Show Up and Refuse to Leave Keynote


Net Smart by Howard Rheingold

Connected: The Surprising Power of Our Social Networks by Nicholas Christakis

Presence by Amy Cuddy

Mindfulness by Ellen Langer

Websites/Apps: (Also mentioned in Demo Slam)

GoNoodle Body breaks and meditation for kids




The Hidden Influence of Social Networks TED Talk by Nicholas Christakis 21 minutes

Your body language shapes who you are TED Talk by Amy Cuddy

Let it Go ~ Think About it by GoNoodle


GAFE and iPad: BFFs 4EVR

This is a beginner session.  Please bring an iPad.

View GAFE and iPad: BFFs 4EVR slides here  or at 

Get your own copy of GAFE and iPad: BFFs 4EVR slides here


Get Google to Give you Time ~ Productivity Tips

This is an Intermediate session.  A lap top or Chromebook is recommended.

View Productivity slides here or at

Get your own copy of the Productivity slides here

Copies of Book Talk assessment (to use with Autocrat Mail Merge) here

Assessment and Pedagogical Documentation with iPad

This is a beginner session.  Please bring an iPad.

View Assessment with iPad slides here or at (Case Sensitive)

Get your own copy of the Assessment with iPad slides here


The Leaders

Thank you Lucy Gray, Steve Hargadon and your colleagues for organizing this event. I suspect that Julie Lindsay also helped out, so thank you goes to you too Lindsay!

The Resources

A google doc (here) includes all the links for this event as well as a schedule for the day.  Julie Lindsay’s soon-to-be-published ISTE book on Global Education is another resource to look out for. 

The People

Thank you to these people for pushing my thinking.

The Day

This was my first visit to any kind of Global Education event.  The day alternated between ignite talks and round table discussions. I have organized my notes to share some highlights from the day.  You’ll get some quotes and key points from the ignite talks and round table discussions that resonated for me. I hope you enjoy them too.

Opening Ignites

David Young is the president of VIF International Education who co-organized and co-sponsored the event.

His message was that Global Education should be for all students. He would like to see more people engaging in global education. He believes it should be integrated throughout the grades and curriculum.  Key points from his talk were:

  • Very few students have the opportunity to engage in global education despite the desire from the world of work to have workers that are globally engaged, aware and active.
  • Global education should not be an add-on, it should be the lense through which we teach and learn everything at school.
  • All teachers should teach from a global perspective.
  • Technology allows us to bring global education to all.
  • Digital badging can provide acknowledgement of skills developed in this space.

Lisa Parisi‘s ignite included these gems:

  • “At first it was about the technology, then it became about collaboration and globalization.”
  • “It is impossible to ignore the global issues we face each day.”
  • “People study in schools about animals, climate and other things from other countries but almost never about the people.”

Round Table Conversation

Topic:Design discussion: How to design authentic global collaboration across the curriculum. Includes the new ‘norms of global

Leader: Julie Lindsay

How do you support discussions between students from classrooms all over the world? Do you communicate asynchronously and synchronously. Do you have teacher directed conversations or less structured time for kids to be kids and just talk? Perhaps not surprisingly, the experienced people in this group believe that a balance of approaches is ideal.  Due to time zone challenges, sometimes a synchronous conversation is not possible. Some teachers would have evening events at their school with students and families to Skype or Google Hangout with other classrooms. I thought this was a clever solution.  As for the conversations, students need some unstructured time to be themselves and let a bond develop. However, participants in the discussion warned that you need to get past the “I like pizza, you like pizza” type discussion and into deeper topics.

Near the end of the time together, people talked about Student Personal Learning Networks. “Who do you have in your online network that you don’t see everyday?” Is a question Julie Lindsay thinks all students should be able to answer.

Terry Godwaldt from The Center for Global Education and Bob LaRocca from Primary Source were also part of this round table. These are new-to-me people with new-to-me organizations. Later in the day Terry talked about Taking It Global.

Near the end of the hour together, Julie talked about A Day in the Life.  She says she puts students into a virtual classroom for synchronous communication. But also has students connecting asynchronously through various blogging and social media services. I love how she said: “It all works, *just*.”  Time zones are a challenge, probably the biggest.

Someone in the group asked where to get in touch with people to get started. Here is what people shared:

Global School Network

IVEACA International Virtual Schooling

Flat Connections

Global Education Conference

Global Educator’s Network

Taking It Global

Cultural Relay Fitness for young girls!

Eyes Wide Open shared by Deb Schiano

International Education Resource Network IEARN


Julie Lindsay’s ignite was titled “Putting the Global into Online Collaboration.” She has lived and worked in six different countries. She is global, and yet, she has a dilemma with the term. Her supervisors for her doctoral program told her to drop the word ‘global’ from her dissertation. So, she has been thinking about what global really means. Is the use of the word ‘global’ acceptable, necessary or redundant when talking about learning online. Great question.

Favourite Quotes and thought bites:

  • What does the word ‘global’ add to online learning.
  • Is ‘global’ a mirage?
  • What happens when we put ‘global’ into online collaboration? What is different? Is there a new understanding of time differences, cultural and daily life?
  • Global is all-embracing and covering the entire world.
  • ‘Global’ and affirmative action.

Julie proclaims that the ‘Global’ in ‘Online Global Collaboration’ is not redundant.

Then, she got ground level and practical by outlining the  Norms of Online Global Collaboration:

  1. Being prepared to connect and communicate.
  2. Having a purpose shared outcomes.
  3. Paraphrase use clear common language.
  4. Perceive: ask for help and share knowledge.
  5. Participate and be visible online.
  6. Positive and encouraged DC, build empathy, assume best intentions.
  7. Produce. Productively co-create and encourage learners to compare, contrast and create.
  8. Be open to the potential and  serendipitous learning that will happen if you let it.

Up next was Amy Shaffer from Connected World. She is intelligent and also quite darling.  Her slides are here. “Do you consider yourself as a creator?” she asked right off the top. She believes that when you bush buttons and see things happen, that we then build faith in the world around us. She uses doorknobs as an example. The doorknob is a button you bush everyday, and it works every time. So you trust that it works.  This is the idea behind The Wonderment. “It’s a space that gives kids that button to push” she says.  A sense of belonging is important in working to make change. And this is the ethos behind The Wonderment.

Screenshot of The Wonderment Website

Amy Shaffer wants to give kids a way to actively engage in their own world at their level.  More great quotes from Amy:

  • You can’t leave behind the possibility for genuine human interactions.
  • The world is waiting and wanting to hear from our students.
  • Education without action is like food without exercise.


Round Table Conversation

Topic: Beyond Mystery Location Calls

Leader: Billy Krakower (Who brought his own power cord!)

  • Pro tip: Use TouchCast to practice Mystery Skype. Use a green screen to upload a different picture so it appears that you are coming from another country.
  • When mystery Skyping, have students keep the same job for 3 times.
  • Skype around the world in two hours.
  • If time difference is a challenge have the Skype at night and make it an event with parents!
  • Link to check out Sharks for Kids

Friends I was delighted to see:

Jen Roberts, Andrea Singer, Jon Samuelson, Jackie Gerstein, Monica Burns,

New connections and First Face2Face Meetings:

Tweeps: Dave Potter, Kristen Downey, Bob LaRocca, Amy Shaffer,

F2F Meet up: Scott BedleyLouise MorganGallit Zvi, Robyn ThiessenTerry Godwaldt


Do you use the Daily 5 and CAFE in your class?

Perhaps you are familiar with this series of books:
I attended “Hacking the Daily Five” presented byVictoria Olson MsVictoriaOlson and Sara Boucher @MsGeekyTeach. Victoria and Sara demonstrated how to integrate technology with the Daily 5. They focused on Google and iOS Apple tools. To get session resources, go to the links below:

They gave a Daily-5-Disclaimer saying they don’t follow every aspect of the Sister’s Approach.  They hack it.  Victoria and Sara do stick with the 5 parts of the program. In each of these areas, I learned something new.

Read to Self New Learning:

    • Literably A website where students can read text and the online service provides a running record.  I think this is pretty cool, but I like that Victoria emphasized that nothing beats the classroom teacher sitting down with a student. Nothing.
    • Google and Explain Everything: Victoria fills a Google folder full of books she has downloaded from Reading A-Z.  Students can then bring those books into Explain Everything and record their reading.  The key idea for me was the idea of using Google and Explain Everything to make a library of things for students to read. I would like to put in shared reading from the previous week, books I have written, classbooks, as well as texts I have access to use.

Read to Someone New Learning:

    • Have two students record their reading and then switch iPad devices.
    • Invite guest authors via Skype and Google Hangout or even invite parents to read to students if they can make a short break during their work day!

Listen to Reading New Learning:

    • Use Popplet or PicCollage to have students create a retell, summary, character analysis or other task to show their reading comprehension and experience with the text.
  • Tools and Websites for Listening to Reading:

Work on Writing New Learning:

Word Work New Learning: 

Websites for Word Work:

And, I was really happy to meet Erica Oakhill and Gloria A (a fellow Canadian)!

Mini Keynotes iPadapalooza #iplza15

Instead of a traditional keynote, 10 speakers were each asked to do a 3 minute talk.  Here were the people and the big ideas.

Sketchnote by Meghan Zigmond ~ used with pride and permission!

  • Rabbi Michael Cohen The pencil is a mighty tool, the iPad too!  (Plus amazingly hand drawn slides).
  • me – The life story of Kevin Mitnick, all time hacker, rapped to the tune of Fresh Prince.  Hack the classroom.

Gost in the Wire

  • Amy Mayer There is a big difference between compliance and engagement. And, “If your kids ask you for a worksheet you are doing it right.”
  • Reshan Richards  Knowing That and Knowing How, Learning THAT and Learning HOW ASSESSING THAT or ASSESSING HOW. #QFAT (Qualitative Formative Assessment Tool).
  • Rafranz Davis You have to make an effort for equality. Real Change is Intentional.
  • Carl Hooker #UndeadLearning Fighting the Zombie apocalypse.

Day 1: One More Thing ~ Adam Bellow

You can see Adam flying his drone, as well as a wonderful overview of the entire event in this iPadpalooza Highlight video.

Adam Bellow’s opening keynote really hit on a lot of 2015 trends: coding, fear of failure, sharing, risk taking and drones. He geeked up, as we like to do in edtech, especially when he flew a drone programmed by Tickle.  His emphasis was on people over shiny things, even though he talked about technology gadgets and apps and services. His putting-people-first message was post App, post idevice. His keynote was centered on being connected to each other and the importance of sharing. By highlighting how quickly the new tech becomes old, he brought a freshness to the people-and-pedagogy-first message.  Student engagement has been a big selling point and focus for edtech evangelists, but he points out that the superficial engagement of new hardware and software is fleeting. Bellow reminds us to focus on the people, the connections, and the learning.

My favourite Adam Bellow Quotes:

  • “It’s not about the apps and tech it’s about culture and people.”
  • “It’s not about what you do but what you share.”
  • “Failed Ed tech initiatives start with a list of things to buy.”
  • “The Device doesn’t matter because they don’t last anyway.”

Tools, Sites and Apps Mentioned in Adam Bellow’s Keynote:

Day 2: 10 Lessons from Steve Jobs ~ Guy Kawasaki

1) innovators learn to ignore naysayers  a.k.a. “BOZOs”
2) costumers can’t always tell you what they need
3) it’s not about the current curve
4) design matters
5) big challenges beget BIG CHANCES
6) less is more
7) changing your mind is a sign of being smart
8) value does not equal price
9) “A” players hire “A+” players
10) the perfect combination to market and sell anything: maximize uniqueness and value
BONUS: some things need to be believed to be seen.
Guy Kawasaki

Day 3: Eric Whitacre

You may have seen Eric Whitacre’s Virtual Choir, if not, take a look.

This was an outstanding, life enriching, keynote. Having a passionate knowledgeable person walk you through something they love is a profound experience.  Eric Whitacre talked about how he got into music, the virtual choir, his process and stories of music and composers. It was an hour of magic.

My favourite phrases and quotes:

When talking about hearing choir music for the first time:
  • “It was like I was standing in the middle of a cosmic Swatch watch.”
  • “It felt like someone was speaking my true name.”
  • “I was surround by a see of people escorting me to the next level.”
On being a composer:
  • “Being a composer is an odd job. I try to steal fire from the gods.”

Golden Bricks

I also especially liked how he talked about how all music, all songs, have a ‘Golden Brick.’ The golden brick is a simple piece of the song that is the anchor of the song, speaks the emotional essence of the piece and often repeats throughout.  He had us listen to Beethoven’s 5th Symphony.

He explained how the “ba-ba-ba BOOM” was the Golden Brick of this piece. Here he is watching the visualization and pointing out the brick as it repeats.



Here is a recap of the sessions I attended at iPadpalooza 2015.


Share it’s so Human –  Felix Jacomino

Share. Tweet. Blog. Crowdsource. Connect. Rinse and repeat daily for best results. Felix Jacomino shared his thoughts and interviews with edtech influencers through his session.  A perfect follow-up to Adam’s keynote, the message to share was becoming the anthem of the conference before noon on the first day.

I think you have probably read or heard about Steal Like An Artist and Show Your Work both by Austin Kleon.  We love this, don’t we?  Always worth a visit to these ideas, don’t you think?

Did you know that Command + F1 on your Apple computer will toggle between presentation mode in keynote and mirroring your desktop.  I didn’t!  Thank you Felix!

Tools, Sites and Apps Mentioned in Felix Jacominio’s session:

Conferences to attend that promise to be as fun asiPadpalooza

Crowdsourcing & Crowdsharing

Tools to help make sharing easier (if you use Google Blogger):

Mixing Paint and Pixels In The Creative iPad Classroom ~ Cathy Hunt

Cathy Hunt‘s general art resources can be found here and iBooks to download are here.  In the session, Cathy emphasized the importance of capturing the process as well as sharing out the product.  She encourages students to do time-lapse photography of their art making using iMotionHD and an iPad stand. She suggests getting iPad stands like the one pictured below or like this or like these.

ipad standShe taught us that an inexpensive stand like this is essential for taking pictures of the process and it’s also important that students grapple with setting up their work stations.  For presentation and sharing the student’s product, she uses Book Creator.

A Book Creator tip that I think you’ll love is to have students crop photos in a square shape and then add to the portrait or landscape books in book creator. This will make for a very consistent look throughout the book allowing for consistent white space for writing descriptions. Primary teachers, don’t you think this would be great for classroom books too?

When we opened an app for the first time she would tell us to “touch the heck out of the screen.”  Touch Everything may be the simplest instructions for figuring out any app that I have every heard in my life.  Brilliant. Stop teaching apps, just open then up and say “Touch Everything” – it’s the Bibbiti Bobbiti Boo of iTeaching!

Using the headphones to trigger photos was another great tip.  Plus, she keeps things simple and easy and goes around taking pictures of student’s art work on their iPads as an easy workflow solution for assessment.

Making kaleidoscope's with MegaPhoto and Craft supplies.

Making kaleidoscope’s with MegaPhoto and Craft supplies.

Art Apps Mentioned in Cathy Hunt’s session:


iGoogle ~ Jennie Mageira

Jennie Mageira knows that many iOS users want and need to be Googly too. This session was about blending the tools together. Her session resources are here.

Jennie points out that Google classroom is great, but there is still a place for Shared Google folders through Google Drive.  She demonstrated that Shared folders is the best option when you want students to be able to see each other’s work.  Good point, Jennie, good point!

She breaks down the apps into those for creating, consuming and connecting.  All the apps she recommends can be seen here.

As a presenter, Jennie Mageira has excellent plan-b-ability. When she was not able to mirror her iPad on the Apple TV, she was quick to turn on Photo Booth and use that to show her iPad.  I think this smooth and nimble use of technology is exactly what we want to strive for and want our students to strive for. There are always glitches and it’s key to problem solve and move forward. Mageira is a pro.

Individualizing Staff Instruction with the ITP ~ Amy Mayer

Amy Mayer is a YouTuber for teachers.  Her channel, FriEd Technology has a vast collection of how-to tutorials to support others. Again, the theme of sharing persisted in this session too as Amy talked about supporting staff.

Her top tools and tips for coaches and learning coordinators that are getting buried by email:


Using canned responses in gmail

Follow Michael Jaber on twitter if you need another guardian angel like Amy to help you out!

I went to the session to hear Amy speak, but you may be interested in seeing her Individual Technology Plan form if you do support teachers who are trying to integrate technology in your board or district.


Explain Everything & #QFAT – Reshan Richards

Reshan Richards, creator of Explain Everything, introduced the notion of #QFAT ~ Qualitative Formative Assessment Tool ~ and makes it so clear how to use iPad. He says there are four ways to capture content on iPad:

    • Photos
    • Screenshot
    • Video
    • Screencasting

He engaged his audience to use a combination of these and the game Disruptus to get depth of thinking and use the tools effectively.

Explain Everything and Disruptus

Crafting Creativity with Canva ~ Lisa Johnson

Lisa Johnson did a standing-room-only session on Canva which is a tool for making beautiful content!  What I liked most was learning about her process for making her Canva pieces.  She keeps a Pinterest board called Delectable Designer Designs where she collects samples of visual messages and content that she likes the looks of. Then, she uses these to guide her own creations. Circle back to Felix’s session, we were evoking Austin Kleon’s book Steal Like An Artist!  It’s useful to know where to start, right?

She also has two more boards to check out for lesson plans and ideas:

Canva Lesson Plans – Pinterest

Ways to Use Canva – Pinterest

For finding more eye candy for creative content creation, Lisa also recommended Creative Market. She also uses images from Noun Project in her Canva creations. Smart!  She also pairs her Canva creations with Thinglink such as this Outlander themed SAMR model interactive poster:

Dean Shareski

Dean Shareski says “Creativity is like a muscle you have to exercise it daily.” He spoke to leaders about being a creative leader like Chris Kennedy who writes a blog titled The Culture of Yes. Every April 1st he writes a gag blog. Dean suggests that it’s important for leaders to work creativity muscles in this way. He reminded the leaders in the room to engage in “cheap failure” (Clay Shirky’s words) and take risks by playing games such as Pecha Flicker Improv.

He also did a session titled “The Airing of the Grievances.”  I didn’t get to go because I was presenting, but I love the title.  You and I can creep his slides here.

It’s all about the sharing and the people!

People I was thrilled to see

….and you may want to follow so all the names will take you to their twitter accounts:

Tracy ClarkCarl HookerLisa JohnsonJennifer FloodDon Goble, Jessica Young,  Debbie SmithMeghan ZigmondSue Gorman, Jennie MageiraCathy YencaReshan Richards, Dean ShareskiJames RichardsonCraig RobleBrian FouttyRafranz DavisCathy HuntRichard WellsCarolyn FooteKyle PearceFelix JacominoAmy Mayer, Todd Nesloney, Rabbi Michael Cohen, Chris Parker


With thanks to….

Massive T-Rex size thank you to Carl for inviting me and for Tracy for letting me stay with you.


Ontario has a renewed vision for education with four main goals.  But, People for Education is kicking it up a notch!

Ontario has goals and targets.  These goals will be measured and yes, EQAO data is part of the picture.  I am cheerful to see from the Achieving Excellence document that there will be a broader focus on gathering data beyond reading, writing and math (through EQAO).  There is a breeze of change and freshness as I see that the government will be looking at broader indicators of success.

Then, there is an even bigger gust of wind from People For Education.

People For Education, and their tireless, no-nonsense and brilliant Executive Director Annie Kidder, are looking at even broader goals and other measures of success that are “publicly understandable, educationally useful, and that reflect the range of skills that students will need to live happy, healthy, economically secure, civically engaged lives.”  On many occasions, Kidder has made the point that EQAO tends to narrow down the purpose of education.  If we only measure reading, writing and math, then that becomes the focus for improvement.

The initiative to achieve this is called Measuring What Matters Most: A New Way of Thinking about Skills and is best described as:

“a multi-year initiative to support the development of educational goals and measures of success which reflect the broad and essential range of skills that graduates—and our society—really need.”

and also,

”The initiative will establish a set of broader goals and measures of success in education that are publicly understandable, educationally useful, and that reflect the range of skills that students will need to live happy, healthy, economically secure, civically engaged lives.”

I think this complements and extends the mission statement from the Achieving Excellence document:

“Ontario is committed to the success and well-being of every student and child. Learners in the province’s education system will develop the knowledge, skills and characteristics that will lead them to become personally successful, economically productive and actively engaged citizens.”

I also think it goes much further than Achieving Excellence.  While the renewed vision mentions innovation, creativity and critical thinking, Measuring What Matters: A New Way of Thinking about Skills explicitly describes what these important skills actually look like and mean.

For example, here are the skills and competencies for creativity:

Skills and Competencies are clearly outlined for:

  • creativity
  • citizenship
  • social-emotional development
  • health

Thereis also a connection made between creativity and critical thinking:

“Creativity and innovation skills allow students to learn more effectively in all academic disciplines and subjects. Critical thinking—a “sister skill” to creativity—involves a process of conceptualizing, seeking accuracy and clarity, resisting impulsive solutions, being responsive to feedback, planning and being aware of one’s own thinking.”

The Measuring What Matters initiative is a multi-year plan with national reach.  I see a lot of discussion and hear a lot of talk of creativity and citizenship in particular, I wonder if the skills and competencies will help administrators and teachers across Ontario and Canada start to bring these ideas down from the conceptual and into the practical application of the classroom.

China Beckons

In about a month, I will be travelling to Beijing and Hanghzou China with Jonathan So  to participate in the 3rd Annual China Elementary Education International Conference.

Jonathan and I were invited by Ann Lieberman through our involvement with the Teacher Learning and Leadership Program. We are very grateful to have been selected and we hope to represent Ontario educators well.

Jonathan and I are guests that represent Ontario Education.  I have been wondering, what makes Ontario’s education system so great? Why do other countries want to know what we are up to?

Education in Ontario is Pretty Great

Did you know that our school system here in Ontario is one of the best in the world?

Did you know that our province has seen a 15% increase in graduation rates and 17% increase in achievement of provincial standards in grade 3 and 6 over the last 10 years? Also, we have closed the achievement gaps between English Language Learners and those students for whom English is their first language.

Not bad.  We still have a lot of work to do, but this is good improvement.

And, we are striving to get even better

For ten years, our education system in Ontario has been improving at a steady rate.  What’s next?

Three words: Inspire, innovate, transform.

In April 2014, the Ministry of Education released Achieving Excellence: A Renewed Vision for Education in Ontario.

The overall mission is to see success and well-being for every learner from early child care through to adult. Schools should build “knowledge, skills, characteristics” to help learners become “personally successful, economically productive and actively engaged citizens.”

The province of Ontario has 4 clear goals:

  • achieving excellence
  • ensuring equity
  • promoting well-being
  • enhancing public confidence

There is a big emphasis on technology for actualizing these goals, especially when it comes to the achieving excellence goal. Below you can see the very first point in the action plan for achieving excellence is to invest in technology.

Ontario has a renewed vision for education.  These goals will be measured and yes, EQAO data is part of the picture.  I am cheerful to see from the Achieving Excellence document that there will be a broader focus on gathering data beyond reading, writing and math (through EQAO).  There is a a fresh feeling of change and think I see that the government will be looking at broader indicators of success.

Inspire. Innovate. Transform.  Focus on excellence, equity, wellness and engaging parents and the broader community.

There are some ideas that I just keep coming back to.  Innovation is one of those ideas. I hear it everywhere, and I think people confuse it with improvement.  Andy Hargreaves spoke about the tension between innovation and improvement and asks the question:

What kind of horse are you?

I recommend watching from 29:10-35:02

He presents a similar matrix to the one I have here:

If you are not improving or innovating, you’re a dead horse.

If you are only improving, you are a race horse.

If you are only innovating, you are a unicorn or pegasus. You are a mythical creature that does not exist.

If you are improving and innovating, you are the iron horse. You have horsepower, but are no longer a horse. You are something greater and more impressive than any other horse.

Andy goes on to point fingers at which education systems are which horse:

  • The dead horse:  USA (although things are looking up)
  • The race horse: Ontario
  • The Unicorn and Winged Horse: Superficial use of Technology (that’s us #edtech)
  • The iron horse:  We don’t know yet.  Will it be Ontario?

Do you agree? Where would you put Ontario’s education system on the innovation/improvement horse matrix?

Could the Iron Horse of Education Change be here?

I think educators and leaders in education ought to remember that innovation is a priority, even when things are tough.  Innovation is not dessert, that thing you get to have when you are done improving.  It’s essential to do simultaneously alongside of improvement.

And a note to my #edtech friends –  don’t be the unicorn.  Innovate and improve or else you are a magical creature that doesn’t really exist.

Note: This blog was revised thanks to Dr. Marc Joanisse who gave me some great feedback about the graphic.

How Not to Be Wrong by Jordan Ellenberg

How not to be wrong: The power of mathematical thinking By Jordan Ellenberg is a story of how we can use mathematics to make decisions and better understand the world around us.  Mathematics is “extending our common sense by other means.”

More great quotes from the book:

“Dividing one number by another number is mere computation; figuring out what you should divide by what is mathematics.”  p.84

“Once your laptop can do it, it’s not mathematics anymore.” p. 283

“When you’re working hard on a theorem, you should try to prove it by day and disprove it by night.” p.433

When to celebrate and when not to celebrate

Be careful of the inferences you make from small data sets.  If you are a teacher or principal at a small school and your EQAO scores shoot way up, or way down, this is more likely numbers doing their thing than something wonderful (or terrible) that you did.  Here is the thing that Ellenberg reminds us so well, small sample sizes can have huge variability.  The results of a small group can fire up and down.  Be mindful that small sample sizes do this type of thing.  If it was a huge improvement, quietly say to yourself that it could equally have been a huge downturn. The numbers in these cases are really only valuable by looking at the changes over a longer period of time.  So, if you are a principal or teacher in a small school, don’t let the yearly data fool you, look at the bigger picture.

Similarly, if you are a huge school, there is something you should keep in mind too.  Are you an administrator or teacher in a giant school? Are you finding that your EQAO scores don’t change much year to year? Well, that’s because of regression to the mean!  Again, look at the overall trends.

In both cases, look at the big picture. Don’t let a small or large number send you thinking things that aren’t true.

Counter-intuitive Thinking and Missing Bullet Holes  

Abraham Wald was a mathematician who contributed to the war effort in WW2 from within Columbia University as part of the Statistical research Group (SRG).  He and a group of brilliant mathematicians were working on how to armour planes so that they would not get shot down.  But, the problem was that adding armour added weight, which took more fuel and rendered the planes less maneuverable (arguably cancelling out any benefit of adding armour in the first place).

So, they looked at the data.  Where are planes being hit?  The plan was to add armour to those parts of the plane.  The researchers found that the fuselages of planes had many bullet holes whereas there were far fewer bullet holes on the engines of returning planes.

So, where would you put the extra armour? On the fuselage!  No, this is not the right idea.  Wald said the armour shouldn’t go where the bullet holes are most, but where there are no bullet holes at all, which was on the engines.  Wald was able to see that the planes that did not make it back for inspection where probably the planes that got hit in the engine.  The planes the researchers were inspecting were able to make it back, so bullet holes had not caused fatal damage.

Where are the missing holes? The missing holes are on the planes that were shot down!  Wald was able to ask: What assumptions are you making? And are they justified?

This connects to the quote above about believing your ideas by day, and disbelieving them at night.  The numbers of bullet holes, or any set of data, must be interpreted. That’s where the mathematical thinking is most essential. Here we use math to guide our intuitions down a more structured path so they don’t bring us down.

More is not always Better and Ferris Bueller Explained

More is not always better.  We know this, but time and time again we think that data runs on a straight line going up or down. More often, however, data is “straight locally and curved globally.” When we stand back, the shape of the data starts to look different.

Remember Ferris Bueller’s Day Off?  Bueller? Bueller?  The super boring economics teacher was talking about the Laffer Curve, taxation and voodoo economics. There is actually some great math in this segment!  You see, governments thought that if raising taxes a little raised a little revenue, then raising taxes a lot would raise A LOT of revenue. Turns out that it’s not a straight line, it’s a curve, a Laffer Curve.  There is a point at which you increase taxes so much that your revenue starts to drop because people either hide their money or stop working. If you watch the Ferris Bueller clip, and look at this diagram, this is the diagram the teacher is describing when there is saliva on the desk from the sleeping teen.

Laffer Curve

This also applies to giving advice, writing a blog, making mistakes in the classroom and missing flights!

Yes, missing flights. If you are always on time for your flight and you never miss one, you are probably spending too much time at the airport.  Mind you, this probably only applies to frequent flyers. (Utils are an economists units for the utility something gives you).

“George Stigler, the 1982 Nobelist in economics, used to say, “If you never miss the plane, you’re spending too much time in airports.” p. 232 

So, other lessons of the Laffer Curve:

If you worry too much about giving good advice, you probably don’t give enough advice.

If you spend too much time trying to be productive, you are less productive.