Wednesday, December 18, 2013

Together, Not Alone in the Math Classroom

Multi-class gallery walk on integers problem-one example of collaborative math:
You may have missed it, if you don't follow math news, but there have been major developments in something called the Twin Prime Conjecture. You may not care about prime numbers, but you should, if you care that your banking data (and any other kind of data is safe). The conjecture is basically that there are infinite number of pairs of primes separate by just one number- for example, 11 and 13, or 17 and 19.

You may have an image in your head of mathematicians working, solitary, alone, crunching numbers, and developing theories that nobody else could possibly understand.  In this case, Yitang Zhang's work led to a flurry of collaborative math work.  Together, mathematicians around the world worked to refine and push his breakthrough further than ever before.

Here is a quotation from the article:

"For weeks, the project moved forward at a breathless pace. “At times, the bound was going down every thirty minutes,” Tao recalled. By July 27, the team had succeeded in reducing the proven bound on prime gaps from 70 million to 4,680."

To be clear, the "team" here was an fully open and collaborative. They worked in real time, and using their combined wisdom, pushed the project much further than anyone could have imagined.

This matters for elementary (and high school) teachers because we often treat math solely as an individual activity.  I myself have memories of sitting in a desk, in a quiet room, textbook open, doing problems in a workbook. We didn't talk math, and we didn't collaborate.

Things have changed since then, obviously, but how much do we see math as an open and collaborative activity in our classrooms?  Not enough, I think.  It all comes from the class culture.  If we are open and truly value student voice in the math classroom, starting from the first day of class, we might be amazed at the culture that develops.

Math IS a social activity. Students learn from each other, sharing strategies and solutions, wondering together about the big ideas in math, scrawling solutions on chart paper, standing and justifying their solutions, and working on bigger projects where we build our understanding together.

Yes, in the end, each student in the end is responsible for having the skills and strategies needed to succeed in math, but together we accomplish so much more than alone.

Wednesday, December 11, 2013

Minecraft in the Classroom, or, Things Look Differently From Different Viewpoints

With many thanks to Budder Champs, and Christmas Craft MC (@nutmegsuperboy). I am, as always, #poweredbykids.

My curiousity about Minecraft came from having a great grade 6 Math class this year. One of the most interesting things about BYOD in schools is the variety of digital experiences that kids bring with them to the classroom.  We can either harness them, or shut them down.  Too often, our tendency is probably to shut them down.

Case in point:  Minecraft.  How could this "game" be used to support learning in the classroom?  I had only a dim awareness of Minecraft, from seeing kids draw "creepers" in the classroom over the last few years. But being a new father, my time for games is, umm, not so much.

I decided to let my two students show me how they could do their math in Minecraft.  The video below came from them choosing to do a question from the Guide To Effective Instruction in Math, in a Minecraft environment, rather than on paper.
What you will notice if you watch the video is that they have physically represented the objects in the problem, used signposts for their text, and recorded their narration using Camtasia.  It is as complete a solution as you would see on the usual chart paper in the classroom.  The question is, where does this sort of task fit on the SAMR model? I think that is a healthy debate to have.

Recently, I had some Twitter discussion about SAMR, after taking a textbook page (grade 6), and letting some students do their work in Minecraft.
The thing here is, some students chose to EXACTLY substitute Minecraft work for paperwork.  As happens when you play in an open environment like Minecraft, others immediately hijacked the task and started building their own structures.

Here's the thing:  I want students to take apart the classroom work. I want them to get messy, to do their own thing, to break things apart and rebuild them.  I am never happier.  There is no "my assignment is holy writ" type of attitude here.  But students finding that they could build bigger, taller, and more interesting structures was a natural byproduct of opening up Minecraft to them in this case.

Next was a cube challenge (one of the curriculum expectations being drawing front, top, side, and 3D view of cube structures!)
The revelation for me here was that we probably don't need to draw front, top, and side views, when we can take screenshots in Minecraft.  It then became debatable how important is is to actually draw 3D views when you can build in Minecraft, then examine the structure from literally all angles.

Next was trying to build some criteria together for the larger piece of work.

3D Structures in Minecraft Blog Post

If I can paraphrase the curriculum expectation, I think "things look differently from different viewpoints" probably captures the mathematical big idea, or the reason for looking at 2D and 3D views. We attempted to wrestle down some criteria, but the list is probably by no means complete.  Our understanding of math as knowing, thinking, communication, and applying will always help, though (the achievement chart).

This is all a work in progress (and this blog post is intended to illuminate the pedagogical side of Minecraft, not the gaming side).  I guess what I am learning matches the big idea- things look differently from different viewpoints.  Yes, I realize that building structures is exactly what Minecraft is all about.  It just made the curriculum expectation a perfect fit in this case (as it would if you were teaching grade 3 or 7 science, and you looked at structures.

What other curriculum matches can you come up with?  How can we go about planning for our classrooms with Minecraft?

Tuesday, December 10, 2013

Communication (6 Cs of 21st Century Learning Writing Project Part 3)

Here are our thoughts on communication. What does it mean to communicate well in the 21st century classroom? Welcome to new writer @techmagfront!


Communication: Giving and/or receiving information

A beautiful sunset, a Van Gogh painting or a Bach concerto are forms of one-way communication. A message is delivered to the receiver. It used to be that advertisers, news channels and teachers were one-way communicators who delivered their message to their audience. In most areas of our lives now, there are fewer one-way communications. In two-way communication, the receiver can respond to the sender. We can email the news station or send a Tweet to an advertiser to voice our opinions about their messages. As teachers, we are no longer ‘pouring knowledge into empty vessels’ - we are using two-way communication to understand what students already know, what they are interested in, what they don’t like, etc. in order to build relationships that will improve teaching and learning.

Technology enhances our ability to communicate effectively. If I can’t write, I can use voice-to-text software. If I don’t like speaking in public, I can record a video ahead of time. If my family lives far away, I can Skype with them to hear their voices and see their faces. We no longer have to wait for news reports because we can see footage and hear messages about world events as they happen via social media. This ability to instantly communicate with people all over the globe has many benefits but also has the potential for problems.
Whether it is through body language, art, speaking, or the written word we are communicating. A clearly stated message is one goal we all hope for when we communicate, and for many of us, we also hope that our communications lead to conversations and to learning something new.


I have learned a lot about communication in the  past number of months. Personally, I can now honestly say I can divide my career into BTE/TE (Before the Twitter Era/Twitter Era). Most of the thoughts I have about the TE probably belong in the collaboration post, but I have never communicated more effectively than I have recently, but for that to happen, I needed to learn a new text form-the 140 character tweet.

When I think of 21st century learning, tweets are just one of many forms of communication our students will need to learn. Others could be emails, text messages, posting to YouTube channels, chatting while  playing Minecraft-the list goes on. Clearly, in the classroom, it's not enough to fall back on our old lists of "text forms".  New types of texts are being created everyday.  Yesterday's Facebook status update is today's SnapChat, is tomorrow's...? We can't possibly teach them all.

The question remains, how will we teach our students to communicate in this world we live in? What matters the most about communication in the 21st century?

Whether the mode of communication is writing or speaking, I think authenticity and authority of voice is probably the most important thing.  

Can you reach your audience, and effectively and persuasively communicate your message? Can you make a personal connection?  
Can your tweet (blog post, essay, speech, video, etc.) stand out from all the rest of them?
Can you argue succinctly and coherently from a point of view?
 What separates "signal from noise"?

Voice is what matters, regardless of the type of spoken or written text forms we teach our students. We must help our students to find their voice, regardless of what medium they are working in, or what type of presentation they are giving.

Communication: making your voice heard.

Jason Richea @jrichea

Communication, like each of the other 6 C’s, receives a lot of dialogue & discussion amongst academic professionals. We often hear in our staff rooms complaints regarding the delivery of messages by our students through their written and oral work. I find myself in these discussions quite a bit, and am constantly reminded at all the different ways messages are communicated.

These ways may have never been so numerous than they are now. And these messages conveyed in all sorts of different languages - and I’m not talking about foreign languages, but the modifications we’ve made to English/other native languages (U know? lol). I think this is a challenge for many teachers to accept and acknowledge that it’s not about the spelling, but about the message. That’s what communication is really about, is it not? Believe me, I’m not about to say that spelling & grammar does not matter; but does it matter as much as it once did?

In a world where we are bombarded by hundreds of messages each minute, it’s the message that stands out, which receives our attention. When we are in our classrooms, it’s the message that provokes thought, dialogue, discussion, critique, and our collective attention that is effective communication. Whether this is lengthy verbal conversation, or a brief 140 character message conveyed in a Twitter chat, it doesn’t really matter, so long as the results are what was originally intended.

In the 21st century, it is so important that we teach our students how to access the media necessary to convey their message. How to convey their message in a way that grabs others attention. And how to use the conventions of the chosen media to do this effectively.  We live in a world now where social media is King, and the communication that we receive revolves around this media. As Clay Shirky once said, 

“The Internet is the first medium in history that has native support for groups and conversation at the same time. The Internet gives us the many-to-many pattern. For the first time, media is natively good at supporting these kinds of conversations.”

Therefore, unlike definitions of the past, where communication is all about imparting or exchanging information between a few, 21st century communication is all about conveying your message in a way that captures the attention of hundreds (or thousands if you are Taylor Swift). Because if you want to stand out in today’s age, and have your voice heard, you are going to have to scream it from the top of the Twitter/Snapchat/YouTube/Facebook/Tumblr/etc.  mountain.

Communication = Capturing the Attention of the Masses

My Post on Communication @tina_zita

Communication sometimes feels so natural that we forget how often we are sharing messages with others in our day to day interactions. From when we wake up to when we go to bed we are tweeting, emailing, chatting, discussing, singing, dancing (well for me the last two are just in my car). If we want to help students become effective communicators in a digital world, we first need to be able to articulate what makes an effective communicator.

Here’s my stab at it.

Effective communicators have a clear message in mind. I don’t mean being eloquent. There are some that can string words together in mesmerizing sentences that have no core message. Effective communicators know what they are trying to get across. They have a clear message in mind. Their voice shines through. This also means that effective communicators know they have something to add to the conversation. No one’s voice is unimportant.

Effective communicators know that they have a toolbox of communication tools and that text is just one of them. Whether I know it or not, through the way I stand, my body language, and facial expressions  I’m participating in the conversation. In a multi-modal world, more and more of our communication tools have transformed past plain text or speech. To be an effective communicator we have to pack our toolbox full of a variety of tools with a variety of mediums. Effective communicators also understand which tools they communicate best with and how to switch between tools which leads us to the following.

Effective communicators understand their audience and are able to adapt accordingly. Firstly, if effective communicators want to understand their audience they have to listen and truly invest in understanding the other side. Secondly, they need to adapt their message to their audience. Communicating with my friend and communicating with my boss require my message to be finely tuned. Finally, they have to change their tools accordingly. A song may be an amazing form of communication when sharing an inspiring message but it may not be the best tool if I am applying for a job. Preparing to be effective communicators in the 21st century requires code switching and critical thought. Our message stays the same but how and when we communicate that message needs to transform between platforms, events, individuals.

If I had one wish it would be for learners in our care to understand they have a message to share, many ways they can share it and to critically make choices on how best to do that each day with the audiences around them.

Communication: clear message, deep toolbox, understanding audience.


The most effective  communicators are able not only to convey their message, but also their passion about the subject, which in turn moves others to think, reflect, or take action.  The way that they convey that message can take on many forms:  spoken word,  song,  poem, video, poster, photograph, painting, etc.  No matter what form the communication takes, it is ineffective unless it inspires others to care.  Also, in order for others to care about the message, it needs to be conveyed in a way that will be relevant to the audience - as teachers, we know that better than anyone.  Think of the greatest communicators of our century:  Martin Luther King, Jr, Ronald Reagan, Pope John Paul II, Steve Jobs - none of them has ever left their audiences indifferent to their message.  Think of a great book, movie, song, or painting, inspiring long and heated discussions. Bottom line, good communication never 'falls on deaf ears' and a great communicator’s voice cannot be ignored.

Communication:  Conveying relevant messages that inspire others.

Thursday, December 5, 2013

Coach in the Middle

The phrase "coach in the middle" has been on my mind lately. We still occasionally hear the phrase "sage on the stage" pop up, usually in reference to older, perhaps lecture-style teaching. I don't happen to know any teachers in elementary who thinks of themselves that way.  I did receive (and nod off during) lectures in university halls, though.

The counter phrase to "sage on the stage" is still "guide on the side," and for a while this one seemed to fit the way most of us teach these days. Desks are organized in groups, the classroom may or may not have a front (the closest to a front often being the projector screen). This phrase though implies more of an observational hands-off role, though, and observation is not really more than 1/3 of our assessment work (conversations and products, projects, or written work being the other 2).

We do know the guide steps in when needed, to talk to students and give advice, but perhaps "guide on the side" is not the best phrase anymore for what we do.  I came across a criticism of the "guide on the side in reading a recent work by Michael Fullan:

Speaking of a recent meta study by John Hattie on the effects of certain types of teaching, he suggests:

"...the guide on the side is a poor pedagogue; or we don’t want “a guide on
the side” anymore than we need a “sage on the stage.” More proactive partnership
will be required."

I've been thinking a lot lately about coaching as an analogue for teaching. A basketball coach, for example, might spend some time given direct feedback to the whole team during a practice, but probably spends a lot more time giving specific feedback to individuals (spacing on a drill, or form on a jumpshot, for example), or to small groups (a centre needs far different feedback than a point guard, for example). 

A coach is always active, in the middle of things.  Perhaps as instructional coaches we might think of ourselves as more "in the middle", than on the sidelines.  This new metaphor would also defuse one of the common arguments levelled at our system these days-that we simply just let kids go off to "discover" all that they will learn, at their own pace, and style. The ever-active coach is always talking, giving personalized feedback, and offering advice for how to improve.

Monday, December 2, 2013

"Be a Man"

This post is prompted by a recent news story about workplace bullying.  One employee was suspended from the workplace for being a bully; another had already left the team due to the acts of bullying.

The workplace happened to be an NFL locker room.  The details don't matter (and they're out there for you to find), but what matters is the response.  I got a bit curious for a few days, and read a few articles. Of course, the player who taunted and used racial slurs seemed to be known to be a bit of a loose cannon. The other player, for his part, was considered "strange" by some of his teammates.

One commentary on the situation by another player trotted out all the usual "be a man" macho code stuff you might expect. Showing weakness, you see, is against the code. Speaking out, speaking up, daring to be different, all against the code.  (The code of "war","warriors",  "brothers at arms".)

Unasked for, some "be a man" memories from my school days have popped into my head:

-being in grade 7 and having another boy saying he'd meet me outside after school. I remember how  the punches felt hitting the side of my head.  I was ashamed. It's not much of a fight when one fighter doesn't know why he's fighting, or even how to fight.  As Neil Young once sang, "the punches came fast and hard/lying on my back in the school yard."
-the same thing happened once more that year. Not sure why that happened either. I was still ashamed. I still didn't know how to fight. Maybe I wasn't man enough to know how to fight? Why were my fists not made to swing in collision arc with someone else's face?

I don't know, but I didn't land one punch, nor did I even try.

I've been thinking about "be a man" lately because I have two boys, 1 and 3 years old.  When you are a father, you think about things like that.  What kind of men will they?  Hopefully not ones who need to fight to prove something about being a man. Hopefully not ones who subscribe to ridiculous cliches of manhood (whether they be the "bumbling dad" stereotype from sitcoms, the "tough guy" athlete, the "action hero", or "patriarchal" family head).  

Here are some ways they can "be a man":

-bake a cake
-write a poem
-read a poem
-run a race
-turn down a fight
-read a book
-tell their mother they love her
-hug a cat
-admit when they're sad
-pay attention to their feelings
-talk about their feelings
-respect all humankind
-not let anyone else tell them how to "be a man"

Most of all, boys, to thine own selves be true. Become the man that you will be. Don't be denied!

Don't Be Denied