Breakthroughs, "A-has", and "Finding the Door"

I highly recommend this article on Yitang "Tom" Zhang's breakthrough on the Twin Primes conjecture. It's readable, inspiring, and full of lessons for elementary and secondary teachers of mathematics.  Don't worry about understanding the math (although it does explain it pretty nicely), just read Tom's story, from unemployed math PhD helping out at Subway, to becoming a professor, to his big breakthrough.

First, our students have these kinds of breakthroughs each and every day.  They don't have to be Archimedes style "eureka" and "jump from the bathtub" breakthroughs.  They aren't Einstein imagining himself on a beam of light, and conceptualizing relativity.  But they are breakthroughs, nonetheless.  Rather than bolts from the blue, these are often subtle and sudden realizations that they are closer to solving a problem than before.  You know, the "a-ha" moments.

These are the moments when things become clear, when they can see their way through a problem. They can begin to articulate a solution through the complex interaction of math processes, content and background knowledge, and classroom culture that we call problem solving.

There is a lovely description in the article of Mr. Zhang walking around and thinking about the problem, until one day, he "found a door".  He realized what tool he needed to solve the problem, and how he would do it.  The unbelievably complex math he was working on began with selecting tools he would use, and finding a way to represent the problem.  Sound familiar?  They should- they're two of our math processes.  If the math processes are the "actions of doing" math, doesn't it make sense that a professional mathematician would use the same processes as our young learners?  I think so- practice, experience, and knowledge background being the main difference.

The growth mindset math learner might say, "I can't solve this problem...yet."  We might change that to "I haven't found the right tool...yet."  Or:  "I don't know how to represent this situation with math...yet."

We could also say, "I haven't found the door...yet."  After you find it, you can walk right through, after all.

10 Good Things

I was challenged by Brian Aspinall to do a #10goodthings blog post, so here it is.

So many good things happened in 2014- reflecting back makes me very happy.   Through good fortune a lot of things fell into place.  These are my 10 good things from 2014.

1)  Minecraft and Math happened.  See video clip about the work of our classrom here.  The real hard work of using Minecraft as a consistent classroom tool is being done by people like @GumbyBlockhead and @zbpipe, and all the schools around the world on the MinecraftEDU servers.  

For me, this was less about technology than about an opportunity for differentiation and student voice.  What will happen if I let them try the math task (or even a textbook question!) in the Minecraft environment.  The results far surpassed anything I would have thought possible.  I kept asking:  "are you sure this will work in Minecraft?", and kept having my skepticism proven wrong each time. 

My blog post about the journey is here. 

2)  The journey into inquiry math.  Pictured is a student's projections using their mathematical model for how many points these players will score in their careers.  We use "wonder as the fuel" in our #GeniusHour math, and saw how questions spark more questions, which spark more learning.  Letting students loose to explore a math topic of their choice was amazing.  Their work exceeded all expectations!  My account of #GeniusHourMath  is here.  

3)  Starting #PeelMathChat with @raspberryberet. Here is a Storify of our very first one.  It is always inspiring to see educators talking math in the evenings, when they could be binging on "Fresh Prince" on Netflix, or knitting a scarf.  But seriously- our PLN is strong, and this is one way we share and collaborate.  

4)  Social time on Twitter (and IRL) with friends like Carla Pereira, Jonathan So, Tina Zita, Helen Chapman, Debbie Axiak, Melanie Essex, Jay Richea, Donald Campbell, Aviva Dunsinger.  Because, you know, it's not all work, all the time.  #Peelnomnomchat and other fun chats often bring a certain needed levity to life.  Now let's all help #Peelsockchallenge take off as a hashtag!

@Carla_Pereira2 these #noms are back! pic.twitter.com/j81eNIsMKm
— Matthew Oldridge (@MatthewOldridge) January 20, 2015

5)  Presenting about Math and apps at #TLDWpeel in the summer (which led to a further 2 part workshop with @tina_zita, and my #BIT14 presentation).  Sitting on the expert gaming panel about Minecraft was amazing too. 

6)  Watching @MathletePearse at #BIT14, and having to sit in the hallway because it was so packed.  Doing my session right after, 3 doors down, and having the room totally packed.  

Also at #BIT14, the power of the people in creating change in education:  the informal yet amazing discussion with @MrSoClassroom and @MrAspinall at #BIT14 on assessment and math (in turn, sparked by a Twitter conversation) spoke strongly to the power of informal networks of information sharing and professional collaboration. I also turned around and @avivaloca was right behind me!

7) Harnessing the power of the #MTBoS to improve my teaching and learning.  When you have a worldwide network of people like Dan Meyer and many others sharing daily, you are never short of ideas.  

8)  Being the host classroom for the learnteachlead.ca project "Loving the Math, Living the Math." This was the most inspiring 3 days of teaching I have ever had.  I'm not even sure what to say  about it.  I've been tweeted from across the province ("i'm watching your video") and even had someone say, "i've watched all your videos."  I can't even put into words how many things I learned about math teaching and learning through this project (or rather, it would be a very very long essay, and a topic for another day.)

It's not me though- it's our amazing Peel students who are willing to grow their brains in math, take an inquiry stance every day, and #EngageMath with us. Together we are strong. Believe in the power of kids, let them be kids, let them talk, and engage their natural curiosity about math and willingness to learn, and they will do great things!

9)  Being hired as an Effective Math Resource Teacher in @PeelSchools. This was a goal i'd had for over 5 years, and included a handful of unsuccessful interviews.  For my personal journey, I think of the Japanese proverb (and personal mindset motto), "fall seven times, stand up eight."

It is the greatest privilege to be able to engage math every single day with our amazing school board-students, teachers, principals, superintendents, everyone.  

10) Trying to live as ethically as possible, and being the best father, husband, and human being I can.  

 Is your hourglass 25% or 75% full in 2015? Do we focus on what we have, or what's missing?