinating conversation with Ann Arden about her sessions. She signed up for a “Themed Thread” (I couldn’t thread through, I was presenting during one) where they had been talking about so-called basics like “definition of multiplication”.

Here’s a problem: As an expert, you cannot see how two identical things could be perceived as different. But as a novice, you may not see how they are the same. Particularly when done with gestures and representations. (This may have pushed me into my recent popular post “Multiplication is Ridiculous”.) A rubber band model was referenced as one representation. Onwards to Friday:

(1B) Supporting Students with Learning Disabilities in Math

This was Connie Quadrini and Connie Gray (their Featured Session, not part of the “Thread” set). I was impressed that someone was translating into sign language in real time over on the right.

Matchstick task is on the screen.
We were presented with a matchstick task, and told to show work and explain thinking to create figure 10. Possible approaches:
a-Build figure 10 and “1 by 1 Count”. (“Creating a model” or “Concrete Representation”)
b-Extend the pattern with repeated addition (table; Additive Thinking)
c-Extend the pattern with a rate triangle (graph; Extrapolating)
d-Create an Explicit Pattern Rule (algebra; Multiplicative Thinking)

There was mention of the YCDSB (York District School Board) Middle Years Collaborative Inquiry Project. It was started with an eye to proportional reasoning and extended to patterning/algebra. Involved teachers Grades 4-9, special education teachers, consultants, administrators, 3 families of schools, 6 days per teacher. Idea of unpacking IEPs through a mathematics lens.

There were pre/post assessments. Mult choice, and open response scoring was assessed not only on completion but also math strategies used. Also clinical interviews. Some results:
-Students who arranged using a linear format with non-visible groups tended to use Additive reasoning, as opposed to Multiplicative (see above; multiplicative can also be linked to determining a unit rate).
-Students who interchanged multiplier and constant had perceptual reasoning listed as an area of need in IEP.
-70% of students indicated that using tiles supported them in learning patterning/algebra, both for those who had perceptual reasoning as a strength and as a need.
-Someone who had “memory” as a need liked the hands-on because ‘you can remember it’.

We also looked at a Caterpillar task and one related to “Doing 6 good deeds every 4 days” extended to 14 days. Despite materials being available, a student working on the latter did not use them. Yet once the learning tool was presented with the model (tracking both parts simultaneously) the student made links easily. Remember: Non-verbal mathematical actions can reveal important mathematical thinking, and learning tools can enable student perseverance through a mathematical task.

That’s all for Part 1, this will be concluded in Part 2 on Saturday (including mention of my own session).

Tuesday, 25 August 2015

ConBravo: Making It Online

This post is separate from the main ConBravo chronology. It focusses on a panel from Sunday called “So You Wanna Make It Online?”. There were three panelists, Joey Baggins (@joey_baggins), who said he managed to gain 300 subscribers to his show over a year, Obsessed Panda, who knows the Cosplay side, and Doctor Holocaust (@DoctorHolocaust), Toronto’s greatest gentleman villain.


My camera may have been visible...
Rule one is, use every opportunity you’ve got. Dr. Holocaust noted near the panel's start  “I’m not the centre of my thing, my character is” (and so that’s what’s on his business cards). Also keep in mind that, psychologically, human beings weren’t built for fame.

If your plan is YouTube videos, you need good equipment. Start with a quality microphone - it’s easier to offend the ear than the eye. Your content needs to be worth watching. Consider “Phillip Franco”, who had quality equipment and advertising, but no noteworthy content, compared to “Toby Turner” who made videos using his phone, but had fun content.

For cosplay, videos come from photographers that you work with. You don’t have to do it alone, but you must search out good quality. Instagram is a big thing. Dr. Holocaust noted that he hates Twitter (“short sentences about people’s lives bother me”) but it IS a way to expand beyond YouTube viewers. Your followers can easily get ahold of you, and can be notified about updates.

Gotta finish inking and colouring
these math characters...
I asked about how to get more viewers for something that isn’t in video form, but that you are doing regularly (like my serial stuff). It was interpreted as getting interest for something still in progress (true, in a sense), so we’ll go with that. For cosplay, Panda said it can be good to show the progress of your work, though you may get people criticizing an unfinished costume. Putting out something incomplete can also make you accountable. “Now that you’ve seen I’m halfway through this project I have to finish it”. (Dragonball fan film was brought up.)

Don’t worry overly about quality - as long as you’re having FUN, that’s the absolute CORE. Be it podcasting, or music, or anything. That enthusiasm will bleed into those around you. Dr. Holocaust told a tale of once dressing as a transformer using a box, and was told by people “that’s silly, leave the con!”. He didn’t. Three years later, he was recognized as “the box guy” and people were taking pictures.

Someone asked about how to get people to buy prints. All I seem to have written is it can be a solidarity thing, “I want to support a person who likes a character that I also like”. Noted that if you aren’t the face behind your stuff, leverage word of mouth. Featherweight makes costume accessories; he did one or two costumes to start, now it’s largely referrals (“I found a guy who can use your stuff”).


I will SHOW you Magic Steve's work!
Those are balloons, if you couldn't tell.
Another key element: Don’t TELL people, SHOW them. All the energy you have to EXPRESS your interests to people, turn it into DOING that thing - or at least starting it. That makes it real. And it may be that when you do it, you hate it: It’s not a failure, it’s something you tried that didn’t work. Move on, try something else. Joey also said that he found reviews weren’t his thing, so he stopped trying that, and now talks more about fandom, which is working better.

A collaboration is a great way to promote yourself, and is usually beneficial for both parties. Terrified to ask? Sometimes, you just have to. Not sure what to collaborate on? Perhaps simply ask the other person to send you some small amount of content. The worst you get is a ‘no’. Work on your PITCH. Aim for a single sentence, and try to relate it back to something that worked. (It’s like “Sin City” meets “Ninja Turtles”?) Dr. Holocaust uses the tag, “He’s the world’s nicest super villain”.

You may be able to get ideas for your pitch from people who play your game (or watch your content). The biggest complaint a panelist once got was “Your videos are great, but no one watches you.” You have to know how to sell yourself. If you’re not doing that, don’t get upset at having no viewers! Once people are hooked, build on that. (I also have here “Never satisfy your reader until they’ve read the book.”)

"Interesting. Doesn't change how my time travel
story is on a totally different blog, hmmm?!"
Don’t jump channels. Joey has lost his audience several times from doing this. Don’t totally shift your brand either - if something’s not working, that’s one thing, but if you decide to discuss gardening instead of reviewing anime, people likely won’t come back. If you lose your passion, don’t do it. If you need to rest for health reasons, do that. Yet often you have to push on - there will be bad days, days you don’t want to record - know you’ll love it later when you see the results.

Things can blow up unexpectedly. ObsessedPanda once took a selfie with some Iron Man friends before going to see the first movie. It was found and turned into a meme for one of the movie sequels - she stumbled on the picture, there were no names attached so no recognition out of it. Or things may not blow up! “If you think this isn’t going to grind you into the dust, you’re WRONG. It’s a huge amount of work.” Try to get people to help you (who can do sewing or special effects or whatever.)


From the panelists: If you love doing it, it pays for itself (Joey). Proofread, proofreading is your friend (Panda). And Doc’s motto: “Life is a war without end. Never stop fighting.”

Photo of Linkara and me from ConBravo 2012.
Because why not?
From me: Don’t be so focused on the long game that you miss the individual opportunities. Perhaps a bit of a contradiction given the marathon run, but hear me out.

Lots of what was said here was things I... not knew exactly, but sensed? For me, marketing and selling myself is the weak link. In large part because once something is done, and out there, I’m moving on to the next arc, or post, never trumpeting what I’ve already accomplished. Which means few know what I’m doing, and worse, I tend to get down on myself because I figure that means the long game isn’t worthwhile.

It goes back to "rule one". Don’t miss noticing a possible pitch, or a brand, or attending a convention, because you think you’re not good enough yet, or too busy with the next project. Because it might be what you need to make the next leg of the journey a bit easier. Thanks for reading!

(Incidentally, I am now personifying math in webcomic form. And I changed the tagline on my time travel serial to "Time Travel Redefined". It's like a cross between "Interstellar" and "Tomorrowland".)

Sunday, 23 August 2015

ConBravo: Music & Media

This post is separate from the main ConBravo chronology. It focusses on two panels that occurred in Room 314: Creating music (Saturday), and Crowd funding (Sunday).


Ben Briggs introduced everyone to “FL Studio” from ImageLine. Their free demo lets you work with all the features - you merely have no ability to save the file. He noted that electronic music is mostly copy/paste. 128 beats per minute is a standard beat for “house” music, so start with a drum machine there. You can “paint” the drum tool into the big board (Digital Audio Workstation).

If you select “make unique” you can alter the characteristics of one repetition. “Stretch” will let you increase the time span, but AVOID that, you want to crop and “fit to tempo”. Your most useful tool is Parametric Equilization, changing the level of frequency on a channel. Muddiness in a sound comes from frequencies existing that don’t need to be there.

Golden Rule: Never BOOST a sound, only CUT. If you need something to be louder, cut what’s around it. This is because you have no control over a boost, it simply creates “more sound”. Note that if you can amplify the upper middle frequencies (harmonics), this will boost the fundamental tone, and make your notes more clear. Mastering makes things loud without distortion.

Some other tips: “Change velocity” means change how hard a key is pressed, so volume. For dance music, you want the kick drum to power through. Space between the notes is almost as important as the notes themselves! You need vibrato and things. Don’t set out to copy, but if people get on you about “this sounds like..." remember that there’s only 12 notes, so “there’s gonna be some overlap”.

Amusingly, you can write a lousy melody and then put a chord progression underneath so it makes sense. That trick works the other way too! Ben also noted that he tends to listen to his own music on loop, not out of ego, but because that way he can hear the things that he needs to improve. There was some Q&A at the end, including Grant Kirkhope, but I didn’t write it down.


The “Crowdfunding and Online Patronage” panel featured Lar deSouza and... I think Grant Kirkhope. (Should have written it down.) It was noted how Patreon started as a video sponsoring site, and has now expanded. There is a crowd sourcing problem, in accountability of subscribers, as much as content creators. Such as someone who subscribes, looks at content, then immediately unsubscribes so as to not pay the extra money. (People are entitled assholes. “What’s this money used for?” What do you care??)

On Kickstarters: Make sure to ask for the money you need. There’s a danger in getting LESS, yet still needing to fulfil goals. Yet avoid asking for more than you need too - be honest with yourself. Really think and plan goals properly, don’t propose any stretches that might clutter your creative universe; you may think you won’t get much money, but you might. Note that crowd sources work if you HAVE an audience, it won’t CREATE an audience (there’s so much other noise out there). If you can make it without a Kickstarter, go that route.

Kickstarters will work best if you have the content, and only need to print and ship - kind of like a pre-order. But be clear that’s what you have (or don’t have!). Sobering tale here of “Goblins”, where Tarol had a company run things. Their Kickstarter pitch was that it was done, but then they backed off saying more testing was needed, and then the money and company vanished and Tarol was left on the hook. Effectively people stealing using his name.

IndieGogo is different, in that while Kickstarter is all or nothing, the former can pay out based on partial funds. Either way, be sure you ALWAYS DELIVER. Expect a big spike in donations at the start and end of a Kickstarter. In fact, you can almost predict if it will work when still near the start. If you’re close to your goal near the end, you CAN kick in the rest yourself, but make sure it doesn’t look like you’re doing it to get all the money (and run away).


“You cannot do enough research.” Your homework can include looking at the relative worth of OTHER Kickstarters who are doing a similar thing. There was The Pomplamousse Kickstarter, they did a blog post breakdown showing they took a LOSS in the end, but ate the excess themselves because they were glad to be able to reach their audience. Blind Ferret is another person who did a blog breakdown. Don’t promise “gold coins” by ball-parking, price them out.

Watch for cost changes! On Jan 1st, 2015 the shipping rates in the US increased by about DOUBLE, leading to many sheepish individuals (in part because the change was not well advertised). Some forget to factor in tax and/or shipping entirely - that adds up, easily into the thousands. Even consider factoring in the cost of hiring someone ELSE to do aspects like shipping, which are really time consuming.

You likely don’t want to use a Kickstarter for marketing purposes. THAT SAID, a failed attempt can be a good way to see if your audience is legitimately there. If you don’t reach your limit, see about rearranging costs, cutting corners. “Can we do what we want for half that amount?” There are benefits to failing!! Though if you intend to try again, keep up your promotion, so people don’t forget.

Don’t assume people know you’re raising money. Tweeting twice isn’t enough, you need 15-20 times to get it to all followers... and yes, some who read everything might get annoyed. But you NEED people to see your Kickstarter before it’s gone. (Or you get “What? I didn’t know and I read the comic every day!” “But did you READ THE BLOG??”) Make sure to connect with people on a personal level at the same time - they’re investing in YOU as much as your product.

Don’t assume people even know what a Kickstarter is. (Do you know about BandCamp?) Ask for ReTweets, and for the word to get out, there’s no corporation behind this. You have to prostitute yourself. (But perhaps don’t ask the Pope to ReTweet about your new Metal album.) Also, don’t run a Kickstarter at Christmas, or even in January, as people don’t have as much money to throw around.

IronSpike was mentioned as a “Kickstarter Queen”, who has begun 7 Kickstarters and delivered on the first 5 thus far. There was also mention of a happier story towards the end: Cryptozoic who came in to offer funds, after a Kickstarter which involved someone running off with the money.


I went to the music panel mostly because of my attempts to produce parody math videos. So it wasn’t immediately relevant to me, but there were enough tidbits of interest (and I stayed to the end). I went to the crowd funding panel mostly because literally everything I throw onto the web, from all my fiction writing, to my new web comic, to non-fiction recaps like this, is earning me zilch. So maybe I should have a donate button?

To that end, mostly I learned I need to do loads more research, and that my tiny audience doesn’t merit a Kickstarter at this point. (People have told me to publish personified math. I still doubt there’s a market, and you’ve seen my drawing, right?) Anyway, as a member of said audience, temporarily or not, I’m hoping you found this post useful!

Thursday, 20 August 2015

200: No Reason

Welcome to MathieXPensive, post #200! As I did back in October 2013, with post 100, I decided to write another short story of fiction. It... turned into a lemon. So I wrote another one! Here it is, along with an additional experiment in sketching.


Time travel was not only possible, it had already occurred. Once you accepted that basic premise, everything else fell into place.

Marie stared at the six computer screens displaying the results of her calculations. The forty something woman leaned back in her chair. She drew some strands of her long, dark hair to her mouth, nibbling on them. Maybe that was a bad habit, but it beat nibbling on her fingernails, which she’d long ago decided was worse. Besides, it didn’t matter if this gave her split ends - it’s not like anyone came out to visit her any more.

“I can do this,” Marie concluded.

She pushed herself away from the desk, heading for the stairs. She stopped. She turned. She walked back, grasping the small red cube next to her central keyboard, and after a moment of hesitation, she activated it. Setting the personal device to follow, she released it, and it hovered in the air next to her.

She turned and strode across the room again, the cube keeping pace. “I’ll be leaving shortly, Al,” she stated, as she started up the stairs.

“For how long?” came the not-quite-electronic voice. The red light flickered within his - the voice sounded male, so why not ‘his’ - 5cm by 5cm by 5cm shape, more or less in time with the sounds.


The artificial intelligence - a male ‘AI’, hence her name for it, Al - first reacted with silence. For what had to be an incredible amount of time in electronic terms. Marie briefly wondered to what extent such mannerisms had been preprogrammed in, and to what degree it had simply adapted to her own expectations over the last thirty odd years.

Thirty years. She’d received Al at fourteen, and he had been her only constant companion since that time. What had become of her life?

“Have I displeased you?” Al questioned at last.

“Nope,” Marie asserted.

“Are you gravely ill?”

“I hope not.” She reached the landing and headed down the hall towards her bedroom.

“Are you getting married?”

Marie stumbled, and nearly fell. The unexpected question, combined with the very thought of her hooking up with ANYONE, of either sex, made her laugh out loud. She turned to regard her device, needing to lean up against the wall until her giggles had subsided. “Why Al, I never knew you had such a quirky sense of humour.”

“Marriage is the next most likely reason for you to want to terminate our association,” he countered. “Seeing as your new significant other would want you to spend your time with them, and not with me.”

“Al, when was the last time I had a real date?”

“One year and 232 days ago.”

Marie pursed her lips. Damn. Had it really been that long? Who had that even been? James? Sue? “I think that was a one night stand.”

“You called it a date.”

“Yeah, well, I tend to use a lot of the wrong words when I’m around other people,” Marie grumbled. “Since people are such jerks.”

“You say that a lot lately. I am starting to wonder if it is for my benefit, so that you can sneak off and see people when I am inactive.”

Marie eyed Al. “I wish I could figure out when you’re joking.”

“Me too,” Al agreed. “I am constantly refining my humour subroutines.”

“Keep working at that.”

“It will be difficult to do once you’re not around.”

“Point,” Marie granted. She pushed off the wall and resumed the trek to her bedroom. “Sorry.”

Her device kept pace. “So why are you leaving?”

“Because I have to travel back in time to convince myself that I can invent time travel. Which happens to be a one way trip.”

“Your efforts have been successful then?”



Marie looked over her shoulder. “One moment. Al, why was marriage more likely to you than me succeeding in my research?!”

“Merely because I did not realize that you would leave immediately upon your success. Why is it you need to leave today?”

“Predestination paradox. Look it up.”

Al went silent again. This time he was probably connecting to the Cumulus Cloud or whatever they called the information branch of the web these days.

Marie reached her bedroom. She kicked off her shoes, pulled the curtains closed, and began to remove her clothing. She idly wondered why she’d even bothered to cover the window. She had no neighbours, not this far out in the woods. Her latest food delivery had come two days ago. There was no reason for anyone to be out there. What was she worried about, peeping squirrels?

“This does not compute,” Al concluded.

Marie pulled down her jeans. “How do you figure?”

“I have found no reason you need to leave today.”

She straightened to pull off her shirt, kicking her pants aside. “I solved the equations today.”

“But you did not expect to solve them today.”

“I guess not. How is that relevant?”

“You are changing your clothes.”

“No duh, Al.” Marie threw her shirt overtop of the little device. The cube’s hover position descended by about a half metre. “What of it?”

“A predestination paradox, or causal loop, is a form of paradox that occurs because there is no apparent source for an item or concept,” Al clarified. He was trying to make his voice sound muffled. Marie rolled her eyes.

“I already knew that,” she pointed out. She headed for the closet, deciding not to bother swapping out her underclothes.

“For instance, you are given a ball today, and at SOME future point, you travel back in time and give yourself the ball. The item hence has no origin.”

“Al, you don’t have to explain it back to me!” Marie said. “It’s what I used to complete the equations! Once I realized that I was the one who spoke to me back when I was twelve, everything fell into place.”

She pulled out her red dress. She stared at it. Between it, and the conversation with Al, this was becoming more real.

“I grant that, in your case, you claim to recall a sharing of information with yourself, rather than a concrete object,” Al continued to speak. “But whether it is information or an object, you seem to have missed out on the fact that you retain certain aspects of free will.”

Marie fingered her dress. “Except I don’t,” she asserted. “It’s funny. People have always told me to give up this research, that I was wasting my life, that I should find a nice full time job, be more social, and basically turn my mental capabilities and quirky nature towards something of actual worth.”

She half smiled, pulling the dress against her body. “Except for that time, when I was twelve... the only time in my whole life that anyone, adult or otherwise, EVER believed I had this in me.” Her smile vanished. “So of course, it turns out that, by listening to the old lady in the red dress, I sealed my own destiny. And in all my life, the only person who ever had faith in me... was me.” She swallowed. “People are such jerks.”

“This still does not compute.”

Marie shook her head to clear it. “You’re not making sense,” she objected. She began pulling her dress on. “I solve the equations, I travel back in time to tell myself to never give up, loop closes, end of story. What’s your beef?”

“There is no reason you need to leave today.”

“I just TOLD you--"

“There is no reason you need to leave TODAY,” Al insisted.

Marie adjusted the straps of her dress as it fell into place. She eyed her shirt, hovering at waist level. Then she walked over and snatched the clothing off her device. Al rose back up. “You’re saying that, because when I got dressed this morning, I didn’t choose to wear the clothes I’d be wearing to time travel - that means I don’t need to time travel?”

“Correct. Not today.”

“What in the hell is the point in waiting?”

The red light inside her device flashed silently a few times. “What in the hell is the point in not waiting?” Al finally asked.

Marie found she could only stare.

“Besides, the human memory is fallible,” Al added. “Perhaps that dress is not, in fact, accessorized the same way as it was when you saw it over thirty years ago. Perhaps your hair is not yet the correct length. Perhaps you should take more time to think things through. There is no reason you need to leave today.”

“Y-You can’t be saying you’ll MISS me,” Marie protested, dumbstruck. “You’ll be deactivated, you won’t know! Besides, I’m always either grousing and complaining at you, or whining and moaning about how lonely I am, and how much I need to stop reading those god awful romance books. You should be glad to be rid of me!”

Al rotated in the air. “I am not emotionally impacted by your departure. I am merely saying that there is no reason for you to leave today.”

“I can’t figure out why you’re saying that.”

“Nor can I,” Al admitted.

Marie realized she was chewing on her hair again, and she made herself stop. She went to grab the tool that would allow her to zip up her dress. Seriously, she thought, the sum total of all of human knowledge was now accessible via a simple verbal interface, yet there were still no pretty dresses that could self-zip.

“Look, I can’t take you with me,” Marie sighed. “All electronics get fried. It’s a fundamental aspect of the time journey. I worked that out years ago. Five more days of study, heck, five more years, it won’t change that!”

“I understand.”

“I mean, shielding, MAYBE,” Marie yielded. “You’re not that big. But that’s not my area of expertise, which means not only having to TALK to people, but years, DECADES more work.”

“I am not saying you have to take me with you.”

“Then what ARE you saying?” Marie demanded, now fully zipped. She was starting to feel irrationally angry.

Again a pause, then, “I am saying is that there is no reason you need to leave today.”

“Oh, for - give me something to WORK with here, Al! Do you think you’ll somehow be lonely?” Marie asked. “Should I give you to some nice young girl who will appreciate you more than I did? Though it would more likely be to some thirty-something, because you’re not exactly state-of-the-art any more, even with your upgrades..."

“As you have yourself pointed out, I will be deactivated. I will not know you are gone.”

“So WHY are you being so damn ARGUMENTATIVE about this?” She brushed down her dress and put her hands on her hips.

Her personal device now rotated around it’s axis several times, a sign that Al was struggling to find an English way of parsing a particular concept. At last, the red light pulsed. “You are special,” he concluded.

Marie was sure she’d misheard. “I am WHAT?”

“You are special. If you leave today, no one will know this. Except for me, and I will have been deactivated.”

“Oh, I’m special all right. Special needs.”

“That is not what I mean. Perhaps I did not find the correct word.”

Marie pinched the bridge of her nose. “Is that what this is about? You think I should be rubbing this in the noses of everyone who told me my research was pointless? That I should stick around to publish a paper? Because I can tell you exactly how THAT will go.”

She sat on the edge of her bed. “My relatives will smile at me but have no idea what I’m even talking about - like normal - my colleagues will pat me on the back and request to apply my methods, hoping they won’t have to speak to me - like normal - my detractors will rush to discredit me, pointlessly attacking my sexuality and ethnicity - like normal - and I’ll never get another date because half the world’s population will believe I’ve become unattainable while the other half will - like normal - think I’m a hopeless geek!”

Her fingernails dug into her palms. “Though apparently it’s been 597 days since my last major night out, so I guess THAT one matters less.” Marie shuddered, then began to chew furiously on her hair. “I don’t need all that stress in my life, Al.”

“I did not mean to distress you.”

“I know.” Marie bit down more gently, before pulling her hair gradually out from between her pursed lips. She stared at the floor. “It has to be today.”

Al didn’t say anything. Marie wondered if it was another extended pause for her benefit, or whether he, in fact, had nothing to add. “I understand now,” he said at last.


“But I do wish others could have seen you as I see you.”

Marie curled down towards her knees, pressing her palms to her face. “Yeah, well, surprise! We don’t always get what we want in life.”

“Indeed. People are such jerks.”

She went from being on the verge of tears to laughing out loud. She couldn’t help it. She looked back up at her personal device. “Al, have I ever told you that you’re wonderful?”

“Not since you were fifteen.”

“Oh. Well, you’re wonderful. And I’m sorry for not saying it more.”

“You are also wonderful. Perhaps that is the word I was searching for.”

“Perhaps.” Marie looked up at him. Slowly, she stood, and walked over, drawing in a long breath. “I’m deactivating you now. You won’t see me again.”

“All right. Goodbye, Marie Melendiez. It has been a pleasure.”

“Yeah.” She plucked him out of the air, running a finger along one of his edges. “Yeah, it has been. Thank you, Al.”

His light pulsed out once more, with no accompanying voice. Marie’s grip tightened slightly. She unset the follow command, and deactivated him. And then stood there, looking down at the inanimate cube in her hands for at least a minute, before carefully placing Al onto her bed.

“I guess, in the end, you had faith in me as well,” she realized. “Go figure.”

It took another minute before she could turn around and walk out of the room, but once she had, she never looked back.

The temporal trip itself was not hard. She’d had the hardware in place for years. All it had needed was a way to target, which Marie could now provide - namely, her twelve year old self. That day, in the park, after school. She knew it would work now, since it had no choice BUT to work. Predestination.

The one hitch was that she was only able to set a date, not an exact time - after all, it was always afternoon somewhere on the Earth - so Marie was rather surprised when the trip ended. The sun was lower in the sky than she’d anticipated.

But that surprise was nothing compared to the reaction she had upon catching up with her younger self. Because there she was, young Marie, sitting on the bench... talking to a woman in a red dress who was definitely NOT her, as that woman was a bit too tall, and her hair was a bit too short, and all at once, Marie realized that her perceptions of the world had been full of distortions.

This changed everything.

Enjoy that? Enjoy time travel? I'm blogging a time travel serial as well! Go see!

Alternatively, you can comment below. Possible topics:
-Whether Marie is a sympathetic character or not.
-How predictable any of that was.
-My writing style. Again, I don't do short stories much, they tend to turn into epics. But I had some feels for these 2,500+ words.

Regular posts on the blog resume this weekend, with the rest of ConBravo.