cc licensed (BY-NC) flickr photo by Jack Amick

A few years back my friend Bud Hunt published an unusual post on his blog; it was titled Going South. In just a few short sentences he shared that he'd be spending a week visiting his grandfather's garden. "As best as I can determine, the first reference on the Internet to my grandfather, a man that I know far too little about, is this one." he wrote. There was one link in the entire post; the words "this one". You can tell from the comments, not every reader followed the link.

I was talking with a couple of English Language Arts teachers today. They're planning to have their classes do most of their writing online this semester. We were talking about how they might use a Mother Blog model to do that. They'll use Google Reader to monitor the community; subscribing to both the posts and  comments of their students' blogs.

I wanted the two teachers I was talking with understand how to help their students learn to read and write hyperlinked text effectively. I shared with them the story of Bud's "Going South" blog post. It's a poignant lesson in reading and writing linked text. (In the privacy of my own thoughts: This will also be a nice memorial to Bud's granddad. In a way, he'll teach and touch the lives of generations beyond his immediate family.)

A Better Metaphor for Life Long Learning
In his book, Everything Is Miscellaneous, David Weinberger talks about the difference between writing on paper and writing hyperlinked text. Paper has physical limitations that digital text doesn't. It starts and ends. It's only so wide and so long. A paper book can only contain so much content. Even if it's one of many volumes in a larger work.

Have you ever started reading an article online, say in Wikipedia, clicked a link, then another? And another. Only to find yourself two hours later having explored a web of ideas unique to your personal interests along the way. Eventually you stop. Not because you're "finished" but because life imposes other demands on your time.

Digital text is different. It's a much better metaphor for life long learning. And you can't write linked text if you aren't reading. Lots. (It's taken me years of reading to write this blog post.)

New Media, New Process
Not too long ago Dean published a post about writing hyperlinked text. He had collected a number of comments in a storify archive and reshared a video Will had made about his writing process. (Think that through as a writing process.) Watch:


This sort of process is another thing I shared with the teachers I was talking with:

• Using a mind mapping tool, like mindmeister, that includes hyperlinks is different.
• Clipping ideas contained in text, images and video using a tool like Evernote, which allows you to create web pages & hyperlinks is different.
• Writing by stitching your ideas together from hyperlinked sources is different.
• Reading that text is different too. It matters where you publish it, online or off. Different media (paper or digital) carry different messages. 

I'm fascinated to see the student writing that emerges from this semester.

I'm also curious; is there anything different about how you teach reading and writing digital text? Any advice for us?


UPDATE 20 Feb 2012
Check out Bud's thought provoking digital writing workshop (a network of Google Docs): 
Reading 1.0 - How Digital Changes Nothing. And Everything. Is All.

When I'm asked, in email or face to face, to explain how I use < web based tool > (blogs, wikis, podcasts, what have you) with my students I usually begin by saying: "That's not a short answer." While knowledge of how a particular tool works is important, it's really a distant second to the questions:

What do I have to teach?

and

How can I best help my students learn this?

This is the first in what I hope will be a series that explains how I think about answering those questions.

The slidecast and the videos are best watched in Full Screen mode.

Slidecast

Teaching (a pedagogical framework)

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Video

A higher quality video is available via my blip.tv channel.

Audio (8 min 4 sec)

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Transcript

Years of research into teaching and learning have uncovered some basic fundamental principles of how all people learn. This will just be a quick overview of how I've tried to bridge that research with my practice and what I'm calling a pedagogical framework.

But first an excursion into the world of photography. The photographic technique of framing involves finding something that draws the eye, that sits around an object to draw the viewers' attention to that thing. Here's an example.

The lady is the object of this picture the eye is naturally drawn to see her there in the centre as she's framed by the windows of the subway car.

This is a strong example of framing as we see this man walking through the arches and those arches form a frame. The eye is inexplicably drawn towards the centre of the picture where we see the man.

In this case, a more subtle frame. And yet nonetheless it's clear that the horse is the object of the picture because the tree — which we don't really look at, it kind of sits in the foreground, the eye is really drawn towards the horse — provides a frame to see the horse.

What does this have to do with teaching and learning? Just bear with me.

First the three pedagogical principles, drawn mainly from this book: How People Learn. It was written in ... I believe it was 1999 and then it was updated again in 2000. Studying years and years of research they pulled out three fundamental principles of how people learn. As an outgrowth of that book another one was written called How Students Learn, specifically in the areas of History, Mathematics, and Science. These books have been absolutely seminal in forming my thinking and providing the pedagogical framework around which I structure all the teaching that I've done.

Typically when kids come to school they think of the world as flat. They have no reason to think of it as round and they come to school and we tell them the world is round. What studies have shown is that once kids leave school and they're asked to explain what they've learned: "Well the world is round." And their conception of the world is that it's a giant pancake. That's an interesting preconception that kids bring with them when they come to the classroom and teachers need to know that. Because the first principle out of the book is that "students errors and misconceptions based on previous learning" are the first thing that teachers have to try to connect with when they're trying to teach new content.

In this example, one drawn from mathematics, kids are often taught that multiplying is repeated addition. Multiplying is not repeated addition (although that's a good place to start) and they think that the answer to any question, when they multiply, has to be bigger than any of the numbers they started off with. Given a problem like this, fractions, well kids find that really hard, they just mul... they see the two the three and they know they have to have an answer that's bigger than either of them. If we know that that's the preconception that kids bring to the classroom then that can inform our teaching in constructive ways.

The second principle out of the book is that understanding requires not only factual knowledge, knowledge of basic facts, but an understanding of the basic ideas or big ideas of the discipline, whatever the discipline is that happens to be that you're teaching. Because knowledge isn't actually built in hierarchies knowledge is actually built in networks. For example, take something simple like three quarters. It seems like a pretty simple idea. But the number three quarters can be represented in a variety of ways. All of these are equivalent ways to write three quarters. It might have meant money, seventy five percent, it could be the ratio of three to four, point seven five or another way to write the fraction three quarters. Now even this extends beyond that because, "three quarters", well I could have been saying the money, three coins, three twenty five cent coins, which is seventy five cents. You see all these ideas are connected one to the other.

I might have been talking about a piece of cake; that I have three quarters of a cake. And it's implicit in that idea that each of those quarters is the same size. That each piece of cake has to be equivalent in size. But that's not always true with all ratios.

For example the ration of three red Smarties to four blue Smarties. I've got seven Smarties in total. And those Smarties don't all have to be the same size for my ratio of three red to four blue to be true.

These implicit assumptions make learning this material difficult for kids, and we as teachers make assumptions because we understand from the context that these things are clear. It could be seventy five percent off everything. That these ... All of these ideas actually live a network all one related to the other. The underlying assumptions that we make as experienced learners is that we take, from the surrounding context, what the meaning of each of these numbers is. And yet each one is related to the other.

That network has to be made explicit. That network of concepts has to made explicit to students. No matter what fundamental idea you're trying to get across to the students. In this case, the idea, the big idea, is really one of proportion.

The third principle out of the book is that "learning is facilitated through the use of meta-cognitive strategies". The degree to which we can get kids to think about what they're learning as they're learning it will deepen that learning. And they found that this made only moderate increases for high performing students, but for low performing students the use of meta-cognitive strategies made for dramatic increases in their performance.

Error analysis is a great example of this kind of thing; you've probably caught that one really quick. But as you look at this picture and try to find the error look how you're thinking about it. Look how you're paying attention to certain details; finding what's the same, what looks exactly identical? Where is the difference? Where is the thing that stands out one different from the other? And if you pause to reflect even as you're thinking about this now you'll notice that you've deepened your own thought as you look for the error in just something simple, like a picture of three Mounties.

So that's the framework. That's the framing. That's the ... Those are the ideas that sit around any pedagogical approach that you want to take in class. Any time you want to structure or design a learning experience for students these three principles:

Connect with kids preconceptions.

Learning should be networked. Ideas are networked. You need to understand basic facts but also the big ideas around which knowledge is structured.

And engaging kids in meta-cognition as they're learning.

This provides the framework for how we teach.

There's one last thing not to exclude in any of this and that's "community". It's alluded to in that book but not listed as one of the fundamental principles; but "community" is a pretty big deal. Because the degree to which we can get kids working with each other and collaborating and helping each other in their learning, which is what genuine learning looks like, is the degree to which they can deepen and accelerate their own learning.

This provides a wonderful example of exactly what I'm talking about: Why do geese fly in this "V" shape? It seems quite distinctive to see the Canadian geese flying in that pattern. It happens in the Fall, around October, and then again in the month of March as when ... as the geese leave in October and return in March. Why the "V" pattern? Because the flapping of the wings of the lead goose actually provides a little lift for the geese just behind them. And that's true for each goose behind every other goose. And so they're able to fly greater distances. Of course this puts undue pressure on the lead goose. So throughout the flight the geese are constantly shifting positions and rotating their spot in the "V" shape flight pattern. So that different geese take the lead at different times. And by working together the geese are able to fly for much greater distances than any of them would be able to fly on their own. And together they accomplish great things which is the very distant migration patterns of the Canada geese. Of course over short distances, if everybody goes their own way, well, yeah, you could have some success, and when they all land that's what it looks like. And they all kind of come down and each one chooses their own pattern and the "V" is broken up. And occasionally, you know, you need to do that, but by and large, for the most part, it's through that collaboration that great things become possible. And that's part of that framework that I talked about.

It's just like we learned in kindergarten: When you go out into the world, hold hands and stick together.

... was the title of the Keynote address I gave to 500+ educators at this year's B.Y.T.E. conference. The sense I had of the audience was that many of the ideas I talked about here were new to them. A quick survey of the room while giving the talk revealed only about three people had heard of Wolfram Alpha and I think about the same number had heard of the TPACK Framework.

I hope I get a chance to do this talk again. There are a number of things I think I could have done better.

Anyway, if you're interested, here it is in various formats. You pick how you'd like to take it in.

Audio

Download (20 MB)

Slidecast


Ustream Video (thanks to Chris Harbeck

actually, it was 11 minutes and 45 seconds.

This is the slidecast from one of three talks I gave on Friday October 9, 2009. I was in Virden Manitoba participating in the NIBBLE Conference for the Fort La Bosse School Division.

More coming soon. Everything will be aggregated on the Senior Years Information and Communication Technology wiki I'm maintaining to share all the work I do in Manitoba with teachers across the province ... and you.

From the archives ... I started writing this post in November of 2007.
A LONG TIME COMING
A while back, Dean and Bud got me thinking. Bud's tweet contains more than a kernel of truth.




Shortly after reading Bud and Dean I was listening to David Suzuki on the radio. He mentioned in passing the idea of "in depth news reports" on television. Generally, that means they're going to talk about an issue for about two minutes. Some issues need to be explored in more depth than that. I think pedagogy is one of those issues. In particular, I think I need to explore my own teaching, articulate my own pedagogical practices, open them up to scrutiny and shore up the weak bits.

George Polya's ideas have been very influential on me and my evolution as an educator. Since reading his Ten Commandments For Teachers I have tried to model them in my practice. Although Polya (1887-1985) is no longer alive, I consider myself one of his students. This series of blog posts is my record of what I'm learning about the craft of teaching.


IN BROAD STROKES
In chapter 14 of Polya's book, Mathematical Discovery, he talks about the teacher's attitude and structures his thinking around what he calls The Ten Commandments For Teachers. This is the first in a series of posts digging into this in depth; maybe four, maybe ten; one for each commandment. We'll see.
Although I've been thinking about it for a long time, I've got more questions than answers about these commandments. I want to share my thinking and questions here because:
(1) I want to capture my where my thinking is at today so I can come back and reconsider it in the future.
(2) I'm hoping people wiser than I might share some of their insights. I'm hoping the give and take inherent in blogging about it might push my thinking and practice; make me a better teacher.
So push back at any weak bits below or share your own teaching tip.


THE TEN COMMANDMENTS FOR TEACHERS
In chapter 14 of Mathematical Discovery Polya lists his Ten Commandments For Teachers. They have been a guiding light for me as a teacher since I first read them.

1. Be interested in your subject.
2. Know your subject.
3. Know about the ways of learning: The best way to learn anything is to discover it by yourself.
4. Try to read the faces of your students, try to see their expectations and difficulties, put yourself in their place.
5. Give them not only information, but "know-how," attitudes of mind, the habit of methodical work.
6. Let them learn guessing.
7. Let them learn proving.
8. Look out for such features of the problem at hand as may be useful in solving the problems to come — try to disclose the general pattern that lies behind the present concrete situation.
9. Do not give away your whole secret at once — let the students guess before you tell it — let them find out by themselves as much as is feasible.
10. Suggest it, do not force it down their throats.

MODELING PASSION: Be Interested In Your Subject
Polya identifies the single most powerful and infallible teaching method: "If the teacher is bored by what he is teaching it is a certainty that all his students will be too." I believe the inverse is also true: If a teacher is interested in what they are teaching their students will be too. Actually, "interest" by itself may not be enough; passion is a virus. There is a contagion in passion that can be passed on. I would rewrite Polya's first commandment as: "Be passionate about your subject." If you can't do that then I guess interest will have to do but if you don't have even that, do something else.
If you were a student in grade 8, and your teacher began a new unit of study like this what do you think your engagement with the material might be? Passion Based Learning is powerful stuff. There's something magnetic about a teacher who is passionate about what they are teaching. Passion leads to Interest leads to Life Long Learning. Kids need to see that their teachers are interested with their subject and constantly trying to get better at what they do. If we don't model the drive for excellence in what we teach why should they be interested in doing excellent work in our classes?

The teacher's most powerful pedagogical tool in their toolbox is tucked away in their attitude, demeanor and engagement with what they are teaching; we call it modeling. It's such a fundamental idea. Surprisingly, some quick searching on the net reveals very little written about the importance of modeling in education as a general pedagogical practice. Even wikipedia has very little to say about it; the closest article to this idea is called Modelling (psychology). It seems to me we need a few good educators to flesh this article out a bit on wikipedia.
A while back Dean asked, Can A Fat Man Teach Phys. Ed.? His answer: "Yes, but ..." It all comes back to the importance of modeling.

I'm reminded of Benjamin Zander who says:

Our job is to awaken possibility in others ... You know you're doing it when their eyes are shining. And if their eyes are not shinning, then we have to ask ourselves, "Who am I being that my [students] eyes are not shinning?"

... not all, but many of them. What I really like about this set is that the fellow who puts them together often references and links to the source articles or research where the snippets are taken from.

If one of these images (all cc, I asked) strikes you in some way, follow the link back and copy it to the comments here maybe sharing what struck you. I'll start it off below.

I'm not sure if images will embed in the comments here (I'm testing this with my first comment below) but I've got apture installed on my blog so linking to the image should create a popup view of it when you hover over the link; like this.

I've had this sitting in draft for about 7 months. It goes all the back to the end of May when I had the good fortune to attend the Microsoft Innovative Teachers Conference held here in Winnipeg. The line up of speakers was excellent, but Rick Van Eck stood out as the highlight of the entire conference for me. (I blogged about Rick's Breakout session at the time.) He has a very down to earth, practical, honest approach to using COTS (Commercial Off The Shelf) games in education. Unfortunately the question period isn't included. Rick really shined during the Q&A afterward where his direct, honest, polite replies to pointed questions impressed everyone.

Anyway, I've mentioned this talk several times in passing since I saw it and now I can point people to hear the man himself. It's short; 22 min 21 sec. Worth every minute. You can click through Rick's slides below the video as he speaks.

(Download mp3, 25.4 MB)

Slides:

Microsoft Innovative Teacher Conference--Keynote

View SlideShare presentation or Upload your own. (tags: games learning)

This is the closing keynote presentation given by Les Foltos, Director of the Puget Sound Center for Teacher Learning and Technology, at the Microsoft Innovative Educators Conference held in Winnipeg on May 29, 2008. (The site appears to be down, or broken, now. I thought it was supposed to serve as a commons around which a growing network of teachers was going to built. I wonder what happened?)

This is the last podcast from the from the conference I recorded. It's a little noisy to listen to. We were all talking in small groups trying to crystallize what we had learned over the previous two days. The good news is we talked about many of the same things that we had discussed in the previous day's Ustream. The voices you hear talking in our little group are me, Clarence Fisher, Chris Harbeck, John Evans, Andy McKiel, Kathy Cassidy, and another lady whose name, unfortunately, I've forgotten. She was sitting in a neighbouring group and kept looking over at us, interested in what we were talking about. So, I invited her over and I'm glad she joined us. I think we all got a lot out of this conversation. Give it a listen and add your own two cents in the comments below.

(Download File 30.0Mb, 62 min. 30 sec.)

UPDATE

Great news! Chris found the Ustream recording!! Good on ya Chris. ;-)

Watcher beware: a surprising amount of time is devoted to discussing Dean Shareski's eating habits and his coffee mug — we had a lot of laughs. ;-)

Time: 36 min. 13 sec.

Live Videos provided by Ustream.TV

This is the audio from Richard Van Eck's breakout session at the Microsoft Innovative Educators Conference. It's full of very practical ideas for how to incorporate using commercial off-the-shelf (COTS) games in teaching a variety of subjects in the K-12 curriculum. Rick's presentations are very grounded with very little flash in his slides but lots of good concrete ideas to take back to the classroom. The night before this session Rick gave a keynote presentation on games based learning. He was asked if the kind of learning kids do in games based learning transfers well to the content areas. He looked the questioner straight in the eye and said, loudly and clearly: No. Then he fleshed out that answer. I still might be able to track down the audio from the keynote. If I can get it I'll publish it here. In the mean time this is a very practical talk about how to begin using COTS games in your classroom.

At about 19 minutes in Rick tried to get online but was locked out. Thankfully, Chris Harbeck was there and had the password. ;-)

| View | Upload your own

(Download File 14.6Mb, 30 min. 30 sec.)

I've long held a ravenous appetite for learning how the brain works and how those capacities can be leveraged to help kids (and me) learn. I recently bought the owners manual. A few days back Jeff Utecht tweeted about a Google Talk by John Medina, authour of the book Brain Rules. John is blogging and sharing some great stuff.

Garr Renolds adapted some of the Brain Rules for presentations. As I've blogged earlier presenting information is something teachers do every day and we need to learn a lot more about how to do it more effectively. So, for my own future reference, and yours if you like, here is John Medina's Google talk, Garr's presentation, and a seemingly unrelated presentation by Dean Shareski whose K12 Online presentation on Design Matters continues to push my thinking every day. Look at how this presentation of Dean's adheres to many of John Medina's Brain Rules; and Dean hasn't even read John's book yet.

| View | Upload your own

| View | Upload your own

In future posts I hope to share how what I'm learning from all this is making it's way into my classroom. I'd love to hear how others incorporate these ideas into their work as well; in education or elsewhere. When we share these ideas and applications, whether they work or not, it helps us all learn.

UPDATE

Dean referenced this video at the end of his presentation; it's well wortht the 4 minute look:

Today I swung a meter stick around the classroom like a samurai sword. I called it: "My great and mighty swuhord!" It's become my standard opening for the unit on conic sections which we'll be studying in grade 12 pre-cal for the next week or so. This is followed by playing with paper; folding it to create a parabola according to the locus definition — but I don't tell them that's what we're doing right away. Here are the slides from the class:

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As I swung the swuor ... meter stick, I spoke Japanese with a feigned accent: "Kawasaki, Susuki, Honda! Sony Mitsubishi!" (Yeah yeah, they're not all Japanese. I know.) My lips kept moving soundlessly after I finished speaking. We we're rolling on the floor laughing. We had to stop for a laugh break. Talking straight faced about mathematics, my lips continued moving for a few seconds after I spoke throughout the rest of the class.

Here's the thing though, when I started talking about the connections between the geometry and the algebra behind parabolas I had their complete attention. They followed every step of the way. Even those that don't usually pick things up quickly the first time picked it up fairly quickly when it was reexplained.

I've always tried to use some humour in my classroom, but reading an article about two years ago really inspired me to try to inject even more humour in my teaching. It's called USING HUMOR IN THE COLLEGE CLASSROOM TO ENHANCE TEACHING EFFECTIVENESS IN "DREAD COURSES". This is part of a larger course for college instructors on how to be better teachers.

Why don't they teach this stuff to pre-service K12 teachers? Why didn't anyone teach me this stuff before I walked into the classroom? There's certainly plenty of research out there supporting the use of humour to enhance teaching and learning. For example, this article from the Journal of Statistics Education Using Humor in the Introductory Statistics Course was written almost six years ago. From the article:

• • Humor Builds Relationships and Enhances Communication
  When students talk in class (I'm going to use this one!): “What! I hear voices again. My psychiatrist told me that if I keep taking my Prozac the voices will go away.”
• • Humor is a Stress-Reducing Tool (preparing for tests)
  If you make certain very egregious errors (for example, a negative probability), not only will you not get partial credit, but we will somehow manage to take points off of exams you are taking in other subjects. We might even take away points from courses taken in high school. In fact, one day, when your children and grandchildren are taking my class, we will take away points from their exams too! Alternatively, “Give me a probability greater than one and I will take away your car.”
• • Humor Makes a Course More Interesting
  "Education is the only paid-for commodity regarding which, the less you provide, the happier the customer."
• • Humor Enhances Recall of Information
  Years - some would say days - from now, students will have forgotten much of what we teach them. But they remember the humorous methods used to illustrate important points.

This is probably my favourite joke in the article:

A statistics major was completely hung over the day of his final exam. It was a true/false test, so he decided to flip a coin for the answers. The statistics professor watched the student the entire two hours as he was flipping the coin ... writing the answer ... flipping the coin ... writing the answer. At the end of the two hours, everyone else had finished the exam and left the room except for that lone student. The professor walked over and said, "Listen, I see that you did not study for this statistics test, you didn't even look at the exam questions. If you are just flipping a coin for your answers, what in the world is taking you so long?" Still flipping the coin, the student replied "Shhh! I am checking my answers!"

Humour relaxes us and helps us think better. Shouldn't something like that be a part of every curriculum and instruction class?

And speaking of Things They Should Have Taught In The Faculty Of Education, what about presentation skills? Stuff like how to use your voice, organize text and images to convey ideas, how to "work a room". Shouldn't this also be taught in Faculties of Education? Teachers are "on stage" every day, several times a day, presenting content and "working the room" to help kids learn. This seems like such a "no brainer". Does any Faculty of Education anywhere specifically teach presentation skills in the way the teacher in this video or this one (from teachers.tv in the UK) gets that help when he tried to go "From Good to Outstanding?"

In the last several years I've given a number of presentations to many different audiences. The skills I've developed have spilled over into the classroom. Compare how I taught this class last year:

| View | Upload your own

to how I taught it this year:

| View | Upload your own

The image in that last slideshow introduces what I think is another powerful teaching practice: metaphorical thinking. A binomial distribution is displayed graphically as a sort of bar graph called a histogram (the dogs are lined up in a way that is reminiscent of a histogram). Also, an experiment is binomial if and only if it has exactly two outcomes, typically described as "success" and "failure". Do you see this characteristic displayed in the image? My students did. But that's a post for another time.

David Truss has a great post called Assessment & Rote Learning: Math Conundrums. I tried to leave a comment. I discovered I'm passionate about what Dave had to say. The blog, or my cocomment plugin, borked (yes, that's a technical term) and wouldn't let me leave the comment so I decided to share it here. You may like to read Dave's post before continuing with this.

---

Breathtaking post, or was it three? ;-)

Assessment

I did the same exercise with my dept. We also had the same vastly differing results you did. At a provincial in-service about 9 or 10 years back I participated in the same exercise using real student generated work. Results varied from around 33% to 80%. This is one facet of Academe's Dirty Little Secret. Anyway, in my dept. we've been looking at how we assess all the content in all the courses we teach; one course at a time, one unit at a time. We're trying to develop a consistent approach to assessment at least within our building. We'll be "at it" for a while yet.

Basic Skills

Fluent knowledge and recall of basic addition, subtraction, multiplication and division facts are essential for ANY student to experience success in math. I'm on the same page you are Dave.

A grade 9 student, who struggles (mightily) with her multiplication facts, and I were talking about this last week. As I was trying to help her I asked why she thinks I feel it so important for her to become fluent in her recall of the multiplication table:

"I know, I know, some day I might not have a calculator and I might need to multiply two numbers."

[Oy! Who tells kids this stuff? And do they really believe that? -- I mean the adults, not the kids. I know the kids don't believe that.]

"No. That's not why. You'll always be able to get a calculator if you need to multiply a bunch of numbers. That's not the reason. It's that you need to know the language of math so you can join the conversation."

"If your teacher is trying to teach you why multiplying pairs of negative numbers always have a positive result, or why, when we divide fractions, we 'multiply by the reciprocal' they're going to talk about stuff like 7x8 and assume you know it's 56 and go on to discuss some deeper ideas. If you're hung up on 7x8, need to pull out a calculator, you're going to miss the entire conversation. Your brain will be back 5 steps while everyone else is talking about this other stuff. By the time you figure out what's going on you won't know what's going on. You'll feel lost and confused and fall farther behind."

"Why do I need to know math anyway?"

"For the same reason you need to know how to read. Because it's a fundamental way that humans communicate with each other and understand the world around them. If you can read but you can't understand mathematics then there will be giant tracts of things happening in the world around you that you'll never understand."

[Whew! Went on a bit of a rant there. I'm going to get a cup of tea ... Cheers Dave!]

A study was released about 5 days ago. The title: The Advantage of Abstract Examples in Learning Math. A number of articles about it share the title" Concrete examples don't help students learn math, study finds. (Supporting material can be downloaded as a pdf here.)

From the article:

Teachers often use real-world examples in math class, the researchers said. In some classrooms, for example, teachers may explain probability by pulling a marble out of a bag of red and blue marbles and determining how likely it will be one color or the other.

But students may learn better if teachers explain the concept as the probability of choosing one of n things from a larger set of m things, Kaminski said.

If Ms. Kaminski (one of the authours of the study) tried this in any high school classroom she'd bang up hard against a confused wall of silence from all except the most gifted students.

About 2500 years ago Aristotle wrote about how presenting an argument from the general to the specific (deduction) is only one of two forms of presenting information (teaching). Arguing from the specific to the general (induction) is the other. Both have their place.

Anyone who has taught mathematics in a high school classroom knows kids really need to learn and understand both. Often, they just can't grasp general concepts until they have seen several concrete examples. This is what Aristotle calls induction. It is a weaker form of argument than deduction (arguing from general principles to specifics) but is a necessary step in the learning process. Generally speaking, kids find inductive arguments far more compelling than deductive ones, even though the reasoning behind deductive arguments is far more sound.

One of the authours of the study also said:

Story problems could be an incredible instrument for testing what was learned. But they are bad instruments for teaching.

Sometimes a study is just plain wrong. This one is just plain wrong. "Story problems" are excellent tools for both teaching and learning, particularly when students are taught to recognize the underlying patterns of the general mathematical ideas they contain. I find teaching mathematics is something of a dance; constantly flipping back and forth between induction and deduction and guiding students through the process of teasing out the underlying patterns that tie several problems together; problems that on the face of it seem to be quite different are in fact the same ideas in different clothing.

In general, mathematics is the science of patterns. It is the job of the classroom teacher to help students recognize and identify those patterns so they can use them to solve many different problems as they come to recognize the connections between seemingly disparate situations.

I wonder too about the methodology of the study. The article says: "students were taught artificial mathematics". It seems possible (likely?) that the results were skewed as a result of the interference effect.

Dean Shareski tweeted that these results might take root. It made me think of the controversy surrounding The Learning Pyramid. I hope Dean's concerns don't materialize. From teaching hundreds (thousands?) of students over many years I know this study is just plain wrong.

Chris and I were invited by Cheryl Prokopanko, along with six of our students, to participate in a panel presentation at Canada's first Pan-Canadian Interactive Literacy Forum.

Preparing for today led to a collaboration that involved introducing my students to Box.net, where we shared our evolving presentation slide decks in a space where we shared access, and several skype calls with Chris.

Cheryl opened the presentation with an overview of Manitoba's new Literacy in ICT curriculum continuum which has evolved over the last several years (next year is the first year implementation is required by all schools in the province). It began with this video ...

Then Cheryl introduced Chris and I and our students. Chris and I bookended the kids presentations. Chris made some opening remarks, I made some closing remarks (actually, it was an invitation). But the highlight of the entire event was the kids. They so rock! Watch and see ...

| View | Upload your own

... and it continues with my students, then me, here ...

| View | Upload your own

We ended off with a question and answer session (Podcast: 16.8 Mb, 27 min. 55 sec. Now available as a slideshow with photos from the presentation) which you may find interesting. Some of it is hard to hear but there are some really great moments; like when one of the grade 8 students explains texting to a 63 year old member of the audience.

When it was all over the kids were swarmed by people who wanted to chat with them and hear their thoughts. Chris and I hung back and just left them to soak up all the well deserved accolades they collected. Each kid spoke for about 5 minutes and each kid must have spent over 5 hours preparing for it; and it showed. Chris and I are so proud of them.

On Tuesday I was invited to speak to Alec Couros' eCurriculum and Instruction class; EC&I 831. Alec is a great host. He has an easy comfortable manner and everything went off very smooth in eluminate.

When Alec first asked me to give this talk, a few months back, we discussed what form the presentation might take. After a bit of brainstorming I decided to continue the meme Clarence Fisher started, continued by Doug Belshaw and Dean Shareski, in his K12 Online Keynote presentation.

So, here is my riff on "A Day In The Life." The slides are below. Alec posted a summary of it on the course wiki and the full video and audio recording in Elluminate is available here ... I wonder if there's a way to capture the Eluminate recording in some sort of screencast format?

| View | Upload your own

As always, your questions, concerns, compliments, complaints, confusions and comments are welcomed and encouraged. ;-)

Ed. Note: The image below titled "The Learning Pyramid" is NOT based on any verifiable research; perhaps, no research at all (see this and that). This pyramid is widely cited yet it is, as Christopher Harris shared in a recent email, a hoax. Nonetheless, I stand by the idea that the marriage of teaching and content creation is a powerful pedagogical practice. (see the comments)

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A paradigm of instructional design that suggests we create learning experiences for our students where they create content that educates.

I had a conversation with a couple of friends who teach at university. We were talking about how much variation there is not only in the nature of assessment in different classes but also what work merits an A (the highest grade) or an F (failure). Some professors consider a mark of 85% an A, some require more others less. Some determine students entire grades from a single exam or paper; others require several short papers, a mid-term, final exam, and a major research paper. And these variations can occur when different instructors teach the same course and students receive the same credit (or not) for different work.

(It's amazing to me that student societies don't protest this sort of thing.)

We're no better at the K-12 level. I once attended a workshop where 30+ math teachers graded the same set of three problems. Each teacher decided how many marks each question would be worth and converted the marks to a percentage. Scores varied from percentages in the 30's to the 80's.

I guess this is academe's dirty little secret: there are no assessment standards.

To its credit the National Council for Teachers of Mathematics (NCTM) published a set of Principles and Standards for School Mathematics in 1995 (updated in 2000). The document includes The Assessment Principle. These are guidelines only. Not all math teachers are members of the NCTM, not all math teachers are aware of these standards, and adherence to the standards is voluntary not compulsory.

One of my friends shared that she is required to ensure her classes achieve a predetermined average grade. I think that's unethical. Sometimes you get a strong group of students, sometimes a weaker group, more often it's somewhere in between. There really is no way to "predetermine" a class average. We all agreed it should be possible for a class to all achieve A grades or F grades.

I don't believe a student's grade in any course is a measure of their intelligence. I do believe it is a measure of the time, energy, and effort invested in the class. But I digress, that's another issue.

As we talked some more about assessment and pedagogy the conversation got a little more intense as I challenged my friends by saying: "If all you do is lecture do your students really need you? Couldn't they just read your assigned text, show up on test days, write the final exam and be done with it?"

That started us on a bit of a heated discussion about instructional design and assessment. What became really clear to me is that most instructors in university teach and assess their students at the bottom of Bloom's Hierarchy.

At one point, one of my friends said: "Look, we're not going to throw out hundreds of years of tradition because of what we think sitting here discussing this."

"That's not a fair criticism. It's not like there isn't scads of research in teaching and learning that I can point to supporting what I'm saying. I'm not making this up as I go along. The fact is, if you just lecture to your students, on average they're going to retain maybe 5% of what you say. You can do a lot better to make their learning sticky."

"If you really want to ramp up your teaching have your students create content that educates. That will naturally engage them at a higher cognitive level."

"You can require your students to demonstrate their understanding of what they are learning by having them apply their knowledge analyzing and evaluating relevant novel situations or problems. Better yet, get them to create content that educates an interested learner and they will automatically incorporate all those levels of engagement while they make their learning sticky. I don't need to tell you that there's nothing like having to teach a thing to make you really learn it.

Terry Freedman asked me to contribute an article the the second edition of Coming of Age: An introduction to the NEW world wide web. It was originally scheduled to be released this month but due to circumstances beyond Terry's control publication has been pushed back to January 2007. Terry recently emailed all the contributors to the new edition to say we should feel free to publish our articles on our blogs in the meantime. The second edition has over 50 articles; I'm really looking forward to reading it.
In the past few months a number of people have emailed me asking how I orchestrate the use of scribe posts in my classes. This article is a step-by-step guide to using scribe posts with your students ... and then, how to take it to the next level. ;-)

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Distributed Teaching and Learning
The Power of Pedagogy and Audience
by Darren Kuropatwa

All my classes are hybrid classes. They have both a face-to-face component and an online component. Each class is supported by a blog. The class blog is used in a number of different ways but in this article I will focus on two ideas, Scribe Posts and Feed Windows, pedagogy and audience; the first leads into the second.

Harnessing the Power of Pedagogy: The Scribe Post

This straightforward idea has incredibly powerful consequences.

Each day, except for test days, a different student is responsible for the daily scribe post. This is worth 5%-10% of their class mark (see below), everyone who writes a scribe post gets their marks -- non-blogging students don't (it's their choice). They end their post by choosing the next scribe. Over the length of the course these scribe posts grow into the textbook for the course, collectively authored by the students; one student at a time, one day at a time.

The first scribe is a volunteer. The teacher's daily involvement is limited to updating a post called The Scribe List which is at the top of the links list in the sidebar of each class blog (sample class blog). The Scribe List is an easy way for scribes to see who has already scribed and who they can choose next. Once the whole class has been scribe once we cycle through the class again. I teach in a semester system (full courses are taught in 4-5 month blocks). In my classes, every student will be scribe a minimum of three times; some will write four scribe posts. In this way, the responsibility for teaching and learning is distributed both across the class and the semester.

The assignment is simply to post a brief summary of what happened in class each day. The instructions given to students look something like this:

Write a brief summary of what we learned in class today. Include enough detail so that someone who was away sick, or missed class for any other reason, can catch up on what they missed. Over the course of the semester, the scribe posts will grow into the textbook for the course; written by students for students. Remember that as each of you write your scribe posts. Ask yourself: "Is this good enough for our textbook? Would a graphic or other example(s) help illustrate what we learned?" And remember, you have a global audience, impress them.

The mechanics for teachers, aside from updating The Scribe List, also requires the occasional reminder to students to stay on top of their scribe posts. Occasionally, if the day's scribe is sick or away for any other reason give the class a few minutes, perhaps while taking attendance, to decide among themselves how they are going to deal with this issue. (One of the ideas behind the scribe post is to make students responsible for their own learning.) This essentially requires that a student volunteer to "cover" for the scribe who should pick up the routine again the next day.

This simple idea has lead to some incredible student work. Early scribe posts tend to be entirely text based (example). As the class progresses, successive scribes begin to try to outdo each other and their scribe posts begin to incorporate text, images and colour used in meaningful ways (example).

When scribes reach this level of excellence they are inducted into The Scribe Post Hall Of Fame. The students first name only (to protect their identity), grade, subject, link to their post, post date, inductor and reason for induction are all recorded on a wiki. This is a further motivator for outstanding student work as different classes compete to be the Consecutive Hall Of Fame Scribe Post Record Holder.

Anyone can induct a scribe post into The Hall Of Fame. As a matter of fact, it's more powerfully motivating and has a greater impact when the inductor is not the student's own teacher. You can find a list of class blogs that use scribes in The Hall Of Fame. Feel free to add yourself and your classes to the list. (The password for the wiki is: iscribe) You'll notice that all the 2005-2006 School Year participants are math classes. That's because I began this project and I teach math. Nonetheless the pedagogy is easily transferable to other domains. Anne Smith, an English teacher in Colorado, has started using scribes in her English World Literature class. Alison Elkins, a grade 5 teacher in Winnipeg, has also had some success using scribes in her class (Alison's blog has moved, the new blog is here). This year, 2006-2007, we also have a badge that teachers can put (copy and paste) on posts that get inducted into the Hall Of Fame. Some of the benefits brought on by the Scribe Post Hall Of Fame are:

• Recognition of outstanding student work.
• Additional motivation for students to produce their best work.
• Encouragement for other students to excel.
• Build students self-esteem by using this forum to generate widespread public recognition.

Of course the question arises, what does it take to get inducted into the Hall Of Fame? In a post to my class blogs called "Create a Scriber's Guide to Scribing", I asked two of my classes these questions:

• How do you go about writing a scribe post? Do you do anything differently in class when it is your turn to scribe? If so, can you describe what you do differently in class when you are scribe?
• What makes a scribe post worthy of entry into The Scribe Post Hall Of Fame? Specifically, what should be included in the post for it to achieve this recognition?
• Compare the first scribe post you wrote to the most recent one. What, if anything, did you do differently?

I'm going to patch together three different students answers but all their answers are worth reading. They answered here and here.

Manny: "When I write my scribe posts, I try to make it as so my classmates go, "ohh!" and "yeah that's it right on." That is my first priority because I want everyone in the class to do well, "we're all in it together" (at least that's how I feel anyway). During class, if it's my turn to scribe, I feel pressure that if I don't do well in helping my peers I'll let everyone down. So in class, I open both my eyes and ears wider than normal, and my pencil taking notes on just about everything related to the topic."

Corrie: "I think to be able to make a scribe post worthy to be in The Scribe Hall Of Fame, is the content. I think that's no. 1. But you also have to look at it differently. You have to be creative with your scribe. I think you should try to be different, do something that no one has done before. You should try to stick out from the group. To be recognized content and creativity is most important ... well that's what I think."

Teddie: "When comparing my first scribe and my very recent scribe I can see the quality of the scribes improve greatly mostly because of the competitiveness of the other scribers to make the hall of fame."

If you've already looked at the examples I've linked to you'll see the quality of work this pedagogy fosters in students. If not, you may be asking "Why should I do this?"

Having a daily scribe has improved both the student's learning and my teaching -- since I insist that they summarize their learning each day I had certainly better provide the content for them to work with. On my professional blog, A Difference I wrote about the impact of having daily scribes on my students and my teaching. I encourage you to read it. In the meantime consider this: Medical school is often considered one of the most academically demanding educational experiences a student can have, and so it should be. The paradigm in medical school that leads to deep learning is "watch it, do it, teach it." Scribe posts will bring that paradigm into your classroom, regardless of what you teach or how old your students are. As a teacher you know that there is nothing like having to teach something that leads to learning it well. Scribe posts make your students teachers ... with a global audience.

Harnessing the Power of Audience: Feed Windows

Once you have created a class blog where students are publishing what they are learning then we can open Feed Windows to each other's classes. Feed Windows are dynamically updated (via RSS) windows into other class blogs. If you can't regularly publish new content to your blog then as long as someone is publishing on a blog to which you have a feed window open new content is added automatically, all the time. This results in really distributing the work of teaching and learning across the globe.

Every blog has an RSS feed (see the article earlier in "Coming of Age" by John Evans, What Are RSS Feeds And Why Haven't I Heard About It?). Using one of the (free) services outlined below you can add feed windows to the sidebars of your classroom blog(s).

It’s too early to identify all the ramifications, good and bad, of using feed windows, but one thing is clear; there are benefits for both students and teachers. Students benefit by getting access to other students and teachers around the world who are learning the same or similar content. Teachers benefit by keeping the class blog a dynamic environment for students and getting pedagogical inspiration from other teachers. For example, my idea for wiki solution manuals came about because of something I saw happening in another class in the feed window on one of my class blogs.

It may be objected that feed windows lead to information overload. Also, what if objectionable content comes through the feed window? The information is there for students who need it or wish to make use of it. They are not obliged to access it. As regards inappropriate content, while possible, it is highly unlikely to occur as students work to outshine each other in their educational efforts. Also, feed windows are only opened to the classes of blogging teachers; the edublogging community is a safe self-monitoring community. Will mistakes happen? Yes, but they really just provide an educational moment for everyone involved. (see my blog post Safe Blogging Resources under the headings Podcasts and Stories From the Classroom).

These two ideas, Scribe Posts and Feed Windows, lead naturally from one to the other. Using Scribe Posts encourages student creation of outstanding content. Using Feed Windows distributes that teaching and learning across the globe. This provides fertile soil for more creative teaching and learning with web 2.0 tools.

How To Install A Feed Window On Your Blog

At the time of writing (September 2006) I am aware of five different ways you can get a feed window for your blog. All these tools are free of charge although one will give more design choices for a small fee.

These first four sites will generate html code that you just copy and paste into your blog template, the last is entirely automated. You may have to experiment a little until you have the Feed Window placed exactly where you would like it. Keeping it in the side bar makes it always accessible from the front page of the blog.

Feed2JS
http://feed2js.org/
The Grandaddy of them all. Alan Levine really originated the idea of using RSS feeds to redistribute content in the form of del.icio.us links. He not only had the original idea, he created the first tool to make it work. And it's free. This is the tool I use on my professional blog, A Difference, but I also use a little html coding.

Grazr
http://grazr.com/
Grazr is a web 2.0 site that automatically generates the code to produce a Feed Window on your blog. You select an RSS feed and a few formatting parameters with a few clicks of the mouse and the html code is created on the spot. Copy and paste. With Grazr you can actually wrap several feeds into a single Feed Window and graze the content from several classes.

FeedoStyle
http://feedostyle.com/
FeedoStyle is a similar web 2.0 service to Grazr but each feed will have its own window. Also, formatting options are limited unless you upgrade to a paid account. Prices vary from $5.00 US to $15.00 US. The basic service is free.

RSS to Javascript
http://www.rss-to-javascript.com/
This is a completely free service. Click on a few buttons to customize the look of the Feed Window. You can preview how it will look before you click the [Generate JavaScript] button. When you do just copy and paste.

Blogger in Beta
http://beta.blogger.com
Blogger (by Google) has recently updated their software. It's currently in beta but has a host of new features that make it superior to the original service. One of those features is the ability to just paste an RSS feed into a form and Blogger will automatically create a Feed Window for you. Then you can drag it to wherever you want it to appear in the sidebar of your blog. It really doesn't get easier than this. Blogger is a completely free blog hosting service. This is the one that I use with my classes.

Endnote
Question: 5 marks just for writing a blog?!? If I wrote, "I really can't be bothered to blog about this, but I need the 5 marks", would that get me 5 marks?