Changing directions

(I thought I should squeeze this in given a link from a popular blog, Continuous Everywhere.)
I closed off my teaching this June for a year; in the fall I'll be returning to life as a PhD student at OISE, the Ontario Institute for Studies in Education at the University of Toronto. I'll be working in the Curriculum Studies and Teacher Development program -- two big areas of interest for me. Stay tuned for updates.
I'll hopefully have considerably more time to write & reflect. The only external responsibilities I've kept are the Auxiliary, the ECOO conference in November and PCMI, of course. For me, that's not a lot. And I'll be commuting in on the GO train (public transit) so there will be about 90 minutes of downtime each day in which to put pen to paper (electronic, that is).
I'm looking forward to have the time to "think deeply of simple things". My focus will be on teacher development, an interest developed over my time with the folks at PCMI. It's so energizing being around these folks -- how do we capture the experience at PCMI and make it more accessible to math teachers everywhere, efficiently & effectively?

Made the paper!

Okay, I didn't quite make it into print... but the electronic version isn't half-bad. I was working on the waterfront when, during one of those brief-but-violent thunderstorms, a sign fell onto the walkway, narrowly missing a number of pedestrians. So I got to stand in the rain to make sure no one else would get hurt until they managed to get the sign removed and the other reinforced.
Working with the police is a great experience 95% of the time. Even getting soaked in the rain just standing there has a charm of its own although most of the time it's just helping the public with questions and concerns. Halton is a pretty safe area so we don't have the problems of major urban centres; most evenings when I'm on duty the computer lists only a few calls through the night. The remaining 5% of the time is both depressing and disappointing -- people in serious trouble. But, we're there to help regardless of the perceptions of those involved. My only regret is that because our shifts are infrequent we don't get the closure on the situation that the regular officers do.
I always encourage teachers to get involved with their local Auxiliary; their most serious needs parallel our down times so they mesh well. And the skills and knowledge are something we don't often encountered in teaching. Check it out!

Where is everyone?

While I admit to being quickly on board most things (except the iPad, that is... that's a tool for my 65-year-old Mom) I'm disheartened by the slow pick up of online learning networks (via Twitter, Ning, Facebook, etc) by my colleagues. We're a 1:1 school and the faculty are pretty comfortable with technology -- but I see very few of them (well, okay, maybe 3 out of 100) that are actively engaged online. Is it really just an issue of time, given that independent school teachers have a very long academic & athletics day followed by the same prep time all teachers require? Are they unaware of the benefits of connecting and collaborating online? Or does that beg the question?

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 8.5x11. 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? :)

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.

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 ...

I think I want to SMAK my kids

I've been thinking about how to assess my Grade 9 and 10 students this year ... I did a lot of experimentation last year with my accelerated Grade 8 students;they were open to trying things out since acquisition of skills and open-ended problem solving was right up their alley. Here's one change I can make:

So, there are four units in both MPM1D and MPM2D ("Ontario" for Grade 9 and 10 math respectively). For those paying close attention, there are only three in 2D but I break the Quadratics unit into two pieces. Beyond the typical written assessments (test and exam) that we're required to do by the school -- we have both Christmas and June sit-down exams -- and the evaluations & projects that the other teachers determined while I was in Utah, I'd like to introduce a SMAK at least once for each unit: Show Me Application and Knowledge. Yeah, it's a lame acronym... I'll try to think of something better.

My idea is that each student will choose a 10 minute period outside of classtime in which to show me their understanding by explaining pre-assigned or randomly chosen questions and by just explaining the important topics of the unit in their own words. I'd also like them to reflect on their learning process, homework, participation and all those other bits & pieces of our classroom. Pretty open ended on both sides of the conversation but I really want to evaluate their understanding of each unit based on a chat, 1 on 1. I tend to collect a lot of anecdotal observations (thank you iPod Touch!) in class during kikan-shido but this will provide me and them with a personal video asset for each student (oh, did I mention I was taping them?) I also haven't found blogging to be particularly effective in my classes and want to have a good record of their "voice".

I'm going to have to structure this: first, start by taping myself several times discussing learning & mathematics (first one, "Welcome to class") and having them use these as a model for their first SMAK. Using Jing to explain their problems from homework will also make them more comfortable in verbalizing their explanations (and hearing their own voices).

And this will be graded using a rubric. Because each SMAK will be unique in content there's no realistic marking scheme and the marks given will be for completion, thoroughness and quality. If one student spends most of the time given a great solution to an application while another devotes most of it to explaing how they finally learned how to factor, clearly explaining how they grew as a student then both would be graded highly.

By the end of the year, I'd like to have them create their own video ra

Image by mstephens7 via Flickr

ther than have me sit there for 10 minutes with them, guiding them through. It wouldn't surprise me if, as they realize I'm taping them, they'll suggest it themselves. Hopefully they'll have seen enough examples to gauge the depth I'm looking for and the breadth of options when it comes to their explanations. We'll see.
Is this feasible? My class size is usally about 16 kids: that's 160 minutes x 4 = 640 minutes = 11 hours per year. That's about the time it takes to mark a set of exams but spread across the whole year. Times three classes, of course.

Social Technology & Education @ Harvard

Sandwiched between two great motorcycle rides through upstate New York & Massachusetts, I attended the Social Technology & Education conference put on by the folks at Elgg. They held it in the Radcliffe Gymnasium, a former gym converted into a very elegant discussion space.
The conference evolved organically: people volunteered to present and participants came from a variety of academic, medical, non-profit and commercial situations. There was little advertisement and people heard of it through word-of-mouth (okay, well, Twitter). Now, unfortunately, almost 280 people signed up but not everyone showed; I think by making it free, people felt they could sign up, take a space and not show. Always have a nominal fee, just to show some level of commitment!
The presentations were varied so I'll pick out the high points for me; given my background, a lot of it covered issues we've already had under consideration for a while.

• It was a real pleasure to meet Dave Tosh, who despite his Scottish accent hails from Oshawa of all places! His most important reminder for me was that "Just because they use Facebook doesn't mean they are tech savvy... their mates are on Facebook so they are motivated; they're not motivated to do your site" So not only do we need to ensure they have a reason to use our online tools we also have to provide some level of training and support; it won't be automatic because the students (faculty, staff & parents) don't want it or need it to be.

• Real innovation comes when we take something for granted ... Christopher Sessum's presentation mentioned this, and apparently it comes from Clay Shirky's book Here Comes Everybody. I haven't read it but picked it up from Chapters when I got home from Boston. Sessum's notes and presentation are here; he has a similar presentation style to mine, so you'll need to read the notes. I can remember when we first started out at RCS and discussed this issue with Paul Kitchen. We wanted the laptop to be as fluid to the student and teacher as the pencil or chalkboard was. We were only a decade & a half ahead of our time.
  

• Christopher's (and later) presentations mentioned Etienne Wenger and Keith Sawyer a lot: I haven't done a lot of reading that discuss the development of communities of practice so they're now on my reading list. Developing communities is a lot of what we are trying to do with PCMI and so reading about the progression of professional learning networks has become important.
  

• Shelley Blake-Pollock, from TeachPaperless ran through his work with Twitter. Shelley takes a more blunt approach than I'm comfortable with although I think we perceive the end result similarly.
  

• Liz Davis did an excellent rundown of Ning; she's convinced me to use it for my courses (if I can't get Elgg up and running in time). We're using it right now for the PCMI group but Liz has given some great examples in her classrooms. There are some limitations, in particular using mathematics, but it's really the conversation and discussion, not notation.

• Jim Klein showed how his district in Canyon Country, CA used Elgg as a structure to build a community of faculty, staff, students and parents. I'm not sure whether or not his theoretical understanding of the process parallels Wenger & Sawyer (I've got read them, first) but the practical outcomes that he showed, linking students from across grade levels and subjects, speaks volumes. I can only make linkages between my own classes and classes outside my school but I think beginning a conversation with a larger academic community is important. I'd love to be able to use a tool like Elgg in this fashion but it would require considerably more time to develop & program than I have. Hence I'll likely be using Ning.

For a one day conference, there was lot of excellent discussion. That it was put together so quickly and with little budget gives me hope for things we have planned in the future!

(Most of this post was lost thanks to my crappy Dell tablet... I'll come back and relink things tomorrow.)

Working Groups

Before I start dealing with reflecting on the content of the classes, I've got two more aspects of PCMI to mention.
The first is the most productive: The working group. Each of the teachers is assigned a working group in a topic of secondary mathematics for the afternoon (Wednesdays off) in which they, typically in groups, will produce a product useful to classroom teachers.
As the person in charge of a group this can be very challenging: these are all energetic, enthusiastic and talented teachers -- who all teach in very different classrooms. So what may be appropriate for one school system could fail utterly in another, not just in terms of content but departmental expectations, school standards, etc. As the working group leader I have to steer these folks towards a consensus: a project that is meaningful to them, useful to others, and able to be accomplished in three weeks. Most of the time this takes the form of a lesson plan or activity that is refined throughout the three weeks -- I find that too limiting and I'll discuss what we did in a later post. I will say my group this year (go Discrete Math!) took on a huge challenge and did an amazing job; I was overwhelmed with how they took on their responsibilities and always questioned "how can we do this better, or different?"
We also spend some time looking at different problems in the mathematical area and we're always fortunate to have 200 world-class mathematicians running around in the corridor (well, they don't run so much as shuffle) to snag for a few hours. It's funny when you speak to them at lunch and then after lunch realize WHO they really are. They typically stride the mathematical world like colossus and you've asked them if they liked the carrot cake! :) We were lucky enough to have Joe Malkevitch (yes, THAT Joe Malkevitch) spend almost two hours discussing problems with us -- starting with the Art Gallery problem and then seeing where that took us. That is how lucky we are at PCMI!
The other group of activities I have to mention are the cross-program ones. This is a huge umbrella and can cover things like I mentioned below, James Heibert discussing the TIMSS Video Study results, at least two Clay Scholars every year discussing their work (with us! High school teachers!), Gov. Huntsman (at the time) speaking of math at the state/national level, and even Tom Garrity explaing how "Functions describe the world". The level and content varies so greatly, an exhaustive list would be its own (rather dull) blog post. Suffice it to say, it's the kind of opportunity you would have to hang around Harvard for, for at least a few years.

Reflecting on Practice

Once we're done the morning of math (with a brief coffee break) the teachers all get back together for an hour of math education pedagogy. Like the mathematics we cover, each year is something a little different. For example, in previous years we've focused on Lesson Design (with Drs. Nicole Bannister & Gail Burrill), Teaching through Problem Solving or Learning the Open-Ended Approach (with Dr. Akihiko Takahashi).
This year the organizers tried something a little different; they tapped six of the returning participants to look at Questioning in the Classroom from the practicing teachers' perspective. As one of those teachers leading the professional development it was a considerable challenge to not only meet the expectations of the participants and the organizers but also our own expectations -- my colleagues are amongst the premier educators in the States (National Board certified, AP consulants, you name it). We began with a working weekend in Denver in the spring, pulling together resources and a timeline -- our biggest fight was avoiding putting too much in. And then, when actually talking about pedagogy with professional teachers there is a huge struggle against anecdotes; everyone wants to share their stories. In discussing Questioning we want to move beyond what we do now and move towards something better. And so we start with what the research said.
This blog post is only to set the scene for a series of posts; I will go into this at greater depths in the future but our motivation was the results of the 1999 TIMSS video study -- James Hiebert presented the results to us in 2003 at PCMI and it was the most astonishing moment I've had in a lecture in a long time and it has been the prime motivator in my teaching ever since:

Almost all (ed: statistically 100%) of the problems in the U.S. that start out as making connections tasks are transformed, in a variety of ways. Often a teacher steps in and does the work for the students-sees students struggling, gives a hint that takes away the problematic nature of the lesson, and tells students how to solve it. These are not incompetent or poorly intentioned teachers but simply teachers who have picked up very well an American way of teaching mathematics. One of the cultural agreements we have made in this country, with ourselves as teachers and with students, is that it is the teacher's job to tell students how to do the problem and how to get the right answer-that it is not fair to allow students to struggle or be confused.

In other words: we are far too nice. So, for the past six years I have worked hard not to be nice and tried to persuade colleagues near and far to cowboy up¹. I've presented on this at OAME directly and in any other presentation that I've done I've pressed the point. It was encouraging to see Dan Meyer come to a similar conclusion in his presentation to open source programmers (yes, the context is a bit bizarre but makes sense if you follow his blog). Be sure you should watch the video.
_________
¹I include "cowboy up" only because I had to explain the phrase to Gail this year :)

Graph is created from data produced in the TIMSS video study and is from here: http://www.mathforum.com/pcmi/hstp/sum2009/reading/Hiebert_Improving_Math_Teaching_2004b.pdf

The 830 at PCMI

PCMI is a 3 week program; each day from about 830 to 1040 we have what can best be described as a math class. But it's unlike any math class most people have ever had.
Each day starts with its own problem set designed by the class' organizers, folks from the Education Development Center and Harvey Mudd College. The problem set is well structured, beginning with a simple idea or concept and then continually developing in both depth and breadth, although this may be obvious only several days later. The questions are also in categories: Important (things you'll need to know for upcoming days), Neat and Tough (can be really tough! Clay Prize tough!) -- we aim to get through at least the important stuff in our morning together.
The classroom is composed of 12 tables of 5-6 people each (we do have guests from the other programs) and as a table we tend to worth through things together; there's a table sandbox monitor who is there to ensure that the teachers exercise all those collaborative skills they try to encourage with their students. Not only that, but we never tell people ideas, we create a situation in which they can they discover it themselves. This is not easy and like any skill takes practice and continual reinforcement. It is at the heart of the whole morning class (indeed, of PCMI) and the mathematics could almost be the motivation for appreciating this whole process. It's why I call them "organizers" above and not teachers -- it's not instruction as you know it.
The math is very accessible and very deep - low threshold, high ceiling - and it is too easy to look at it only superficially. Teachers will occasionally race through the questions to get them done (remind you of any students?) and will miss out on the complexity of the mathematics. I remember my first year doing the same thing.
As one of the participants said "I've taken courses in number theory but never understood prime numbers until now." This has been true for every topic I've encountered at PCMI -- teachers seldom get the chance to think deeply of simple things that Al Cuoco of EDC, and one of the course's authors, encourages.
If you visit PCMI @ the Math Forum you can click on Class Notes to read over the problem sets from previous years. Or, to get a very insufficient glimpse of the questions, the MAA has a book of Al's work Mathematical Connections that includes material we've looked at during PCMI. It's condensed (remember, we get three weeks) and doesn't have the same level of personalization that our questions set have -- the authors adapt the problem sets from day-to-day to build off of our ideas, suggestions, questions & comments.

Precursor to PCMI

I've had the opportunity to come early to Park City and help set things up: there's actually a lot of infrastructure to put in to place. With (at least) 7 different groups running simultaneously around the conference centre, there's the usual classroom/lecture facilities to complete but nowadays we add on a considerable amount of technology: LCD projectors, wireless & wired networks, speaker systems, the typical. And, because we're mathematicians... a lot of chalk boards and coloured chalk. Lots. And old school overhead projectors.
But in the teacher room, because we've got at least 60 participants spread across 12 tables, we have a desk-based microphone/speaker system so that they can hear each other across the room, two Mimio electronic whiteboards (an excellent alternative to Smartboards!) tied into an ELMO document camera and three LCD projectors and, because we break this large room up into three smaller rooms, the need to have it all work as a common space and as separate rooms. Lots of cabling criss-crossing the room that has to be taped down.
So that's my first week - the participants all start to arrive on Sunday. I'm lucky that there are a number of returning folk along with the rest of the staff; it's good to see old friends! Most folks have the chance to come back for a second year -- and if you come back for a third you're conscripted to help out working with the new teachers.

Going back six weeks...

So the end of school was a bit of a flurry and I left meetings early to head out to Park City, Utah (home of the Sundance Film Festival) to participate in the Park City Mathematics Institute for the seventh time. If you're a math teacher and never been... you're missing out!
I first attended PCMI in 2002 -- by pure luck. I was teaching Ontario's Linear Algebra course and stumbled across their webpage which discussed that summer's topic, Gaussian Integers. I cross my fingers & applied. After attending as a participant for two years I got invited back to help out as staff. It's a lot of work and I don't get all the fun that participants have but I learn about math and teaching and learning in a different way. And I get to work some amazing people, both staff and participants, and great friends.
PCMI is hard to describe. I call it "math camp" when asked just to make things easier. Let me try to be more descriptive since I have the time: PCMI is a three week residential program that has about 60 teachers participate in daily 2.5 hour problem solving sessions that build around a topic, an hour of pedagogy, a 2 hour small working group session in the afternoon on a topic specific to the teacher's classes and a variety of afternoon and evening sessions, lectures and activities on recreational or research mathematics.
While the teachers are doing their thing, there are also about 250 undergraduates, graduate students, university faculty and research mathematicians doing their own courses & lectures on a specific theme, usually tangentially related to the teacher's morning problem solving topic. For example, this year's topic was L-functions -- this is a cutting edge area in number theory (and is the hot new thing in cryptography). Next year, it's image processing. The addition of all these "real" mathematicians running around (and these are sharp folk... Clay Scholars, Fields Medal winners, Nobel laureates -there's no math Nobel but sometimes the topics cross science/economics boundaries) lifts the matheamatical conversation and is an important reminder that math is continually developing... and is crucial to both our day-to-day life and to our future. Plus all these smart folks reminds me what it's like to be a student in my class...
The applications come out in the fall... if you're a math teacher, you should apply. Three weeks is a long time but the Park City area is beautiful, the PCMI teacher community is amazingly supportive and the math is a lot of fun.
Over the next couple of weeks I'll describe what went on this summer at PCMI. I did twitter throughout so feel free to Twitter Search but I didn't have time to blog.