4 George – Playing in Public

Remember those days when the snow first fell and the streets froze and you just couldn’t wait to get outside and play?



The first snowfall usually happened at night and, if it was early enough in the evening, you got to marvel at the many-colored flashes of tiny crystals fluttering to Earth and the multihued sparkle of snow twinkling in the building drifts.



Or maybe the first snow fell during the day and you inhaled upon seeing big fluffy white pillows sprinkling toward Earth, some melting but some also blanketing the yard or field or grove of spiring trees.

Perhaps it was long ago? Perhaps it was this year? Perhaps you were only a child or you rejoiced into adulthood?

Either way, you know you wanted to play.

Playing in Public

George Couros recently challenged his PLN to sketch people, particularly children, Playing in Public and document the process of sketching in a video.

The first to respond to this challenge (actually her response resulted in the challenge going public) was Malyn Mawby. Her terrific sketch and video set the bar high for future responses.

It also inspired my sketch.



This sketch features children playing in the snow: building snowmen, sliding on the frozen river covering the pavement and throwing snowballs from behind snow forts.

medium: pencil – HB2
time: 2 hours (draft and trace)
digitizing: 6 photos – 6 minutes
editting photos: 6 hours (see below)

The Concept

In the Northern Hemisphere, Winter is approaching and snow is beginning to fall. I found this in stark contrast to Malyn’s sketch of her girls playing on the beach. I also recognized that Malyn lives in Australia where Summer is just about to begin. What an opportunity, I thought, to illustrate that play is an all-year activity!



I was inspired also by the recent first snow that we experienced this season and my desire to build a snowman with my nephew. It will be too cold and the snow too dry to build a snowman when he does visit his uncle. So this sketch expresses a dream as much as anything.

I also recognized that sculpting of sand castles and snowmen and snow forts was similar enough to deepen the parallels between Malyn’s sketch and mine.

The children in my sketch are generic, pulled out of my head. I did not have anyone in mind, nor did I sketch from any photographs. I liked Malyn’s illustration of distance and collage in her sketch and tried to emulate these. However, unlike the children in Malyn’s sketch who are her girls over several years, the children on my sketch are contemporary. I think Malyn’s use of time to sketch her girls is personally nostalgic to her, so I did not want to replicate that effect and affect.

My decision to design the sketch as I did was strongly influenced by my own nostalgia: my memories of building snowmen and forts, of throwing snowballs and of sliding down an icy road, all in the name of play and fun. I remember also making snow angels, skiing cross-country and downhill, tobogganing, building quinzees, playing tag and hockey, and snowshoeing, but the sketch had only so much room.

Play is engaging in an activity to gain a state of flow. It does not necessarily need to be outside nor involve many people. Sketching, like the sketches Malyn and I produced, are also play, as is engaging in some work, such as wood carving or even math problems.

I write, paint and learn for fun. Everyone does something different.

The Process

The Sketch

I drew my sketch in three drafts. The first draft was just a small ghostly outline to develop my concept and place and frame subjects. My second draft was a full-page (8.5″ by 11″) sketch that probably was the better draft. It was more freehand and wispy, much like Malyn’s; however, I sketched it on a scrap sheet and the type on the opposite side of the sheet was clearly visible. I inked in the second draft and traced it systematically to produce the final sketch.

I am a mediocre drawer at the best of times and often rely on paint (oils) to bury my sketchy drawings. This time I did not have that luxury and, in Malyn’s words, my sketch is naive. (Yeah, there really is such a style; I was astonished when I learned this.)

Like Malyn, I have trouble with faces and hands. In my case, mitts served to bury hands. But my faces were a problem. I wanted to show enjoyment, so I needed to draw faces.



Yet, all the noses I sketched are gigantic. Additionally, the faces are masculine. Look closely at the girl sliding on the road. If she didn’t have hair, she would be another boy in a male dominated sketch! Insincere political correctness aside, I wanted to show girls and boys playing together, so I wanted some girls. That slider was a nightmare to sketch. It took some heavy editting just to imply she was indeed a girl and not some guy with a strange toque or wig on his head. Notice, no one else on the sketch has hair!

So sketching was definitely a fun and often comic challenge.

The Photographs

I took pictures of the third draft of the sketch at various intervals during its creation. A tripod and frame to place the sketch in would have helped with squaring, leveling and maintaining the same height for each photo. The photos I took came out with my sketch crooked and even trapezoidal. I ended up editting each weird product of my photography with Windows Paint, even though it took hours to do so.

In hindsight, I could have taken one photograph of the final sketch and deleted objects as I saved the editted sketch. This would have made an even smoother video, but it rang of cheating to me. I was rather enjoying sketching, photographing, sketching and repeating the process.

The Video

Below is the final video of my sketch. Enjoy.


I used Windows Movie Maker to create the video. The audio was clipped from Play in the Snow, a 1945 education film in the public domain and presented by Encyclopedia Britannica Films on Prelinger Archives. I used RealPlayer to trim and convert the film’s MP4 video into MP3 audio clips, so I could use these in my video.

The sound is a bit crude and out of step, but it carries the spirit of kids enjoying the Winter season.

Troubles with George

In his challenge, George forgot to mention that he wanted a silent video. So I spent hours adding audio to my video, only to get a tweet that silence works best. Fine, I can do that. George then also asked for a video in MP4 or AVI format. Okay, I’ll see what I can do.

It was not as obvious as it looked!

I was only following Malyn’s lead.

How do I convert RV and WMV into MP4 or AVI on my machine? I searched RealPlayer. I searched Windows Media Player. I searched Windows Movie Maker. Hmm! This was a problem.

I finally did discover how to save my original Movie Maker project as an AVI. The option was not as obvious as you might think. I also removed all the sound from the project. So, this is easy. Save. Check and test to make sure the new format took.

213 MB!

Are you kidding me? That is 40 times larger than the RV and WMV versions with sound. This is six photos stitched together in a video folks. What went into that 213 MBs?

Okay. Upload the silent video into George’s dropito.me box to go with the RV and WMV versions, with audio, that I already uploaded.

Forty two minutes later, the silent video is finally uploaded!

Watermark? What watermark?

I replay the silent video on my computer. No watermark! Perhaps it is a dropito.me thing?

So, I upload the 213 MB video into my Teaching Resources webspace. Another 42 minutes later, the silent video is ready again.

It works!

Troubles with George!

Reflecting on Fun

This was a fun project, even the part regarding the enormous silent video. Playing is engaging in any activity that leads to a state of flow. In this case, humour also played a big part. George can ask me to create another video for him any time.


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.



On Videos

It is July 22 and I was hoping to upload my first video, a humourous take on my last post, and add it to that post by today. I have been itching to create and publish a video for a long time. I’ll spare you the excuses and just admit that I missed my deadline.

Well, actually, I didn’t.

My first video, which I created in 2003, is now dysfunctional. It has fallen to the harsh reality of technology upgrading. What used to run quite smoothly, had a catchy tune, Whispering Bells from The Del-Vikings, and had two video clips, Two Spheres of Earth and Whispering Waters, that seamlessly fit that tune, has now a title very aptly chosen: Haunting Catastrophe. 😀

The video was meant as a lab assignment, the audience of which was the lab instructor and me, so I did not worry about copyright. I did credit the guilty, including myself, but I had no need to ask for permission for any of the clips.

If you followed me on Twitter back in February, you will likely remember my campaign to get permission from A&E to clip a Mr. Bean video for my Noticing the World post. I never did get permission, but Mr. Bean (Rowan Atkinson?) was generous enough to clip and upload the video for me exactly as I asked. (Thank you again.) I linked to that clip since I still did not have permission to embed it.

Still, I thought you might like to laugh at my first video. So I uploaded it to my YouTube channel despite the copyright infringements in it.



Feel free to laugh at the end credits. 😛

And I will get back to that video I am working on for my last post.

Update: YouTube seems to have updated the video for me, so the credits work fine. Nice, and yet I leave you nothing to laugh at as I intended.

Videos like images serve many purposes in posts. They convey a lot of information in a little space. And they break up text into eye-appealing pieces.

If a picture is worth a thousand words, a video is worth a thousand questions. If that sounds familiar, I said it a few times on Twitter. A video shows action and suggests change, continuity and flow. It entertains and informs and like text reveals more about the creator than the created. In educational posts, it opens inquiry and evokes emotion.

Videos teach, regardless of their content.

Video Stats


Duration: 5 sec
Effects: fade in from black, two-line fade in and out, fade out to black
Transition: none

Clip 1

Duration: 15.13 sec
Effects: none
Transition: diamond out into clip 2 (duration / overlap: 1.25 sec)
Name: Two Spheres of Earth (.mpg)
Authors: Tony Phillips and Patrick Barry
Created: April 22, 2002
Source: Space Science

Clip 2

Duration: 25 sec
Effects: audio silenced
Transition: spin into credits (duration / overlap: 1.25 sec)
Name: Whispering Waters (.mpg)
Authors: Ron Roy and Frank Josephs
Created: unknown
Source: Mood Tapes


Duration: 4.58 sec
Effects: scroll, up stacked, fade out to black
Transition: none

Total duration

47.20 sec (clip-by-clip duration: 49.61 sec)

Audio Clip

Name: Whispering Bells
Band: The Del-Vikings
Created: 1956
Source: Stand By Me Original Motion Picture Soundtrack, Track 4, Atlantic Recording Corporation 1986, CD 81677

Pi Day: Part Tau

There has been increasing buzz about Pi and Pi Day lately, probably because July 22 — 22/7 — is approaching. And though any web search can find this buzz, I would like to add a comment about Tau Day (June 28), which is adding noise to the excitement.

“Ya! Do tip: Laud Tau, at dual Pi, today!” “I prefer Pi”



Tau, having been recently replaced by phi as the symbol of the Golden Ratio, is a proposed symbol for the value 2*Pi, lauded (to borrow from the palindrome above) by those who think 2*Pi is a better measure in all ways than Pi.

This claim, of course, has created a heated but sometimes hysterical discussion, and post and video “war”, between two extreme camps: the Pi’s and the Tau’s. Add to this a third camp, those who argue for Eta (Pi/2 or Tau/4) as the standard, and a fourth, who promote Pi/4 (Tau/8) instead, and we have a mathematical event to behold.




Of course, none of this really has serious implications, since we all know that Pi/3 or Tau/6 ¹, the sextant, with its relationship to the equilateral triangle, radian, Babylonian sexagesimal system, Earth year and rational cosine value, is the real fundamental unit of the circle.

It seems we are confused.

This of course is all in good fun. Yet tell that to Tau Beta Pi and Tau Alpha Pi, the Engineering and Engineering Technology Honor Societies, whose society names are at risk at both ends.



It’s happened before

Nor is this the first time a math convention has been questioned. In fact, it is not even the first time a circular measure has been questioned.

Before there was trigonometry (the study of measures of closed three-kneed figures or triangles), there was circle geometry (the study, which we still have — but lacking the now analytic trigonometric part, of regular closed no-kneed figures or circles). In circle geometry, the chord is king and emphasis is on the geometry and measurement of the circle, line segments and angles. Everything was working really well.

Then came sine!



Sine, of course, is half a chord, chord/2. It seems weird to us now, but at one time sine was the oddity trying to replace the convention. Yet, when it did become convention, a new field of math was born.

In a history shamefully oversimplified, circle geometry split into two fields and, for the sine portion, analysis, ratios, angles and triangles became the emphasis, so leading to the title of trigonometry. Circle geometry continues to deal with geometry and measurement. And the chord is the usurp outsider.

And history we witness

So we have Tau (whole), and Pi (half), and Eta (quadrant), and Pi/4 (octant), and Pi/3 (sextant). I wonder what history will come of this.

Importance: A rose in the classroom

Does it really matter what constant we use as the base unit for circle measurement? They are just names. Some formulae will work better in some situations than others, and this will change with situation.

How we choose to deliver the concepts to students is far more important than what we call them. Truth be told, all systems should be taught interconnectedly with no mention of which might be the opinionated best.

The key is engagement and problem solving. Students need to understand how to use the math, why it works, where it is used and how it is used. It would benefit them if they learn their own formulae, and we help them “conventionalize” these to fit what other mathematicians do and say.

Changing of the conventional Pi to Tau, or Eta, or either of the other measures, might change the nature of circle and trigonometric math in ways we can not predict at present, but that will come in the future. Today we have these five fundamental units, which are all arbitrary, math-founded and related. Who is to say which is best?

By any other name, is a rose not still a rose?



More resources

Want more? Visit Benjamin Vitale’s June 28th Pi is wrong! Here comes Tau Day, watch Vi Hart’s Pi is (still) wrong, and read Bob Palais’s original π is wrong! which started the Tau, then two-pi, movement.

Then read Mike’s response to The Pi Manifesto, from the creator of Spiked Math Comics, then the continued debate on On Pi Day we eat pie. On Tau Day we eat Taoists? and ‘Tau day’ marked by opponents of maths constant pi, including its comments.

Given that we are rather gossipy creatures, most of the posts, discussions and video have titles that attack poor Pi and its Day, or Days (March 14 or July 22). But a few out there attack Tau as well. The Eta’s, Quarter-Pi’s and Equilateral’s just cling where they might be heard. Sounds like a school yard, doesn’t it?

This post actually started as an update comment to my Math Challenge: Pi Day, but the comment morphed into a post of its own, so I decided to make it so. If you are interested, please visit my Pi Day math challenge post.


¹ Given its Babylonian pedigree, perhaps we should call Pi/3 Sedis, which is six in Assyrian.