It still tests my shorthand, except this time my shorthand was typing directly into my laptop. (Is there a term for that? Honestly, the main problem was autocorrect.) For this post, I’m keeping the point form I used, while cleaning up the sentences for you. Doing otherwise may cause it to linger on my hard drive even longer - not unlike my recap plans for the rest of the conference. I’m not sure if this format means I end up capturing the heart of their talks - what do you think?
TALKS: ROUND ONE
1) Sunil Singh: Mathematics Is...
-1971: An invitation by Willie Wonka, nestled in the movie scene was a song.
-“Creativity is intelligence having fun.” -Albert Einstein
-Show having fun with numbers. Start with pi, both irrational and transcendental. Then see numbers 1-49 in factors.
-“Prime Climb” is a game on Amazon, primes are colour coded! A Seattle based company “math 4 love” made Prime Climb.
-Also see James Tanton’s yellow book, “Arithmetic = Gateway to Love”
-How do teenagers see math? Bounded (textbooks) or boundless?
-BOOKS: “The Math Olympian”; “The Crest of the Peacock”; “Mathematician’s Lament”
-Mathematics is Imagination. But there’s more, let’s bring in Keats, Mathematics is also Beauty and Truth.
-“What was our philosophy again?” Math has a right to... beauty.
2) Matthew Oldridge (@MatthewOldridge): Mathematical Surprise
-On Mathematical Mess: Are we prepared to be surprised by student thinking and our own thinking?
-Given time and space, your students will ask questions. Try a “wonder wall”, an open space for thinking, with questions written on chart paper.
-Teaching Rates: “We knew the math and we still didn’t predict all the strategies.”
-Using Minecraft to construct bar graphs? (The game is literally an infinite space, what could happen there?)
-“I didn’t think of that.” There are so many methods and strategies. The thinking is there, we have to let surprise emerge.
-The start of a proof for area of a trapezoid? Critical insights.
-“What’s a fair price?” (Go to price per kilogram? Conclusion: Food in vending machines is obviously overpriced.)
-One student generated a model for points scored by a hockey player.
-“I left this slide blank if I was running out of time.” But it’s space to think, let’s call this the metaphor.
3) Chris Suurtaam: What’s Important?
-In math teaching and learning, RESPECT everyone: Teachers, students, parents, administrators, colleagues.
-All students are able to engage in mathematics and to extend their mathematical thinking. It’s a right.
-We need to think about equity issues. “There is no time limit in terms of exploring mathematical ideas.” Everyone has the right to feel value learning and to feel capable as a learner.
-Students learn in different ways and it’s that diversity that should be valued. They won’t all be hitting the same target at the same time. Don’t measure a lesson like that.
-A lesson is successful if by the end of it, the students’ thinking has moved from where they were before.
-Value the math that students bring, and the various ways they work. All solutions involve mathematical thinking, not just those that are symbolic.
-We learn mathematics by connecting mathematical ideas. Mathematical thinking is at the centre of learning.
-Assessing What Matters: What IS the important mathematics? I’m not talking about an assessment event (e.g. test) but the ongoing listening and thinking.
-Assessment shows students what you value and what mathematics is important to know and be able to do. If we say we value problem solving, then assessment should value those things.
-Attentively question, listen and respond to students’ thinking and engage them in important mathematical tasks.
4) Ron Lancaster: The Rubik’s Cube
-On the Rubiks Cube, Contests, TV commercials, and a great teaching and learning tool for all.
-Books and puzzles: A Rubik’s clock is just as good as the cube.
-There was a 1981 Rubiks cube contest at Ron’s high school, led to teaching how to solve. It’s the math in the cube that is amazing.
-Sequence of turns and order. Doing movements over and over again, the cube will come back to original position. Can provide a big picture view of mathematics.
-1/7 loops back around. Related: f(x) = (x-3)/(x+1), the x comes back in sequence, f(f(f(x))). 8 perfect shuffles will restore a deck of 52 cards. Inverse function can be taught through this.
-Number of positions for a 3x3x3 cube: only by visiting the 12 worlds. If you unstick a colour and swap it elsewhere, the cube becomes insolvable. You must divide by 12 to get the overall Rubik’s formula.
-Becel margarine commercial, a move that twists the centre of the U; centres of the cube also.
-Doug Henning trick on NBC special: Tosses cube into the air, it’s solved. LIVE DEMO
5) Kyle Pearce (@MathletePearce): Engagement
-Hi. Web: http://tapintoteenminds.com
-Engagement is a buzzword. There’s many types of student engagement but no clear answers.
-It does NOT look like making good notes. “A simple question like the following will appear on your test.”
-Behavioural engagement might improve with technology, but not their engagement of the MIND. What measure is being used?
-Next tech tool: Cards and Smartboards. That saw improvements to success rates, had a working formula for standardized tests - but are students just being compliant?
-OAME2012 shift, and joining the MTBoS, hundreds of math teachers.
-Saw that innovative uses of technology can improve things, but it’s merely a bandaid solution.
-Traditional lesson plan worked due to familiarity rather than engagement. Promoted memorization rather than connections.
-Do not give a crossword puzzle with all the solutions listed on the page. Algorithms aren’t engagement or understanding. Task based assessment format allows interconnectedness.
-Never stop trying to find new ways to leverage the natural curiosity that we all have.
(You can view Kyle's Ignite on YouTube: thanks @jgibson314 !)
6) Marian Small (@marian_small): Pushing Deeper
*Quick happy birthday for this weekend.
-No news! It’s all about high expectations. I am just “one more push”.
-You can settle for correct answers or you can push for more insight, more connections, more sense-making. You can settle for “That’s right” or suggest “That’s great, now what about this?”
-Practice your “one more pushes”. Such as (moving through grades):
>‘What sums can you get if you add two next to each other numbers? What sums can’t you get?’
>‘If two sides of a triangle are 4 and 6, what perimeters are impossible?’
>‘Draw the greatest obtuse angle possible. Are you sure it’s the greatest?’
>‘Can 25% of one number be 75% of another number?’
>‘Remove one data value so that the median goes down more than the mean.’
>‘When might a line with a slope of 3/2 look steep? Look not so steep?’
>‘If an angle doubles, does the cosine for it double, more than double, less than double? Does it depend?’
>‘Create a spinner with unequal sections where the expected value is -0.5’
-I push me all the time to refine and improve, to differentiate, to share substance as well as meaning. You can push students for deeper insight and understanding, as well as more “generalizing” (things bigger than one little problem).
-Make thinking about your practice and questioning your normal game plan.
-We all started with “one more push” (pun on birth).
7) Dan Meyer (@ddmeyer): The Express Lane
-Which line in a grocery store is fastest? “Think about that for a second. Now five more seconds.”
-“The express lane has great PR unless it’s a scam. ... Yes it is.”
-What information matters/doesn’t matter to find out? (asked audience)
-Number of items someone has is a particular idea. As items increase, what happens to total time? Get data, model with equation. Total time = 3 * items + 35 seconds.
-There’s a flat rate of time to pay and chat with checkout person!
-Situation on slide: Need 173 seconds for 4 people with single digit num of items, versus only 155 seconds for the single 40 item guy.
-Featured on national TV, “In the Fast Lane”, art of zigging and zagging. (Dan lost. Models don’t always describe things perfectly. “I got nailed by produce.”)
-“All models are wrong, but some are useful.” - George E. P. Box
-A slide to reiterate the 6 step modelling with Math: Shouldn’t only be calculation. There’s the humiliation of the Validation step.
-Remember: Each person in line is a standing version of 10 items (due to flat rate).
8) Amy Lin (@amylin1962): Creative Spaces
-Our math classrooms are usually more row based. We’ve been trying to improve those classrooms, like a game it comes with instructions.
-In the game of mathematics, it’s about addition, we’re adding more games and technology, to increase scores and grades... because that’s winning the game.
-Is it? What is the goal? What is winning?
-Turn class back into a playground, play is valuable. Play is now apps on a phone and video games.
-We can create successful classrooms by being creative and giving students choices. Maybe the goal shouldn’t be adding, but empowering. We’ll get feelings of confidence. A better chance of deeper understanding.
-Problem of math anxiety? Can add a fun game, they get high scores and rewards, or can have tutors and video lessons and worksheets to help prepare for exams.
-“I’m going to launch a campaign about creativity and to abolish grading.”
-Promote student thinking and conversations. Want to get a space designed for students to WANT to engage. Maybe the new solution is more about what you cannot measure.
-I want to start “The Math Movement”, a community of educators who sense that something is wrong with the old game. I think we will win because we will see students light up and be driven to share what they learn with us.
-Open minds and hearts play in creative spaces. That’s a win for us.
(Insert Session Break)
TALKS: ROUND TWO
9) Jonathan So (@MrSoclassroom): Doers v Doing
-We want students to become “Doers of Math” instead of just doing the math
-“The purpose of teaching is to help students learn.” (Fosnot and Doik.) Could see them as two separate things. Or “If learning doesn’t happen there is no teaching.”
-Common complaints: “Didn’t they learn this last year?” “Why am I doing review over and over again?” If I am the common denominator each year, then I need to change. We need to build mathematicians.
-A close minded way of learning fractions - only looking for answers? Use same thinking, but now explaining solutions and being forced to talk about the math they’re seeing.
-Students need to present solutions in a generalized way. They need to feel comfortable trying out new ideas. Where we can take risks.
-A Working Framework: Role of the Teacher, Environment of Learning, Accountable Kids.
-What really impacts our students? Gr 4/5 class: talk died in asking rote questions but with big idea questions, then kids talked.
-Three Types of Questions: Interrogation, Going Beyond, and Comparing. With all three there’s a big idea to every one of them.
-Two Important Talk Moves: Wait Time and Revoicing. Allow time to think.
-Don’t be passive observers of the math. Are kids just doing the math or being doers?
10) Mary Bourassa (@MaryBourassa): Big & Small
-Making big shifts and small steps to grow as a teacher.
-Change your words, change your mindset. Set the culture in your classroom, and then can connect with all students.
-Big changes requires collaboration. Join the MTBoS; Twitter is her daily PD.
-Investing time in social media has paid dividends. Read blogs every day, find out what other teachers are doing. (Mary has shoutout of 5 websites.)
-Next, start your own blog. Share your practice, it helps you reflect, you get feedback. “If I can blog, you can blog.” “I didn’t think anyone would ever read my blog.”
-If you’re ready for a bigger shift, spiral an entire course with activities.
-If that’s overwhelming, smaller changes: Warm ups. Can be big impact in small time. Gets students into math mode. They can argue about math, start collaborating.
-Warm Ups Sites: Estimation180, Visual Patterns, Which One Doesn’t Belong (a book of shapes, goes to graphs, then Mary runs further with it).
-More small changes: No hands up. Hinge questions. Random groups. @dylanwilliams review stations. 3 strikes (N Kraft). Teamwork. teacher.desmos.com activities.
-“Change can be had, but it all starts with a big or small step from you.”
-“Be willing to take risks, students need to see us do that.”
(No Paul Alves - not sure what happened)
11) David Petro (@davidpetro314): Pi
-There’s a link at the bottom for all references: http://bit.ly/petro-ignite-2015
-This particular March 14 was Epic Pi Day. 9 decimals deep into pi. Einstein was born on Pi day. Coincidence?
-Random nature of Pi guarantees that your birthday is in Pi. (website can find it)
-Feynman Point (repeated digit) that looks not random is the definition of random.
-Exists unofficial record for digits of Pi: not acknowledged by Guinness Records.
-There’s a poem that goes 31 decimal places deep into pi.
-Pi in the Bible, Kings 7:23? Pi in Congress, in Alabama wanted to make it 3? NOT TRUE. BUT Indiana did try to make pi “3.2”.
-Could the average sinuosity of all rivers in the world be pi?
-Buffon’s Needle, dropping of toothpicks: what is probability of toothpicks lie on line? (Asks low/high estimate?) It’s 2 / pi, yet no circles are there.
-Two transcendental numbers and an imaginary number walk into a bar. There’s a proof from first principles on an Ignite session out there.
-“Reflect” on PIE/314.
12) Nora Newcombe (@kittydundana): On Quantity
-As a Cognitive Psychologist, knows Piaget: Space and Number take years to develop. Children confuse number, length and density. This is both true and untrue!
-It’s true in some ways. Toddlers can remember where we hid something in a sandbox.
-Babies are able to notice PROPORTIONAL quantities (compared with another) more than ABSOLUTE quantities. Proportional reasoning is what supports scaling.
-Demonstrations of babies isn’t about number, it’s about magnitude and general quantity.
-As they grow through preschool into elementary, they’re connecting things. Spatial is linked to number lines. The number line is both spatial and numerical. It joins integers with values in between.
-Yet students eventually LOSE some of the between, because we focus on discrete values so much.
-They don’t remember that a unit is a distance. They think a unit is the slash marks on the number line. Perhaps don’t line up everything with zero? Kids in early elementary school lose the sense of measurements.
-Also fractions are difficult (but important). How to get around problems in that reasoning? Proportional reasoning and scaling are deeply related initially, yet proportional reasoning also is related to fractioning.
-Think about number and space together. Use CONTINUOUS as well as discrete representations.
-Putting lines in between integers shouldn’t be of a smaller size. Number line can then be used for fractions and negatives.
-Push the number line so that it’s important, not merely discrete integers.
13) Don Fraser (@DonFraser9): Take Numb out of Numbers
-How to use the new technology? The best motivator is success, but also important is the hope of success. “We can’t spell success without U.”
-Look at the numbers: 1,2,3,4 and in your mind, circle one. Mostly people pick 3. Why? I have no idea. (Do you?)
-Shopping is an excellent source of real world math. (Image in store: “Was $3.99 now $3.99 save $0.”)
-A growth mindset in math means?
-New book: Becoming Steve Jobs. At $25/bag, air travel is becoming very expensive. Measurement. Peanuts comic.
-Linking math and writing. On average, Americans open their refrigerators 22 times per day: There’s no way this is true? Add all values together, averaging.
-Canadian license plates show there’s at least two aspects to math. “Yours to Discover” (Ontario) and “Je me Souviens” (Quebec).
-Do more rich people put toilet paper over the top? 2/3 of Canadians are right kissers, tilting right to kiss. Regional thing? Pose questions.
-Thank you for making a difference with the students that you ignite.
14) Al “The Big O” Overwijk (@AlexOverwijk): Reinvention
-If you told me years ago I’d be standing here, I’d have told you you were crazy.
-You know that I love to tell stories: My courses were unit based, moving easy to difficult, review, test. Do it six or seven times, call it a course. Then exam.
-They’d feel good about themselves, I’d feel good about myself, but it didn’t work for all students.
-What I valued was the content in the course.
-I told students I was the world freehand circle drawer, and despite the show, I still had disengaged students. Bruce said that I was the problem, I needed to change.
-We focussed on process. Focus on uncovering curriculum rather than covering curriculum.
-Here’s a prompt: (image of shirts). What do you notice, what do you wonder? How long to fold them? Why do you have that many shirts? How much surface area? (image of shirts in hallway)
-The sky’s the limit. Create something with low floor, high ceiling. Like “Beardo Weirdo” data when growing beard (on blog).
-Using “Visible Random Groups” & “Vertical NonPermanent Surfaces”.
-Get more teachers: Collaborative lesson studies. We learned about student learning. Testimonials from students.
-Some groups go the “wrong” way, we learn from their mistakes. Some take an inefficient way, some go right to an expectation.
-“It is better to make a story than to tell a story. It is better to have students make mathematics than to tell them mathematics.”
-I look forward to hearing your stories. If not now, then when, if not you, then who.
15) George Hart: Printing Manipulatives
-3D printing for the Mathematics Classroom (http://Georgehart.com)
-Want a Sierpinski Tetrahedron? His start was 3D Printed sculpture.
-You can create shapes and colours. Complexity is FREE. You can make complex things the same way you would make a cube or a sphere. Easy to program a fractal in two or three lines.
-How to take these things into the classroom? If you want a “MakerBot Cupcake”, “Strut Connector” or “Twelve-Stick puzzle”: can print the pieces. Mathematical models of all sorts of things.
-(10,3) a Lattice. Stellated Rhombic Dodecahedron. If you make a half dozen of them it’s so easy to see them fit together. Hollow and light.
-Screw puzzles. He has a bunch, come see him later. Tricky to assemble.
-“I’m not a classroom teacher, so I’m leaving it to you to see how you can use it in the classroom.” Have students create things and/or argue over how to work with things.
-You can write an equation for anything and make a 3D print. (Venn Diagram Candy dish shown - or anything else they want.) There’s some way you can use this to get students to be really excited!
-Classroom modelling. It’s cool! It’s fun! Shows the creative side, and teaches the importance of exact details. Gets students/teachers excited about math.
That was it! I left pretty quickly to get to another session. Feel free to comment on whatever stood out the most for you!