Thursday, March 28, 2013

On Seeing Sir Ken

not last night
My university brought Sir Ken Robinson to campus last night, as a cap to our community reading project and an invited lecture series. See: #SirKenGVSU for the twitter action; university coverage with audio; Dave's reflection on a math story he told.

Beforehand I was wondering how much would be new? I love his two TED talks and the RSA animation and overshare them with students, but you do notice recurring ideas. Appropriately. I also was wondering if he was tall - as he looks imposing in his TED videos. (He's not just not tall, it turns out.)

He's charming, funny and a natural performer. Really funny, like Ricky Gervais as an academic. Inspiring, too, and if you get a chance to see him, take it. He has new PBS special coming up, for his new book, and I will be watching.  He is a self-promoter, and has a robust ego, probably appropriately.

He incorporated his traditional messages:
  • creativity is important
  • all people are inherently creative
  • disbelieve the big three myths about creativity
    • creative people are the exception
    • creativity is only valid or valuable in the arts
    • your creativity is fixed
  • current education crushes creativity, or at least discourages it
  • people who find their element, the connection between their passion and their creativity,  are happier, healthier, more productive and have greater impact.
  • we cannot plan our career, as we have no idea what's coming
His new push was to create a culture of innovation. He seems to see stages of development of creativity:
He applied this mostly to education, talking about Finland and the Blue School (a school designed by the Blue Man Group), and a USC art history grad who went on to become an art evaluator for an auction house, traveling the world.

His upcoming book answers my disappointment with The Element. It's Finding Your Element on how to develop that connection. He also mentioned a major rewrite for the new edition of Out of Our Minds.

My struggles are that his stories, like the art school grad, Blue Men, Johnny Ivo, Nobel winning chemists, etc., confirm the myth of exceptionalism. They don't remind us of the students in our classrooms that we can't get to try. They also tend to wind up with 'and now they're famous and rich.' That is not going to happen for everyone. It can not. Why does his vision look like for me? For that student? (You know the one.) I was glad to hear the Blue Man story, too, because so many of his stories are of the individual, while much of what I know about creativity relies on collaboration.

I'm also left wondering why we can't convince our politicians and decision-makers of the value of this approach to education. Someone asked a question about that, sort of, and Sir Ken joked a response that boiled down to we don't know how. 

Yet, for a couple of hours last night at least, I felt like this is possible. And his encouragement for teachers who are trying to make this difference is very valuable. I was reminded of and consoled by the many teachers I know locally and through the mathtwitterblogosphere who are making these changes happen for real.

¡Viva la revolución!

Wednesday, March 27, 2013

Number Addict

I have an addictive personality, so why would I even start a game called this?

Number Addict is a free iOS or Android game. (Also has a Facebook page. The sequel is a 99¢ app.[App store link]) It's a Tetrisish puzzle, where you are trying to amass groups of equal numbers to score them. Two nice wrinkles: it takes a group of at least as many as the number to score them, and you can combine adjacent numbers by addition up to the max number tile available. (Which increases as you level up.) You can see upcoming tiles, so this and the adding makes for many strategic decisions. I think it's good for reasoning as well as mental compositon of whole numbers.

The scoring is completely non-obvious. Scores increase both for number scored and how many in a group. This post is really just about sharing my data for a possible lesson.

In an effort to continue to seek the most boring possible video, here is a screen capture of me playing the game. I used and the Air Server app to make the video. 

(It has a fun song 'Pocket Calculator' that I muted for the video. Most Boring Ever.)

But, I spent some time (too much) gathering screen caps of scores... (google pdf)

So I've even collected the data for Act 2... (google doc)

That's editable if you gather more data...

Some questions are obvious. What are the missing data points? What will the level 9 scores be like? (I've never gotten there!) What's the pattern to the increase in scores? Is it determinable or were the programmers just having fun?

If you give it a try, share what you find in the comments!

EDIT: collected a bit more data... great patterns. If you want it to verify student work, here's the spreadsheet, and here's the evidence.

Tuesday, March 26, 2013

Cat Chase

Play the game!

I've been filling up the blog with my class notes from Learning Creative Learning, but an assignment from there really turned into a fun project.

In Week 6 we were supposed to remix Scratch projects from other users. I - of course - looked for math games. First I found 15 Seconds by jOHEEN_c which was an integer game. I wanted more leveling, so found Maze Levels 1-5 by Cats_Are_Awesome. I didn't wind up using their code, but I did learn a lot about Scratch by working through their programs.

I wanted the levels because increasing challenge is key to engagement. I have about 10 screens of increase, after which it levels out. The movement is a little challenging for me as an old guy: the cat follows the mouse instead of being controlled directly. The game forces you to add and subtract positive and negative, but gives you choices on how to get the target. I did add a restart button for if you got stuck that lets you proceed without having to play all the levels over. Is it a problem that the game never really forces an end by becoming impossible?

The game is on the Scratch website, where you can play it or download the code. (Scratch is free to download, of course.) All Scratch submissions are cc 3.0, which is very nice. (Direct link to video, made with
(You can embed the Scratch program directly in a webpage, but it starts immediately, which can be aggravating.)  I would be very interested in your feedback on the game, and delighted if you or your students would be interested in remixing it.

Music credit: Upbeat Ukelele Song by Akashic Records, via Jamendo.

Thursday, March 14, 2013

Turn Me Right Round

What makes for these mathematical mini-obsessions?

Whenever I put something up on, I make sure that I pose questions on
at least 10 posts from other people. (I also never skip. [So will I ever have questioned everything? #anyqs] Though for some it can be hard to find mathematical questions. [Orange.]) On a recent trip I saw Alex Shum's cool revolving door picture.

It reminded me of the problems where you're trying to take a sofa around a corner. (Which reminded me of my very first favorite screensaver, inspired by Douglas Adams, of trying to fit a sofa down a staircase.) Whatever the reason, I immediately wanted to make a GeoGebra sketch.

I made a first pass. That got me wondering how big are those openings? In particular, would a revolving door ever have and opening straight through like the one in the diagram to the left? (Seems to defeat the purpose of a revolving door.)

What are the standards for revolving doors? Thanks to Google and the International Revolving Door Company, I now know more than I ever knew I wanted to know.

In particular:

So much to wonder about these. I love the idea of describing circles as circumscribing a rectangle and it makes perfect sense for construction. But now I want to know about this data. What kind of function is it? Does it make it so the opening is always more narrow the one sector of the door? Is the angle of the opening from the center constant? How do you choose between a 3 wing and 4 wing?

First pass on the data was pretty curious.
Good for making the sketch, but weird. Why would the three wing doors have narrower openings?

GeoGebra sketch for
download or mobile applet
I made a weird little function to give the door openings, 2*radius (0.475 + 0.21 (doors - 3)), so that the ratio is .475 for 3 wings, .685 for four wings.

I liked the opportunity for modeling that this turned into, and it's also a good problem to show where modeling either supports calculation or is more efficient than calculations. Constructing the model in GeoGebra required data fitting, and some algebra to find the appropriate boundaries for the geometric objects.

And it helped me understand why 3 wing doors have narrower opening than 4 wing doors.

Wednesday, March 13, 2013

Open Learning

Creative Learning - Week 5

Video: Audrey Watters, Mako Hill (Moderator: Philipp Schmidt). Opened discussing peoples teaching/learning videos which they did by Hangout. People noted the courage needed to document publicly your learning or teaching. Then on to Open Learning.  Ultimately there was acknowledgement that these methods might not be for all, but they're important.

Audrey started to think about it because of blogging and the way she was doing professional learning. She blogs to learn, but it's also about how she licenses her work. It requires being willing to put out half-baked ideas and to then collaborate on them. Worries that so much of online learning is replicating traditional lecture. (Hmm.)  Mako does open programming on a number of big projects. He sums up his unlearning experiences in a post at his site.

They discuss how blogging is similar to open programming. We need a way to fork with attribution. Audrey is even trying putting work up on github. Mako notes how a big part of the open programming idea is that the user owns the work. I think similar to the idea of student-centered learning. Both this and the Learning Web article talk about the benefits of systems being hackable. If education is not a blackbox, then we can adjust and understand what's going on. (Previously in the course this was a point about technology for learning, that if it's inscrutable there's no learning, and if it's hackable it leads to creation.)

At 54 min in response to a question about the classroom application, Audrey makes a strong statement of collaboration as the first step towards openness. Mako echoes, encouraging students to document learning not just for themselves but in an open space where others can engage. Actually, let's clip that.

Reading: "Minds on Fire: Open Education, the Long Tail, and Learning 2.0" (pdf) by John Seely Brown and Richard P. Adler.; Ivan Illich: Deschooling Society (Chapter 6: Learning Webs); Eric Steven Raymond, The Cathedral and the Bazaar a essay on the development of fetchmail for Linux. (links are all pdf)

Minds on Fire: an advocacy piece pushing for online, social learning. Nothing constructive, I think, but pretty descriptive of the hopes of the backers of this. I liked the pictures.

Learning Webs: "In school registered students submit to certified teachers in order to obtain certificates of their own; both are frustrated and both blame insufficient resources--money, time, or buildings--for their mutual frustration." The article gets into the difference between schooling and learning. It is literally radical and often rambling, which might be off-putting to some readers, but I found it thought provoking. On people's desire to have Aristotle for their Alexander: "The person who can both inspire students and demonstrate a technique is so rare, and so hard to recognize, that even princelings more often get a sophist than a true philosopher." Illich is advocating liberation pedagogy.

Cathedral and the Bazaar: interesting as an analogy for curriculum development. This is what I would like to see; I think it's what tends to happen with Dan Meyer's projects/movements. What does debugging mean? In the midst of writing this, Michael Pershan led a Global Math session to fix his broken Complex Numbers unit. He's put a lot of work into where it is now, but 20-30 teachers put in a good hour to discuss and revise. Great experience. In the video debugging is contracted with the 'you learned it or you didn't' vision of education.

Recommendation: watch the video, skip the parts irrelevant to you. If you're ramble and revolution tolerant, read the Learning Webs article.

AssignmentTeach & Learn = Ask & Answer
1) Go to and choose a site that you find interesting
2) Post (at least) one question and answer someone else’s question (at least one)
3) Reflect: What aspects of the experience contribute to a sense of a learning community? What aspects limit a sense of community?
Learning match (extra activity): Offer to teach something & sign-up to learn something from someone else - Post it here

I'm new to Stack Exchange, but there is a large Mathematics section with 115,000 questions. The questions on the front page were math major or grad student level questions, with some research level questions. Fascinating. I chose to answer a question about mathematically related online games. There was some frustration with posting, getting used to the editor, etc. But not too bad. Here's the question and answer. They wouldn't let me put more than 2 links, so I put them into a Tumblr post

Harder to think about what I would ask. I wound up asking about those Escher spirals I never finished (Tumblr posts one and two) and my secondary sabbatical project, a common core sharing framework. The reputation bit reminds me of Cory Doctorow's Down and Out in the Magic Kingdom... "them that's got shall get, them that's not shall lose."

It's an interesting site, and I'd love to hear from people who like it how they like it. How does it compare to Quora for example? It feels more focused and less social, but that's an initial impression. (I'm not a big Quora user, either, though.)

Monday, March 11, 2013

Pi Day Prep - a #Mathchat

These are some of the resources and topics that came up in today's #mathchat redux on the approaching Pi Day. More than a couple neat things.

Mathchat is a twice weekly twitter discussion with hashtag #mathchat organized by Colin Graham, and moderated by him or Shawn Urban. Also good for finding math resources anytime of the day or night.

Discussion Points
  • @ColinTGraham The materials I developed for my teacher training certificate were based on exploring π, so I have a kind of 'vested interest'!
    • @ColinTGraham #mathchat The main way I started was with Yr9/10 (13/14 yos) using circles with inscribed and circumscribe polygons...
    • The curricular content required measuring and dealing with perimeters, so it became approximations to circumference...
    • With one class, we had tin cans, glasses, mugs, etc and pieces of string which we wound round the objects and measured
  • Joe DiNoto ‏@mathteacher1729 #mathchat -- engaging activities: Do Buffon's needle problem live? Write a script to do it for you? [Extra link: Buffon's Needle]
  • Kara Fromke ‏@karafromke #mathchat here's a discussion starter on pi day: The Time Indiana Tried to Change Pi to 3.2
  • Earl Samuelson ‏@earlsamuelson @ColinTGraham I showed my Grade 10's an animation I made for estimating pi (Archimedes). They liked it; referenced it again today #mathchat
    • @earlsamuelson Screenr - SamuelsonMath31: Estimation of Pi (Archimedes) 
  • @ColinTGraham Or what it is too! RT @mathhombre: it does amaze me as much as we talk about it, as well known as it is, how few know why it is.
  • @ColinTGraham Another interesting discussion I got into with my 15yos, many moons ago, was are more irrational than rational numbers
    • @mathhombre Got discussing with my kids irrational vs rational. They thought maybe every irrational number had a 'name' (pi, phi, etc) #mathchat
    • @mathhombre Now how many transcendental numbers are there... that's a pi day discussion! #mathchat
    • Maths4ukplc ‏@Maths4ukplc @mathhombre @pickover 15 top transcendental numbers which pi probably number 1 closely followed by e. … #mathchat
  • @suburbanlion @ColinTGraham #mathchat I remember a programming class where we used Monte Carlo method to approximate pi/4. I was amazed at accuracy!
  • @ColinTGraham Just in case you didn't know... Tau Day | No, really, pi is wrong: The Tau Manifesto by Michael Hartl  #mathchat
Serious Resources
Not so serious Resources 
  • Ryan R Ruff ‏@suburbanlion . @TCCva is having a #piday pie contest. Students/staff can bring in pies & winners will be picked for best tasting/looking.  
    • @ColinTGraham #mathchat @suburbanlion @TCCva So if someone brings in a square pie, what then? We need to get away from the "pun" sometimes, don't we? 
    • @suburbanlion @ColinTGraham @TCCva I suppose if some pies are squared, that's in the area of good puns ;-)
  • Neil Langevin ‏@neillangevin A Kate Bush song for Pi day … Lyrics here … #lethsd #mathchat
  •  @mathhombre #mathchat Anybody bring up TJ Zmina's classic (mp3)  National Pi Day (Lehrer tune, hence great)

You can always try searching #piday, too.

Have fun, and derive responsibly.

Thursday, March 7, 2013

Powerful Ideas

Creative Learning - Week 4

Video Notes: Panelists Alan Kay and Brian Silverman. Discussing the nature and implication of powerful ideas. Trying to get at the so what. The idea isn't to assemble a list of powerful ideas, then we teach that. The idea is... we're not sure.  Bruner's advice on curriculum: if you don't know what to do, implement Piaget's stages. In other words, create an opportunity for tinkering. But tinkering is not inherenty valuable. When computers were first on the scene, teachers were happy to see students tinkering. But they weren't doing anything valuable because they weren't playing around with powerful ideas. Maybe tinkering should be "design process with materials in hand"( contrasted with engineering process of plan then assemble).They seemed to feel like there is some tension between story and tinkering, which was mystifying. On the whole, chock full of academic hemming, hawing, citation and, hence, not worth your time.

Reading: the star of the reading again was Papert. His article on the Pedagogy of Powerful Ideas. One paragraph: "Or consider the cognitivist who says: Michael will have a better relationship with fractions if he understands the concepts behind them. This might be so if he could really understand how the invention of fractions was as awesome as the invention of the mousetrap and how the intellectual methods that were used to invent fractions could be used to make new inventions of his own. But the cognitivists are not trying to recreate the intellectual situation in which fractions were invented—and (as far as I can see) could not do so in the context of an elementary school math class. They simply want Michael to see the connection between one set of ideas about which he does not care and another similar set." (There's a story in the article about a previously disengaged student recognizing the cool idea behind the Rat Pack. Er, a rat trap.) Close to the end, he notes: "What I am suggesting here is a program of idea work for educators. Of course it is harder to think about ideas than to bring a programming language into a classroom. You have to mess with actual ideas. But this is the kind of hard that will make teaching more interesting, just as idea work will do this for learning."

Assignment: Create a project with TurtleArt, and reflect on any “powerful ideas” you engaged with in the process. (Why TurtleArt instead of StarLogo?)

  • Zeroeth powerful idea: I want a turtle script with some randomness and some pattern. So that in repetition you can see an abstraction of the pattern.

  • First powerful idea is one that's missing: I want variables!  There's no way to save or store a randomly generated number, that I know yet. [Tinker, tinker] Oh... that's what the boxes are.

  • Second powerful idea: progression. Hmm. Is the random too crazy? What if there was progression instead? Only two variables, though. Might have to do same fancy-schmancy manipulation of the numbers. Does it obey order of operations? [tinker, tinker] Seems like no. Parentheses to make up. (Might be stack based like RPN. Explore later.)
  • Third powerful idea: undoing/inverse/solving. If I'm incrementing a value, how do I recover how many times it's been increased?
  • Fourth idea: copy/paste is a very helpful function, but I don't know how to do it in this context.
  • Fifth idea: repeatable blocks. Finally figured out how to make subroutines. The nicer neater structure appeals to me.
Other thoughts about TurtleArt: at first the limitations bothered me, but I do believe in general that restrictions help creativity. The help took me a while to try (I prefer documentation. Nerd.) But it was intuitive once I gave it a go. Never did figure out how to copy blocks or groups of blocks.  Somehow they get the code to save in the .png file when I thought I was just saving the canvas image. That is COOL.

I got my polygons basically working but thought they made for boring art. So rather than fine tune for aesthetics, I switched to spirals. Knowing what I needed to about the program I could make subtle shifts to get what I liked. I did put some randomness in, and made a rule for "finishing" - three runs of the program without adding to the screen meant it was done. Here's my favorite spiral TurtleArt.

Dave in the comments had the good idea of sharing the actual files: polygon progression and spirals. Once you've saved the files (which are .png), just open with TurtleArt instead of your default image editor. Thanks! His point about better social sharing would be a good thing. Scratch totally gets that right. Here's the code to read:

I do like the idea of discussing with students what they see as the big ideas, but it probably needs to be done in an inquiry/tinkering style culture.  I'll be trying that out for some workshop reflections in my classes. 

Image credits: He-Man is totally owned and operated by Mattel, I have no rights to the images.

Wednesday, March 6, 2013

Interest-based Learning & Constructionism

Creative Learning - Weeks 2 and 3
Huh? What? No - I didn't fall asleep in class. We took a family trip! (I.e. look for a vacation math post soon.)

One of the many things to catch up on is the Creative Learning Class. (See Week 1.) Phil Aldridge has been a better student - maybe you should copy his notes, instead.

Week 2 was a video session with Joi and Mimi Ito on interest based learning, main reading the Foreword to Papert's Mindstorms, and the Macarthur Foundation Connected Learning report. More resources linked from the course syllabus.

Video Notes: The Itos talk about informal education. Interestingly a lot of former physics majors who lost interest when teachers couldn't explain things intuitively and relied on formalism and symbolic manipulation. They want education to be motivated, and recognize that learning can be motivated by interest and relevance, but attention to diversity is important. Don't feel like they addressed well the questions about how do you deal with less productive interests and time scale (can't learn-on-demand the night before a recital). Important point: have to have a broad range of acceptable work and kinds of recognition. Broader mission, learning, social networking, traditional rewards. (Again the gamer types.) Joi:"The whole idea of higher ed... is that you need a standardized degree ... so it's all about individual standardized skills." Beware curricularization of all of student interests. Mimi cited Katie Salen's schools that have boss levels after the standards required units. Since academia is geared to formal, structured thinking, those are the learners that flourish. It just doesn't motivate a lot of kids.

Assignment: Read Seymour Papert’s essay on the “Gears of My Childhood” and write about an object from your childhood that interested and influenced you (and share with your group). Also try the Marshmallow Challenge. (Done that, never wrote it up. Dave has a nice piece on it, though.)

Haven't seen too much activity from my group yet.

It was a straight line kind of building and play.
 I was really fortunate to have so many building tools/toys. I'm old enough that video games weren't dominating, but a curiosity. Mattel handheld football was the star, unbelievably. Sometime later Intellivision, but that was more my younger brother's speed. Erector set, Lincoln logs, and, ultimately, LEGO.

Really any robot, really,
though Zeroids and Robot were my faves.
Thinking about it, though, my play was always story motivated: the things I was building were for Micronauts, early action figures and any kind of robot. To some extent it's the same now, where teaching becomes the story that lets me build the things that are fun to build and play with. (Games, GeoGebra, cool math ideas and relationships, etc.) Looking back at these things was suprisingly emotional and I still have strong connections to them.

Recommendation: read Papert.

Week 3 video chat with Leah Buechley, Dale Dougherty (Maker movement) on Constructionism (not -ivism but -ionism), read Papert Mindstorms chapter 1 and The Children's Machine chapter 7 (on instructionism vs constructionism). Also of note: Maker-Education Initiative.

Papert quote from Mindstorms, Chapter 1: "But 'teaching without curriculum' does not mean spontaneous free-form classrooms or simply 'leaving the child alone.' It means supporting children as they build their own intellectual structures with materials drawn from the local culture. In this model, educational intervention means changing the culture, planting new constructive elements and eliminating noxious ones." There was a quote in The Children's Machine I had to posterize.

Video: They discussed the value beyond just making, and that 'just making' misses the point. That is human culture. The difference between learning by doing and learning by making, or why making is not just an activity. "School is famous for being overly structured... do all 9 steps and everyone gets the same result. (Barbie, anyone?) Blend maker cultures to appeal to a wider variety of learners; computation, electronics and textiles or paper, for example. Maker movement won't be equitable and diverse until its part of school. Concern for efficiency is a problem, as is emphasis on content that will make money. The old game design saw came up again, too: too often making is designed to hit a content objective rather than the content being involved in the making the learners are doing.

Part of what they said reminded me of a Star Trek exhibit at the science museum that had a section for what toys the engineers on the Apollo program played with as children.  Lots of construction.

Assignment: For this week's activity, create an Scratch project about things you like to do, then share it. (See 180ish projects in a Scratch forum.

This assignment reminded me of the Discovery Channel theme song.  I love my family and spending time with them, playing games and also making some. I love mathematics and I love teaching, too. Good writing - in book or film or tube.  I love music and any form of art, time in my faith life, that should have a part. Not much here that I can leave out, I guess learning is what it's all about. Boom-de-yada...

Press the green flag to play. Fun to make, once I figured out to do the image changes as costume changes for a sprite. I think I'd like to have Terry Gilliam's old job, if anybody wants to pay me to do it.