Inspiration Against a Lost Generation


This video serves two purposes. First, it is a creative way to communicate a profound and inspiring message for everyone, by juxtaposing opposing tones via a literary twist — a winding and unwinding technique common to folktales. Second, it is a reminder to me, and perhaps to many of you, that this is what my generation felt and talked about when we were in high school and graduating. I find the echo of my thoughts juxtaposed against this video nearly a quarter of a century later rather interesting.

There are so many parallels, some of which we recognize right away, some of which we forget until we are reminded.

For some reason, this video reminded me of my generation’s movement to curb pollution and yet the nearly simultaneous increase in vehicle turn-over and layers of packaging around otherwise small items. Today, our kids and students are still moving to curb pollution, though with a narrower scope — less, if any, emphasis on all the forms of pollution, including light, noise and odor pollution, and more emphasis on pollution that perpetuates and aggravates global warming. There is much happening in the World that they have little notion and control of, as was true for us. However, as we became more pollution, waste and recycling conscious and active, I wonder what their generation will accomplish.

What parallels do you see between the priorities and ideas of your students and those you had when you were their age?


Engaging Kids: A Little Classroom Humour



There has been a recent rash of puns spreading around one of the schools I sub at. It has infected kids at all grade levels from 5 to 12. Of course, being called in to teach occasionally, I happened to walk into this contagious disease with no warning and no defence last Thursday and Friday.

My kids tried to infect me twice with puns on Thursday. Unfortunately, I was rather vaporous on that day, so I did not catch on to either attack and thwarted the jokes.

The Mistaken Challenge

The first attack came from my Science 9 students. I can not remember the pun and ruined the joke anyway. The students grudgingly revealed what they were trying to get me to say (without getting in trouble). I remember being glad I didn’t. My guess now is that the pun must have been inappropriate to school anyway.

(At this point, I should confess that I am a stickler when it comes to swearing or inappropriate topics from my kids. This deters my kids for about 15 seconds after I warn them not to engage in such behaviour. Then the fun begins: trying to find ways to tease Mr. Urban. This particular pun was their latest effort.)

Still, my kids were unaware that I hadn’t caught on. I am sure they have taken my sidestepping of the pun as a challenge, so I expect more cunning attempts to get me to break one of my own rules.

These kids just crack me up. They are so eager and clever. And for the most part, when I ask them to, they willingly engage in the learning activity at hand.

There is always room to play and enjoy class. My kids like joking with me; I am easy enough to let them bait me, yet usually wise enough to get out of their traps.



The Unintended Lesson

The second attack came from my Grade 12 math students. My Grade 12s were a little more cautious with their pun, choosing one that was barely offensive.

But, again, I did not catch on. And how spectacular the result.

I have watched these kids grow up from Grade 7 and am absolutely fascinated at how mature and confident they have become. I can’t tell you how awed and full of pride of them I am. So, yes, I was targeted again.

The pun was simple. My kids asked me “what is that under there?” and I was supposed to reply “under where?”

I did not.

Being obtuse


Really, it never occurred to me to even ask that. Over there were cabinets and shelves sitting without gap on the floor and a well raised table clearly with nothing under it.

I was supervising a probability quiz and wrote it myself along with them. (Probability, permutation and combination just confuse me. I can not make heads nor tails out of them. The quiz had a few sporting coin questions in it by the way.)

So I was thinking mathematically, systematically and about test question quality. I ended up pitching against the ambiguity of vague questions with my kids, particularly the one they were asking me, and they in turn kept trying rather desperately to get me to ask that magical pun-question. Dialogues of the obtuse are so amusing.

It all ended up in laughter and teacher-student bonding that would never have happened had I clued into the pun at any time.

One boy grinned that the joke turned out better than my kids had planned. A girl told me that I really got her thinking about clarity and definitions. Everyone, including me, ended the day with renewed energy and a smile.

Yeah, I was thick on Thursday. I normally take questions and comments at face value. I rarely look for ways to make this or that perverse by some lateral interpretation. I am eager to help.

And I love the way I am, and my kids. They can fool me any time they want, so long of course that doing so does not interfere with their learning activity.

I feel much closer today to these two classes of students, particularly the Grade 12s, as a result of this jocularity.

A little humour in the classroom is engaging and builds strong bonds. I am ecstatic that I subbed these kids on Thursday. A lot was won.



Math Begins With an Answer?

We all hear it; we all say it. Students want the answers; teachers want the learning. But now, it seems students might also begin with, and not just want, the answer, or maybe they ignore everything but the answer, despite our effort to encourage and facilitate learning.

I am in the middle of reading Nat Banting‘s post Measuring Roots. He makes one statement in this post that I wish to address (indeed, my response below is cross-posted as a comment on his post).

I found this statement so profound, I had to stop reading the post and respond to it.

Nat’s statement is here:

For students, no matter how young, math begins with an answer.

Here is my response:

I stopped reading this post as soon as I read the point that, for students, math begins with an answer. (Don’t worry, I plan to read the rest of the post. But I needed to respond to this; it is so mind-blowing.)

I learned under Dr. David Pimm of Open University (UK) and the University of Alberta (CAN) during my Diploma in Math Education studies. He argues that math begins with a question; in fact, it does not exist until a question is asked. All the demonstrating and lecturing about math in the world does not involve math until a mathematical question is asked.

This discrepancy is very revealing. It tells us what math is and what math education is. Most students learn to expect math questions and problems to be short, quick, to the point, solvable and structured around “clean” answers (often related in some way to integer components). They anticipate the answers before they anticipate the questions. I am not sure if they even consider the math, and if they consider the questions mathematical, or mathematically.

I wonder what they are really learning? Is it math? What to them is math? Is this why so many students are so disconnected with math and why they are proud to have failed it and ashamed to have aced it? After all, from their perspective, if answers they anticipate before math, what have they aced?

I think we have done students a great disservice if they ace math in elementary, secondary and even tertiary school without ever actually learning that math is all about the question, the quest and struggle to tackle it and the discovery of pattern that possibly limits to (an) answer(s). They completely miss the point and the empowering strength of math process and pattern. And in the end they really have nothing to use in their lives beyond the “math” lesson.

So, why do they need to learn this? That question makes so much sense now.

I shall now return to your post.

Further Reflection

It is easy to lose sight of our students’ understanding of what we teach. Sure, we anticipate their individual problems and our scaffolding of these problems. We tailor our lessons to help each student. We ask leading questions or offer leading hints to open the door for them to learn. But then we learn that they have a completely different fundamental take on what we are teaching (and how) and what they are learning (and how). Sometimes these takes are so fundamental in fact that we can not even conceive them, never mind address them.

And this is where professionally developing with our PLNs really helps us to grow, to learn, to better ourselves.

Sometimes what we think makes sense only makes sense because we think about it within a certain frame and from a certain premise. David Hewitt would consider this generated, rather than necessary, knowledge. Until the moment I read Nat’s statement, I thought that students shared the same fundamental sense I did; that is, I thought this sense was necessary and common. They might want the answer and to skip the learning, but they start learning when a question is considered and asked, regardless of who asks it and whether it is internal or external. Thinking, in short, starts with a question.

All it takes is one statement, simple to others, even the author, to change our view of what we are doing forever.

Are we teaching our kids that thinking starts with an answer? That an answer even always exists? Do our kids think backward from us — speculating an answer then working through, rather than on, the question and its “solution” until they match their guess or verify no match? Are we teaching them the wrong way, literally?

The way we teach (think) now, we solve problems. Do our students anticipate solutions and then test them, like a computer batch tests scenarios or a player navigates a game? These are very different ways of learning, teaching and thinking. Much skill and strategy is lost by exchanging deliberate problem consideration and solving or playing for rapid testing of many outcome and solution (scenario) possibilities. In a very real sense, problem solving is deductive, while answer testing is inductive. New skills and strategies are needed to solve problems this way. And new methods of teaching need to be added to our portfolios and lessons.

What do you think? Do students start learning by considering an answer or a question first? Are we teaching them the “right” way? Should we teach both directions, or are their still more directions, more senses, we need to consider?

Any thoughts on Nat’s claim and its implications?

I am seriously considering that there is some truth in his statement. Perhaps kids approach learning inductively and deductively. Perhaps some kids approach learning one way under certain circumstances, the other under others, and different kids apply different strategies or strategy mixes differently.

Either way, is there a premise change here?

Three Things I Learned From My Nephew



This week my nephew is on Spring break and visiting his Uncle Shawn. It is a busy week to say the least. During this week so far, we have engaged in several activities, three of which I thought I would share.

A frog, a snail and a cricket



One can only play Go Fish so many times before one wants to throttle one’s nephew.

Same for Memory.

But what if one plays Go Fish with Memory cards? How does that change the game?

The idea to play Go Fish with Memory cards was my nephew’s.

Go Fish with no pip cards is different. Uncle Shawn doesn’t know the names of the cast of Diego and Dora characters. He doesn’t even know the difference between a cartoon raccoon and a cartoon fox. (That’s funny, Uncle Shawn. Me: It is. I swear, folks, the fox has raccoon eyes!)



The first few games of Memory Go Fish with a cast of Diego and Dora character face cards were rather fun, and funny. One has to describe the card one is looking at without showing one’s opponent. And the opponent has to match the description to a card that might be in his hand. It’s like Picture Charades.

Then one plays Go Fish.

This game was fun for both uncle and nephew. But the lesson here is that kids can create rich, engaging learning opportunities on their own. Sometimes we teachers forget this.

By the way, the title of this section, A frog, a snail and a cricket, refers to the description of the face of one of the Memory cards. It was the most complicated card in the Memory deck, but the easiest to describe. Others are Girl Holding Flowers and Girls With Blue Dress and Book . Try to play Go Fish while describing cards like that.

Uncle Shawn is magic

So what does one do with a bundle of energy and curiosity after tiring of playing Memory Go Fish?

One calms him with magic!

Nothing like a Mobius Strip to entertain a six year old.

So, the second lesson I learned from my nephew: astound him and gain thirty minutes to an hour worth of focused exploration.



The trick, however, is to keep astounding him. If he wants more, you are doing well.

My nephew and I constructed the Mobius Strip together; I cut the pieces, he taped them together end to end. I twisted the subsequent strip, making sure he understood what I was doing; I marked the ends of the strip on the same side and held the marks together while he taped the final ends closing the loop.

Each time he asked what were we doing (now), I answered that he would see. Of course, if one is going to make such a promise, one needs to deliver.

Next, I asked questions. Will we get two strips if I cut the original in half? (Amazingly, the obvious answer, and his, is incorrect.) If I cut the new strip in half, will we get one, two or more strips? (Again, the logical answer is incorrect.) How many strips will we get if I cut this brand new original strip in three pieces (thirds)? (Don’t you hate “I don’t know” answers? Force him to give an answer; provide choices: one, two, three or more?)



Then get him coloring. When cut in thirds, the Mobius strip produces another Mobius strip half the arc length of the original and a two-sided strip twice the arc length of the original strip. Mark one side of each strip with one color and the opposite at the same spot with another color. Then let him go.

Concepts of number of sides and number of edges naturally evolve, making the entire exercise rich with play and learning.

Every subject has its Mobius Strips, things that draw the students into play and learning. One has to identify these “strips” and sell them. Delivery is the key.

A puzzle: Sophisticated abstract

Finally, I offer the following object that my nephew constructed yesterday. Think of it as a riddle.



What is it? When my nephew told me what it was, I was flabbergasted. I promise I will reveal what it is in a comment, but I thought I might get any guesses you might have beforehand.

I will give you a few clues.

  • The object is an abstraction of an abstract concept.
  • The concept is one I am interested in.
  • The object contains several recognizable real concrete components that are way out of scale relative to each other.

This is the third lesson my nephew taught me during his visit this Spring break. Kids can think and represent abstract concepts abstractly. Or is this concretely? We teachers need to allow our students to think and communicate in many ways. When we do, they can surprise us with their higher levels of understanding and communication.

And a final picture

What do you think? Another avatar for Stefras?



I would like to thank my nephew for inspiring this post.