Conway’s Law

I ran across this a few weeks ago; now I’ve got some time to put some thoughts down:

Conway’s Law
…organizations which design systems (in the broad sense used here) are constrained to produce designs which are copies of the communication structures of these organizations. Link

Now, this isn’t a law like Murphys; it actually has some basis in research. Conway was talking about computer systems but it seems to be applicable to larger systems. What ramifications does this law have for educational change? Given that communication in most schools is (strictly) hierarchical, moving down from above, are we caught in a design loop that will only reinforce a teaching environment that is predominately lecture based, even if it’s online? Although we’ve been a 1:1 environment for ten years, most of us are still teacher-centric, eyes-forward in the classroom. Is Christensen (from Disrupting Class) right in that we have to start new schools rather than try to change existing schools from within?

But I like the cookie…


One of Seth Godin’s recent blog posts (The Reality of Digital Content – lose the cookie, lose the fortune) has been reverberating in my mind over the past week.

What happens when the people with great ideas start organizing for themselves, start leading online tribes, start creating micro products and seminars and interactions that people are actually willing to pay for? …

I have the challenge of working on the Editorial Panel for an academic journal — while I enjoy the reading and editing of articles and the community of professionals that surround the journal, I’ve found the process of acceptance, publication, distribution and commentary to be out of date. My greatest fear is that, as Godin mentions, the journal will be rendered irrelevant in an environment of PLNs (through blogs, twitter, nings, webinars, etc) developed spontaneously by teachers who see a need, share ideas and engage in deep discussion of pedagogy, content and technology. But, in order to remain tight control over their content, they are reluctant to open their journal fully to the web and the chance to allow their readership to contribute without the organization’s filter. Hopefully time and new members of the Editorial Panel arriving in June will help to encourage them to take a great leap forward.

PodcampTO 2010

Another little conference this weekend; close to home, fortunately. It turned out to be a lot of same-old, same old though:

  • The powers-that-be don’t want us to use social media, or if they do, they haven’t a clue how to do it they just want a Twitter account or Facebook page.
  • There are huge issues with privacy.
  • We’re not really sure of the effectiveness of the money we’re investing but very vocal people tell us it’s working.

Interestingly enough, this wasn’t an education conference; it was for entrepreneurs and marketing folk. PodCamp Toronto 2010 was an un-conference in which people put themselves down as presenters on whatever topic they wanted and the costs were picked up by generous sponsors such as Rogers and GM. A call-out to Rogers for setting up a recharging station for devices – a nice touch if you forgot your charger at home.

What I took away, and this is a big tent, was that businesses are very serious about making money using social media, that they desperately want to get at the information posted anywhere on the net about us (and our students). They also want to spread their information as widely and cheaply as possible and develop a readership at minimum and perhaps a community. Unfortunately, they are challenged with knowing how to use social media effectively with any kind of scaling, safety and consistency. Misery loves company!

On a more macro scale, the other aspect I noticed was the wide variation in presentation skills; you can have very little information but just wrap it up in enthusiasm and levity and you’ll get a lot of positive feedback. In a half hour, one presenter gave out five pieces of data (and even he admitted he was making some of it out of whole cloth) but kept the audience entertained and they left with a buzz. On the other hand, you can have a lot of information but present it as (boring as) a classic chalkboard lecture — even if you are trying out Prezi and obviously have a strong background full of data and anecdotes that could have been sprinkled in for context. Some presentations were obviously done the night before; others were very well polished and the presenter spoke clearly and with confidence.

Will I try to go next year? Absolutely! For one, it’s an unconference, a potential model for education conferences. Because people volunteered to present (in fact, they chose their own rooms & times in a Google Doc) there was no filtering we see at ed conferences. Since our present filtering method doesn’t prevent the duds anyways (usually 75-25 split at the ones I attend) why not open it up? You were allowed to vote with your feet; if you didn’t like a session you could get up and leave … although I only this in two of the sessions I attended (and deservedly so).

I also think it’s important to get out of the group-think I experience at many ed conferences; the people here were all interested in social media but for widely different reasons. Some were private citizens who did it as a hobby; others were in it strictly for the money. There were academics from journalism departments but also teenagers who were learning all the latest & greatest in podcasting. It was an eclectic and energizing mix!

My Olympics Contribution

Fortunately, we’re doing slopes in our MPM1D course and I knew I’d be away for Educon for a day so I continued the adaptation of a slope assignment from last year. Last year things were strictly 2D.

First, they went into groups, each with two sheets of blank 8.5×11. On each page, they were told to place two dots randomly (next year, maybe only one dot). From there, they were to draw concentric rough circles. A few students picked up that they looked like topographical maps — sure enough, when I had them count from 0 going up by 500ft (yes, feet) they quickly agreed they were topo maps. I then quickly dropped the maps into my scanner at home and posted the JPGs to our Ning. From the digital copy, each student planned their own ski run, taking into account whether they were looking for something easy or hard. I’m not a skier but there was lots of discussion of diamonds and circles and green and black.
They then worked on analyzing their runs… what’s the slope of each section? What’s the total length of the run (thank you Pythagorean Theorem). They also transferred the data to GeoGebra to get a 2D representation of the run (where they started last year).
And what prompted me to move to 3D? Google SketchUp! The Jpeg of the topo map can be imported into SketchUp and set as the base. Then, using the contours tool, the contours can be traced and then “lifted” to form a three dimensional representation of their mountain (I got a “Dude….” when I showed that to the class. “Dude indeed” I responded).
A good time was had by all… and a lot of nice discussion of slope and length of segments.

Online assessment

Sorry… I forgot I was supposed to write things here 🙂

And thanks to David Cox’s recent post on ExamView to prompt me to return to writing … not to mention that I’m at Educon this weekend and everyone there is a prodigious blogger.
But back to ExamView. ExamView seems to be another online assessment tool and David writes how he is using it in his classroom and how he plans to use it. I’ve been using an alternate tool, MapleTA and had considerable success with it.
I think the strength of MapleTA over the other assessment tools is that it is based on the computer algebra system Maple — and therefore, when you ask a question or the student enters a solution, it can involve any manner of mathematical content. Not just numbers but also algebra and graphs. And we managed to jury-rig Geometer’s Sketchpad to provide dynamic diagrams (yes, we’ll be switching over to GeoGebra when I find some time).
I think the most important aspect of online assessment is the use of a mastery protocol. A student can continue to practice their skills until they achieve some level of success. Obviously these are skill-based questions; yes, it’s a technological drill-and-kill. But I’m okay with that. It’s the efficiency that attracts me – a student who know how to factor will breeze through the questions and can stop. A student that is challenged can attempt the problems without penalty until they become proficient. The assessments are set up to show the worked solution (not just the answer) so they can see how others would have done the question. The frustration is something you have to work through with the student — I keep track of the gradebook and can see which questions the individual students are challenged by, what their attempted solution and provide some prompting by email (thank you Jing for screencasting quickly) or in class.
There are issues of course. No one knows if your dog is doing your homework on the internet. There is a level of frustration when the student keeps getting the wrong answer — but this is something that happens with regular homework and they can give up too easily on paper. And, when it comes to inputting algebra or matrices, say, online, that can be a challenge.
And the biggest impediment — students don’t read the question. While MapleTA understands that 2(x+3) and 2x+6 are the same answers and will mark both correct, it will not accept x2 for x^2.

Getting the word out on GeoGebra

Maria Droujkova has done some great work putting together some Elluminate sessions on Math 2.0… and she has more to come. On Saturday the 26th she had Markus Hohenwarter, the father of GeoGebra and the chief developer Michael Borcherds on for an hour discussing the past, present and future of GeoGebra. She recorded the session and it’s available online.
What surprises me is that I still run in to teachers that have never heard of GeoGebra — here you have free, open-source math software that almost any computer can run, it’s multi-lingual, it’s being used worldwide at all levels and has thousands of lesson plans and activities available on its wiki. And yet today I spoke to two Masters students who had never heard of it.
In Ontario, it’s problematic since we (well, public and Catholic schools) have software purchased for them by the province and that set includes Geometer’s Sketchpad. Now, GSP is an extraordinary program and we owe a great deal to Key Curriculum Press and Nick Jackiw but the development and growth of GeoGebra is a reflection of our brave new world — collaboration on a global scale, the harnessing of our energies to support people we will never meet. What I do in my classroom can be given (instantaneously) to a classroom in Thailand, Kenya or Uruguay… and vice versa.
So how do we spread the word more effectively? How do we ensure that every preservice and practising teacher knows not only of its existence but also the community already formed?
And, most importantly, how can we port it on to an iPhone? 🙂

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Coaching

As I mentioned in an earlier blog I was at the September meeting of the Math Forum; the theme for the meeting was coaching.
There was considerable disapproval of the term coaching; that it set up a hierarchy of ability or skill, that it brought up visions of movie-football coaches berating their athletes. The word facilitator was proposed as something more appropriate. But what a banal, uninspiring word.
I however suggested that coach was the right word — so long as we envisioned it as an Olympic-level coach. An Olympic coach works with athletes that already have considerable ability; there’s not a hierarchy, in fact, the athlete has the spotlight, the fame, the medals. The coach of an Olympian is a specialist; he doesn’t focus on every football position but emphasizes one activity at considerable depth. It’s not that the coach is the better athlete, it’s that the coach has the knowledge and skill to help the athlete reach great competency and the background to be credible. The coach knows how to communicate, to decide the right next step, to plan the process to get the athlete to the next level. He sees the big picture; it’s not just the athleticism but the diet, the lifestyle, the mental attitude. He knows when to use the soft touch and when to put his foot down.
It’s certainly what I hope I achieve when working at PCMI – these are already good teachers who are looking to improve. It’s a challenging role, and as much sleep as I miss or stress I endure I do enjoy it. There’s not so much an opportunity at my school, where there’s neither time nor appreciation for such a process.

Respect. It’s not what you think…

I’m an occasional participant at the Math Forum at the Fields Institute in Toronto. It’s a meeting of folks interested in math education research held monthly; I’d get there more but academic and other responsibilities often overlap. Even today I was supposed to be at school for Homecoming but it’s been a year since I made it and the topic, on teacher-coaching, was well worth it.
At lunch, I sat myself amongst some folks I didn’t know and the conversations ranged wildly. At one point, the conversation turned to how teachers had lost the respect of the public, that it was different in the past, and so on. Blame was placed on the former provincial government for taken an aggressive and demeaning approach to teachers. And I’m certainly not denying there is some truth in that effect that government had on the perception of our professionalism. But there’s more to it than that.
The woman who initiated the conversation gave the example of a parent who had called her with a question. The teacher was quite offended that the parent said that his son “Chris doesn’t believe you’re helping him enough.” Now, she even corrected herself when she changed the word “believe” from “think” and how she then explained what extra help options were available to Chris. I didn’t get a chance to add to the conversation because another tablemate (thankfully) quickly changed the topic to the pronunciation of certain Swahili words.
This teacher seems to be mistaking respect with obeisance— she seemed indignant; the parent had no right to ask her a question about the instruction in or out of her classroom. I even think the parent phrased the question respectfully; the teacher could have quoted the parent with “I don’t think you’re helping Chris enough” but the teacher was specific in how she remembered the conversation, the parent was already placing the responsibility for the misinformation on the student.
Our classrooms, our instruction, our approach, our philosophy should not only be clear and open with our parents but also open to being questioned — the wonderful thing about the age of communication is the opening of discussion. And not just discussion — the simple distribution of information on homework, assignments, testsextra help times. I still remember a time when you would go to the doctors and take their direction without questioning. Not nowadays — there are other perspectives, updates in the field that an interested participant may bring to the table.
I know some of my parents aren’t happy with my approach to mathematics teaching. They want pat formulas & algorithms that will help them help their kids at home; they don’t want to see their children struggle with hard problems or not know all the answers when they used to in previous classes. They want to see worksheets and pages of questions like they remember. They want marks to be added up and averaged. And I understand their concerns and I’m always happy to take time out to explain the hows and whys of my choices in our classroom. Their questioning is not dis-respectful; in fact, I think it’s part of their parental responsibility to question if they have concerns.
What is disrespectful is not supporting the teacher outside the school. Like a couple with shared custody, we have to work as a team and can’t be disparaging of the other, even if we don’t necessarily agree with them. It’s not always easy to share custody but it is possible.

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Setting up Ning

School for us doesn’t start until September 14th but I’ve completed all my computer changes for the year (dual monitor, 1Tb hard drive & 500Gb network hard drive, N-router & card, new headphone-mic) and my nephew has gone back home so I’ve got no more excuses to avoid getting down to work.
I had to decide how to work it this year: two years ago the school decided to use Sharepoint for our course management system. From a user perspective, it was less than successful although I do understand they’re using it as a complete portal for the school. Having used Blackboard for the previous 6 years, it was hoped there would be major steps forward but Sharepoint seems stuck on the centralized-control paradigm and the opportunity to (easily) create, incorporate & share content by users (outside of Word documents) is limited. Adding content beyond the basic document is very similar to old Access Reports. Not user friendly.
More importantly, it is Internet Explorer centric. I understand that from a business perspective, it is the simplest thing to require the use of a particular browser. A friend who works at BMO loves Sharepoint… but he is also locked down on his desktop and thinks the new themes in Powerpoint 2003 are cutting edge (they haven’t evalutated 2007 for internal use yet). The police department also uses Sharepoint well but again, they are not exactly a creative industry. We have students & teachers, each with their own tablet and administrative control over it. They are supposed to be experimenting; discovery is their job! And so they use the creative tools: Firefox with all its addons, Chrome (cuz it’s Google), Safari (cuz some have Macs at home), Opera… and other more obscure browsers. And they have iPhones and Blackberries. Sharepoint doesn’t work completely on any of them. Okay, Sharepoint works on your Blackberry if you want to plug in $4000 on the server — and I hope our IT department does do this if only to show they’re thinking proactively.
So that’s one of the main reasons I’m not using Sharepoint for my classes this year. I flipped back & forth between Elgg & Ning and went with Ning because (a) I don’t have my own server (and don’t want to pay for one) and (b) don’t have time to do all the coding. We’ll push Ning as hard as we can this year and see what happens. Maybe Sharepoint will grow in the next year? We’re apparently hiring a Sharepoint programmer ($$$) to do stuff for us.

Math Video Markup

As I mentioned in an earlier post, my students will often be required to submit Jing videos of their worked solutions to a variety of problems. Basically it’s the modern alternative to handing in paper copies of their homework but I get their voice, literally & figuratively, describing the solution with all the steps in-between. I think it helps to reinforce the importance of process over final answer since they have to go to all the work of explaining what they’re doing and why, and also allows me to reinforce correct mathematical language.
When it came to providing feedback to the students, I’ve had to rely on just an email response, describing in text or providing a full worked solution in Jing on my own. What I’d really like is what we have for paper — returning it with the markup on the product. Jing of course lets you mark up the image capture but what I need is video mark up, like they do on ESPN to describe football plays. There’s this neat little website www.markupvideo.com that does this for YouTube videos but of course, I’d like it for Jing videos (it’s all Flash anyways, eh?) Our PhysEd department has Dartfish but this seems more like LoggerPro on steroids and a bit more than what I need to mark up homework. But, we’ll give it a try …

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