I drove down on Wednesday, like usual, and left later than I'd intended (which also tends to happen). Trapped for an hour on a 5 km stretch outside Brockville, had to find a dinner to go. I was staying in a nearby hotel this time, rather than on the campus; it was for only two nights. I made it through registration in good time Thursday morning (after the fun of parking), including dropping off some materials at the OAME 2019 booth that I'd volunteered to bring down.

#### THURSDAY, MAY 3

1) 8:30am: "

__Bridging the Numeracy Gap and Preparing Students for Success in Mathematics__", presented by Anand Karat (President) and Paula Gouveia (Dean), from Humber College.

This was about the Ontario Colleges Math Test - High-School Edition. Their Assessment Development Project's Final Report identified nine topics of need: "Whole Numbers", "Number Sense", "Integers", "Decimals", "Fractions", "Ratios & Proportions", "Percents", "Algebra" and "Conversions". There were also subtopics within each (for instance, "Decimals" included place value, reading/writing numbers, arithmetic, and rounding).

The project started with 10 years of research, initiated in 2004. Assessing questions on all topics was phase one, in partnership with the Toronto Catholic District School Board. Trying them out did have to be voluntary and with parental consent. There were 202 student accounts, of which 101 completed the material with a mean of 46.3% and a standard deviation of 24.2%. Which, it was pointed out, means that you can get to 96% by being two standard deviations away in a normal distribution. This was more about the feedback than the ability measure. The most successful topic was Decimals (the least successful was Algebra).

The idea is a test that takes no longer than an hour, with questions from all nine foundational topics, giving an idea of what first semester math course to take (applied/academic in the case of Grade 8). Moving the project into phase two (2017), they had 427 accounts and 335 who completed the material, this time a mean of 50.9%. Of supplemental questions, they also noticed a correlation between those who said they liked math, and success in the system. They're currently in phase three, AEAC aligned (implementing in 32 schools).

We had a chance to try out the system (student format). Every topic had three areas: Diagnostic assessment, Remediation modules and Summative. You needed to complete the previous area in order to 'unlock' the later ones, with a threshold to achieve in Remediation before you could unlock the Summative. The teacher login account was seen to provide more information, for instance how much time was spent on the app in the last 24 hours.

It was also mentioned how "it's the course, not the grade that makes the difference" in terms of MCT 4C (55% needing remediation) versus MAP 4C (80% remedial), but post-secondary is in a bit of a bind in that if they say a student must take MCT (which isn't available at all schools) students would simply go to a different college that doesn't need it. I have the copy of the presentation slides that they made available, which includes some summary statistics and graphs, for the curious. Their website is http://ocmt.mathsuccess.ca

2) Keynote: "

__Building a Thinking Mathematics Classroom__", presented by Dr. Peter Liljedahl (Professor SFU).

I'd seen Peter Liljedahl's work before, when he came to Ottawa for the Canadian Mathematics Education Forum in 2014 (see my recap post here). Followed by his presentation to math teachers of the OCDSB during February 2017's PD Day (see my recap post here). So I didn't take tons of notes during this keynote, to avoid repeating myself. Peter himself noted how he would both be going through things from scratch (for those who don't know about the "Thinking Classroom") with nuances (for those who do).

We had the preamble of Jane's Class, 15 years ago, with the rich tasks that didn't go well, leading to the research. Around the world there are certain institutional norms, some of them non-negotiated. Thinking and Engagement often travel together. When a lesson as a whole is "too big", too much info, better to find discrete moments. A "good problem" to work on is when there's something left to think about.

One of the key nuances Peter mentioned was how questions flow along the same lines as knowledge, but in the opposite direction. So, it's better to ask peers (for the knowledge) than the teachers (when answers stop the thinking process). Also, don't answer proximity questions (because you're there). To have meaningful notes, it was also mentioned to frame them as "notes for my future, dumber self". We want to move to the model of breaking down the unit, not a blob of stuff.

The optimal practices for thinking: Begin lessons with good problems. Use verbal instructions. Answer only "keep thinking" questions. Defront the classroom. Form visibly random groups. Use vertical non-permanent surfaces. Foster autonomous actions. Have students do meaningful notes. Use "check your understanding" questions. Manage flow. Consolidate from the bottom. Show where they are and where they are going. Evaluate what you value! Report out based on data (not points).

Towards the conclusion, Peter said that the Most Powerful Tool was the idea of FLOW (avoiding the zones of frustration or boredom) and that the Most Important Tool was using Randomized Groups.

3) "

__Using quick activities to collect authentic data__", presented by Jennifer Gravel (Holy Trinity School).

There were six activities which Jennifer walked us through. The first was "Are your Smarties normal?" Nestle claims there's the same number of each when they make the boxes. Try to get a mathematical debate going with one variable statistics (half of table support claim, half disprove claim). Can do box plots by colour, confidence intervals, and there's the Skittles alternative. (Colours are Red, Orange, Yellow, Green, Blue, Purple, Pink and Brown... I had lots of orange, few pink.) This website actually still has results, which is kind of cool: http://bit.ly/SmartiesResponses

The second activity was "How old am I?", a guessing game where you have to estimate the ages of 12 famous people. (Names ranged from Justin Trudeau to Millie Bobby Brown, whom almost no one knew but she was in Stranger Things.) Then Jen gave actual ages, and on a scatterplot, you would plot actual (horizontal) against your estimate. Another debate here: Who is the "Best Guesser"? (The most exactly right? The closest overall?) Then draw the line y=x, and you can use "Guess minus Actual" for residuals, plus you can talk outliers. (Also something that can be done in Desmos.)

The third activity was "Arms and Feet"; record length of forearm from wrist to elbow, and length of foot, in centimetres. It was also a scatterplot exercise though, so we moved on. Activity Four was "How many are there?", based on the German Tank Problem of World War II. The germans would label tanks sequentially, and there was a desire to know how many they had and the rate at which they were being produced. So Jen had tables take 15 Chips from a bag, record the values (from #1 to #n), and then estimate how many (n) chips there were in total.

Our group had more 200s and 300s, so we considered both taking the middle and doubling it (to 458) or looking at sets of 100 (our max number drawn was 310 so we got to 350 somehow). Meanwhile, another group had no 300s and wondered what we were going on about. (The final total was 312, Jen used plastic counter chips from Spectrum. She says Bingo Chips are impossible to handle.) This is a good exercise for Sample Size and Accuracy (how many are needed).

The fifth activity was "Which one is faster?", which involved different methods of shoe tying. Jen had noticed that many students used the bunny ears method for sports shoes, rather than looping one lace around. The idea was to time how long it took to tie with each method. Of course, some students might not having lacing shoes; fake shoes were made as simulations. Leading to the question of whether a paper shoe or a real shoe were influences. (Or the type of shoe?) Discussion points could be bias and sample design.

The final activity was "Random Rectangles". Jen had an Excel file where a number of squares were shaded in, creating 100 different sized tile sets, from a single tile (multiple times) to #64 which was 6 by 4. Question: What's the average unit area for ALL these images? With that done, pick ten random numbers. Find the areas for them, and average them for a total. Finally, have a computer generate a random list of 10 numbers, and repeat the process.

What tends to happen is that the Gut Reaction tends to be HIGH, the eye being drawn to the larger tile sets. (True in my case, I started by saying "8".) The second random method is better, but humans are bad at being random, so the third computer generated one tends to be the most accurate (actual average was 6.3). Jen had an electronic version of her files (and she is also on twitter @JenGravel).

The fourth slot of the day was my *LUNCH*, which I always pick to give myself processing time. People who just grab and go to an extra session amaze me. I also visited the exhibitors, getting an "iTweet" ribbon for my lanyard, a Wipebook scroll, and a bunch of bookmarks (I think - not sure where else they would have come from).

4) "

__So your classroom is thinking... what about students with exceptionalities?__", presented by Janice Bernstein (OCDSB) and Thach-Thao Phan (OCDSB).

My last regular time slot involved this presentation, by the same duo who last year presented "Really everyone has an IEP". The top challenges for exceptionalities (as suggested by the audience, interactively) are processing, attention, behaviour and memory. Exceptionalities include autism (role modelling is essential), ADHD/ADD (attention spans), NVLD (non-verbal, like Aspergers but without the social skill deficits), and receptive/expressive language disorders (when they say "add" but are thinking "multiply").

Visually Random Groups was remarked on (use of flippity.net). Give specific roles for those who need structure (the "Desmos checker", for instance). Gradually build the number of people, and make those in the group aware of the need. We know verbal instructions are best (from Peter's research) but ensure instructions are accessible to every type. I've also written "person in necessary space, move around"(?).

Emphasize how there are many solutions - some more efficient than others. Give small goals so anxiety isn't overpowering. Include a reflection question as homework. Mobility issues was raised, with mention of de-fronting the room. There's also autonomy, when students can use Desmos or other items as experts.

There was then a wine & cheese (@3:45pm), where I spoke briefly with some others from Ottawa, before retreating to consider more substantial food in advance of the later Keynote.

5) 7:15pm Keynote: "

__Teaching Mindset Mathematics Through Open, Creative Mathematics and Brain Science Messages__", presented by Jo Boaler.

As was the case with Peter Liljedahl, I have also heard Jo Boaler speak, back at OAME 2014 (recap post here). Which was four years ago, so I thought I'd see where we were at, it's only that (once again) you shouldn't expect lots of detail. Of note, she also mixed in "seven reasons Jo loves Canada" (she's British). The key idea is a "growth mindset" (eg. I can't do this yet) versus a "fixed mindset" (eg. I can't do this, only some people can). Considering your mindset is good for girls, ELLs (English Language Learners), and those sociologically disadvantaged.

There was an online class, "How to Learn Math", with a randomized controlled trial. The YouCubed Mindset Teaching Guide looked at five areas. "Neuroplasticity" is the idea of the brain forming new connections. "Smart" and "Gifted" labels lead to FIXED mindsets, where having to struggle crushes spirit, and grades define a person. (There was a study in Toronto; I have the names Norman Doidge and Carol Dweck written down.)

Things are gendered and racial-ized. Students were three times more likely to rank a professor as a "genius" if they were male versus female. Give yourself "desirable difficulties" to study, not reading. Iterations with students when struggling. (I have #TheLearningPit and James Nottingham written down.) Also referenced was the PISA test. (http://www.oecd.org/pisa/test/)

Five areas of the brain light up when given a math problem, two of them visual. The Lines and Squares handout was referenced. (10 straight lines can make 17 squares, while 9 straight lines in more of a grid can make 20 squares... what's the smallest number of lines needed to make exactly 100 squares? Don't overshoot.) Not timed! Anxiety impedes the "working memory" (search engine), time is necessary to think.

Mindset Mathematics: It infuses brain science & mindset messages, it values struggle & mistakes, it is creative & visual, it is open & investigative, and it is about about depth, not speed. Also, collaboration.

With that, I'll conclude this post and continue in the next one with Day 2: Open Tasks and Questions, plus extras.

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