Narrative Matters

Last night a group of Manitoban educators got together to talk about teaching and learning and how that learning takes flight when we take advantage of new opportunities offered by technology.

The evening was framed around having the six Manitobans who participated this summer in something called Unplugd, talk about this uniquely Canadian educational summit: 36 of us wrote a book in a weekend.

Anyone who's spoken to me since I got back from Unplugd knows what a transformational event it was for me and that I've really struggled with figuring out how to share what happened to me in a remote corner of Algonquin Park in North Eastern Ontario; a place entirely off the grid: they have no internet and the electricity and plumbing is powered entirely by the sun. The Northern Edge is a beautiful location.

I couldn't attend the event last night so my friend and colleague Andy McKiel asked me if I'd make a short video to share what I learned and what Unplugd meant to me. It's called Narrative Matters, a double entendre: stories matter and it's important to understand how to use storytelling to make ideas sticky. Here's what I made:

Ed. Note: I should have mentioned that The Northern Edge, where we stayed during Unplugd, is 23 km east of the small town of South River. In the video you'll see a brief picture of the South River train station where we disembarked. "The coat" is hanging on display inside that small building.

You can download the book we wrote (pdf or ePub), please do. Then share it.

I facilitated the team that wrote the first chapter: The Change We Need. Andy, Chris, Jaclyn, Lorna and Shelley made my job easy; they're some of the finest people I know.

I shared a story that motivated my written contribution to the book. Many people did, you can find the archive of all those shared stories in the Unplugd video archive. Here's mine as well as my written piece for the book.

You Matter
You matter because you can change the face of teaching and learning in your school. All you have to do is change the world - a little bit at a time. 

No teacher before you has ever taught children quite the way you do. No one ever will again.

The world needs to know what you’re doing. How you go about sharing your passion, your excitement, your enthusiasm for learning with the students in your classroom every day.

You make a difference in the world in the way you do this.

What you want for your students is for them to excel beyond your own expertise in all they learn from you.

It’s the dream of every teacher: to have your students become more knowledgeable, more capable, more competent than you.

It’s a measure of success.

Essentially you share your spark with them.

What we most want is to pass on that spark, this other centred attitude, an attitude towards the world that says: You Matter!

Adopting the attitude: “You Matter”, making people other than ourselves important and finding ways to make them more awesome, in the end, makes each of us a little more awesome. It creates the change we need in the world.

Let's pass that on to our students so they know they matter and understand their job is to make everyone they meet a little more awesome. When they’ve internalized what they’ve learned from us and brought it to another level: that’s success.

No one will ever see the world through the eyes of our students again. No one ever has, throughout the entire history of humanity. They have a unique contribution to make. We help them understand this is also true for everyone they meet.

Imagine a Canada, a world, where every politician, every trades-person, every professional, every store clerk tackled the world in this way? They’re all sitting in your classroom. Learning from you. Teach us too. Share what you know. Share how you know. Share what you learn. We need you too. You matter.

The Character of Test Questions

TentsImage by rwillia532 via Flickr

In my math classes a typical test is modeled on the character of test questions students will see on their final exams: multiple choice, short answer and long answer.

In a grade 10 math class, what we used to call Applied Math 20S, a multiple choice question might be:

A factory makes tents.  The cost of running the factory is $300 per day plus $50 for each tent made. What is the total cost (C), in dollars, as a function of the number of tents (t) made?

(A) C = 350t (B) C = 50t + 300 (C)  C = 300t + 50 (D) t  = 300 + 50C

I like this question because it quickly allows a student to show whether or not they understand what a "function" is and it's easy to grade. While they have a 25% chance of getting it correct by guessing, in the context of the entire test, and their classroom experiences with me (read: conversations), I know if a student has grasped the concept.

Me and my CellImage by dkuropatwa via Flickr

A short answer question might be:

The monthly cost, C,  in dollars, of using a cell phone is calculated using the function C(t) = 0.09t + 20 where t is the time in minutes. What is the monthly fee and the cost per minute for this cell phone contract?

Another quickie that reveals whether or not the student can decode the information given in a function. Another question might ask them to reverse that; encode a function given the description of a linear relationship. As a matter of fact, there's a fundamental principle there about learning math: Anything you can do you should also be able to undo. i.e. If you can decode the information in a function you should also be able to encode information in a function.

Here's a long answer question: 

The cost of a school graduation dance has a fixed cost of $1500 for the band, security, and so on, and a cost of $22 per plate for every person attending.
(a) Write the formula which states how the total cost, C, is related to the number of people attending, n.
(b) What is the slope? What does it mean?
(c) If the maximum capacity of the hall is 225 people, what is the maximum cost of the dance?
(d) State the domain of this function.
(e) State the range of this function.

The question is not ideal; (d) should be a "gimme" if they understood (c) and (e) depends on the formula they created in (a). Mind you, if they wrote an incorrect formula in (a) but correctly applied it in (e) that's worth full marks in (e).

Image by nebbsen via Flickr

Something these three questions have in common is they require that a student understand the meaning of the marks they're making on the page. While every test has some straight forward calculations, by and large calculations are what computers do best. I want my students to understand what the math means and how it hangs together. Computers don't do that so well; although they're getting better at faking it. That's largely because of the cleverness of people who understand the math behind what computers do.

If your assessments largely test mechanical skills that's what your students will focus on learning. If your assessments test for understanding that's what your students will focus on learning. Which would you rather learn?

You don't have to teach math for any of the above to be true, do you?