Things I do

Changing directions

2010-07-01T01:42:00.002-04:00

(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!

2010-06-22T02:03:00.000-04:00

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?

2010-04-09T08:35:00.004-04:00

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

2010-04-07T22:42:00.002-04:00

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...

2010-04-06T21:37:00.002-04:00

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

2010-02-22T07:55:00.002-05:00

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

2010-02-15T22:14:00.003-05:00

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

2010-01-30T09:26:00.007-05:00

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

2009-09-27T21:40:00.002-04:00

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

2009-09-26T20:19:00.002-04:00

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...

2009-09-26T19:38:00.004-04:00

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

2009-08-29T23:53:00.002-04:00

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

2009-08-25T09:01:00.003-04:00

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

2009-08-24T19:17:00.009-04:00

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

2009-08-20T16:26:00.004-04:00

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

2009-08-02T19:11:00.006-04:00

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

2009-08-01T21:03:00.006-04:00

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

2009-07-29T15:03:00.008-04:00

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

2009-07-28T23:01:00.002-04:00

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...

2009-07-24T09:28:00.008-04:00

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.

Do you want us to jing it?

2009-06-15T18:34:00.008-04:00

The English language continues to evolve -- jing is now a noun and a verb as far as my students are concerned.
Jing is the free (or lost cost pro version) program for the Mac and the PC that quickly allows for screen captures. It installs a small button on the side or top of your screen that pops out when you do a mouseover (as shown in the image in popped-out state). You can then quickly draw out a rectangle to snip -- then you have the option of copying it or posting it online on space that Jing provides you. Very quick and easy to snip out bits & pieces of your screen for reference.
That, however, is old news... and doesn't add a lot to the student/teacher conversation.
Where we've found Jing's power is the ability for the student to create very quick videos of their work for us... the question is put into OneNote and then the student solves it, adding a discussion of their reasoning as they work through the problem. Jing has no video editing components to it so they can't clean up their work -- they can re-do the entire video, of course, but you get to hear their mathematical voice. It's something you don't often hear a lot of in a class, especially amongst some students who choose not to be vocal. Teachers here have used it from Grade 7 to BC Calculus; there's a place for it everywhere.
They are a challenge to mark, however... we don't have a lot of tools (yet) to mark up video and just returning a text or image with notes seems less effective than it should be. If anyone has any quick-and-easy suggestions I'd like to hear it.
We (teachers) also use Jing to post solutions to homework; it's much easier to post links to the videos then to distribute the worked solutions by email or wiki. It helps to re-inforce correct language and provides a lot more information than just the written work. And, for a student looking to understand the solution it makes it a lot easier to have the teacher's reasoning made clear for each step. There is an argument to have students learn from reading mathematics but that's an incremental process. Here's a 4 min video (about the max recommended for practical use; in fact Jing has a 5 min max) I remember doing at the airport; that's the convenience of the system. I've also used it to provide solutions on MapleTA, our online homework & assessment tool because, again, you can just provide the link and no need to embed or install. However... you CAN embed them into your wiki space... the code is provided.
There is a paid version of Jing that I will likely upgrade to for next school year. It's only 15$US and adds on a few handy options ... but the students need only the free version to make it using the program successful for both of us.

Paperless?

2009-06-12T19:57:00.005-04:00

California's recent announcement that they are moving to e-textbooks will mean a lot more resources for 1:1 schools. Right now, using a tablet computer means either having a CD copy of the textbook (now a departmental requirement for our texts and fortunately most Ontario publishers have agreed) or several hours spent at the photocopier, scanning the questions in. Some publishers copy-protect their CDs but in the age of snipping tools, it's a lost cause. I understand they're concerned with sales but a quick check of class lists will ensure they're selling what they should.
Since my students have tablets, I use a OneNote file each day for their work: I get to pull questions from the textbook and sequence them the way I want. I can also make different levels of homework depending on the students -- this is particularly nice and, since the students don't necessarily see each other's OneNotes, they don't know who has what. I also put the answers from the text at the bottom of the OneNote for their reference. With OneNote, of course, I can also add in links to resources for the questions, my only little running commentary (either helpful hints & tips or notes about the phrasing of the question, where to find other questions like this and so on. Images, videos and applets can also be incorporated. It's this kind of environment I'm hoping that California will come up with.
I know that many of the math teachers don't do this; it's another little bit of work each day. I just find it inefficient to ask the student to copy the question from the textbook (since an answer in isolation is useless in review) and then flip to the back of the book for the answer. Not to mention most desks don't accomodate a math textbook and a tablet computer (and a soft drink, chips, ipod, etc).
Some teachers do it for the whole unit; I find that a little wishful thinking. So many good questions & thoughts arise from class that I like to tip them in either the same day or the next day -- and it's not just the math stuff I put in, either. Current events, humourous things from them... it all adds a little bit to the work.
If you're a math or science teacher, OneNote is likely only effective if you have a tablet (or a plug-in tablet as I used to use). For other subjects a laptop or netbook would be sufficient.

Microsoft's Live Mesh

2009-06-11T18:02:00.002-04:00

One of the most successful tools I used this past academic year is Microsoft's Live Mesh ( https://www.mesh.com ), a cloud-based file-synchronization and desktop-replicator. I had signed up for it when it was in Beta and have never had a problem with it; in fact, it's worked far better than the Sharepoint system that the school offers. It installs as a service onto your Windows computer and creates a small blue icon that flashes when it's synchronizing.
Since we use OneNote for all of our academic material, it is nice to be able to access your Notebooks from any computer. With LiveMesh, I store the notebook in the LiveMesh folder (which appears to the computer as any other folder) and open it in OneNote as usual. I can work with OneNote, adding, editing and deleting and while I'm working away LiveMesh is synchronizing the local copy on my computer with the copy on the cloud which is also syncing it with any of my other computers (one tablet, one laptop). If I need to use the files on a computer that isn't mine, I can access the files through any web browser, too.
Not only do I store all my OneNote files in a LiveMesh folder, I store all my day-to-day academic files in one. I also have folders for my action research, journal writing, e-textbooks and backups. There have been a few times in the past I will be using my desktop to create school work and forget to upload it to the web for use at school -- by putting it in a LiveMesh folder, it's automatically available to me. If my laptop fails, my files are safe. Even if LiveMesh or the network is down, the local copy is useable.
There are two other things that are nice about LiveMesh: first, you can share the folders with other LiveMesh users. I've done this to distribute large files to my AP Calculus students and to have my Advisor Group do their backups in case their laptops fail. I've also used it to work with colleagues across the country; no need to email files back and forth (normally I'd suggest GDocs for this but not everything is a document/spreadsheet.)
The second is that you can actually log into your remote computer that is running the LiveMesh service. I've used this several times when I'm running a task on my desktop at home that I want to check on or continue with while I'm at school. I don't always leave my home computer on (they use a lot of hydro, after all) but it has turned out handy if I have to work in two places at once.

Three things...

2009-04-07T21:58:00.007-04:00

I managed to sign myself up for a How to write a better blog online course. Because, dear reader, this blog isn't just for you... no, this is to teach me how to be a better writer and a better reflecter (I'll bet that's not even the right use of the word... but I'm going to pull a you can do anything on the internet, grammar and spelling don't count)
So my task today to improve said blog is to provide a list. Totally open-ended. The rest of the 10,000 participants in this online course are mostly marketers, trying to sell something (not necessarily material but also opinion). That's not my goal so my list then is this, right off the cuff. I have to get this done because I have planning to do for tomorrow. I want to use Google Sketchup in my MPM1D Geometry class and that will take a little time.

Three things that will make me a better teacher:

Reflection. Reflection. Reflection. Reflection on what I am teaching, how I am teaching it, how it was received, how it can be improved. The issue, of course, is time. But, as is constantly mentioned, if you find it important, you'll make time.
Patience. As has been previously noted, I'm not particularly patient. Surprisingly, that has no effect in the classroom... I'll quite happily sit with a student to go over mathematics for hours. It's what I love to discuss so I have no problem spending the time or effort. What I am impatient with is bureaucracy. Stupid rules. Rules that are there only to make things fit into neat little forms. I will be a better teacher when I get over the fact that I can't change this. Stop tilting a windmills and do what I can.
Be more of a out-front leader. Previously, I've opted for the sit-back-and-lead-from-behind. Doesn't work. A decade has taught me a lot. Those who push and get themselves out there (and not always in a bad, back-stabbing, conniving way -- which, unfortunately does seem successful for some -- but in an open and sharing fashion) are those that are leading nowadays. Waiting for someone to notice what I'm doing is useless. I have to publish. I have to share.

So that's my list. I'm sure my students would have a completely different one. Hmm... I think I'll make up a Google Form and ask them.
Oh... and I figure a blog posting is better with pictures.

Parents...

2009-04-06T15:27:00.001-04:00

I had a great conversation with some parents the other day. When they first emailed, they mentioned they wanted to talk about their students' math. My first thought was why? Very bright kid, very self-motivated, always at the top of the class - I figured they wanted information on his continued acceleration.
No... they wanted to discuss assessment and grading practices. We had a great conversation, mainly because they have a daughter in the same course taught by another teacher. Now, I have to admit my approach to teaching in my non-Calculus classes is non-traditional for an independent high school. I'm very much a constructivist, I don't like to be the one talking in the class and, most important to the parents' discussion, I refuse to just average scores for tests throughout the year. I patiently track the students' progress through all our assessments and adjust scores as they exhibit understanding (thank god for spreadsheets). It may take all year before a student gets the hang of factoring anything I give to them... but if they finally get it, their scores increase. It also means my students at the end of the year have higher grades but if they understand what I've asked them to learn I think that's what the grade should indicate. And, they've had to work throughout the year to get a grip on things -- I don't have a unit test and then close the book on it.
The parents wanted to know why the rest of the teachers didn't do the same. I didn't have an answer for them.

KenKen

2009-04-02T23:24:00.005-04:00

Over the March Break (when I had some unstructured down time) I ran into a new puzzle form -- the KenKen. While it has a superficial similarity to Sodoku in that the numbers can't be repeated in a column or row that's where the similarity ends. In KenKen, the large grid has been broken up into cages - highlighted areas that have to be filled in with an arithmetic expression to hit the target number written at the top of the cage. There is also an arithmetic operation at the top of each cage. So, for example, if 24 x is at the top of the cage, the cage would have to be filled with as many numbers as cells in the cage and those numbers would have to multiply to 24 (so it could be 2x3x4 or 4x6 depending on the number of cells in the cage and the restriction against repetition, of course). As an exercise in class, it's a good reinforcer of basic skills (no calculator, of course). Once my students have the hang of completing the puzzle, we're going to move on to constructing our own. As always, it's harder to create.
My only concern about KenKen is that it treats subtraction and division as commutative. That is, it treats 6-4 and 4-6 as the same answer, 2. I wish the KenKen authors would use Polish (or pre-fix) notation so that it would avoid this issue. Plus it would allow us to talk to the students about Polish notation. When I went off to university I bought my HP28 ... it was one of the first graphing calculators and, as all good HP calculators did, worked in Reverse Polish Notation. That is, when adding 2 + 3 you entered it 2 3 +. The operation would always go at the end. It means you don't have to use brackets to avoid order of operations. A great little calculator I used until I became one of the testers for the TI82. But that's a story for another day.

You want how much for wireless?

2009-03-30T10:43:00.007-04:00

I'm off in mid-April to the NCTM's Annual Conference; I'm looking forward to it because I'm also attending the Research PreSession (have to learn how to network with researchers in anticipation of starting my PhD) and also the NCSM, which is more for teacher-leaders. Not that I'm a teacher-leader by any stretch. I just like to know what's going on.
Anyways... as I was preparing for my own session (it's on Saturday the 26th, discussing Web 2.0 and aids to differentiating instruction) I checked in with the supplier of wireless access at the Walter E. Washington Convention Centre - SmartCity. If I'm doing some internet stuff and differentiating, I'd like the participants to experience what we do with our classes. Unfortunately, they replied with a cost of 24.95$ a day. And that is for access suitable to "checking email and surfing the web... not recommended for exhibitors or presenters". So much for that idea... it's going to cost me almost 200$ to just equip myself with internet access for the week of the conference. And so I'm going to have to ensure that everything is available locally. Thankfully, GoogleDocs has an offline mode but it may endanger my attempt to use CoolIris as a presentation tool. Instead of being able to model the activities with the participants, it will likely be more of a (albeit very cool) standard presentation on what we're doing.
It's sadly ironic: SmartCity's logo is Making the world smarter. Instead, they are my greatest impediment.

A little off-topic..

2009-03-27T09:54:00.000-04:00

While I'm more than happy to rant again about videostreaming/taping conference sessions (MERU on Thursday?), especially after meeting in New York and hearing half the participants explain why they can't attend the NCTM Annual Meeting in Washington due to hotel costs, travel time and coverage fees... but not today. I'm still on March Break.

So this YouTube video came across my desk... it's not at all serious or educational (put a shirt on!) but I like it because it's in ASL -- and so rarely are music videos made for deaf people. I took ASL a few years ago when I was volunteering in a community with a lot of deaf people. I love ASL... it's visual poetry, it's so emotive (and for someone raised WASP, that was a challenge to overcome). I wish I could use it more often. I tend to drop a few signs in conversation, often without realizing it.
The other thing that made me smile about the video was that it's the way I practice ASL... while listening to the radio I will try to sign the song. ASL is never word for word so it's not as hard as it sounds; a lot is derived from context. It's the way I prepared for living in Switzerland, too... I used to try simultaneous translation of songs into French while driving.

March Break Intervention (Thanks for helping!)

2009-03-11T18:54:00.003-04:00

Well, my public challenge to my students two months ago worked... I got hooked on drinking way too much Diet Coke while writing my final Masters papers and couldn't kick the habit. So, I told my class that if they saw me with DC in my hand, they could use any means necessary to get it out of my hands. My grade eights, in particular, were delighted by the possibility of taking me on (I'm 6'4" and way too many pounds). But, the public pressure not to meant it was relatively easy to switch over to water... I didn't want the embarrassment of being bested by a pack of rabid grade eights, for one.
So, to make sure that something happens, I'm going to publicly list my tasks for March Break. They are:

Finish GeoGebra PD for our PCMI PDO
Restructure question banks and verify the tags in MapleTA.
Design & implement GoogleDocs tracking database/spreadsheets à la CIS 339 Middle School in the Bronx, as seen at Educon 2.1 in January. This is something that's been on my mind a lot; thanks go to my colleague here for finally making us push towards it!
Finish up PhD applications. Do it.
Read 5 books on my reading list. And reflect on them. And write that reflection down.

I think that's enough. I'm sure I'll have an "around the house" list, too. But the internet doesn't need to know about that.

PWN'ing PLNs

2009-03-08T19:44:00.004-04:00

The conversation surrounding PLNs (Personal Learning Networks) continues to grow, both from the perspective of the student and the teacher. A member of my blogroll (and thus, tangentially, a member of my PLN) made a post that prompted some reflection. Since I can't see my school working towards a more liberal approach to boundaries involving subjects, teachers, instruction, etc I'm trying to focus on, and advocating for, the professional PLN aspect. I'm sure there's a cool graphic of PLNs somewhere that encompasses everything I think PLNs are... I scrolled through a few and the best is this one from another tangential-PLN-member Alec Courous but I still don't think it's a complete visual description.
The topic is close to my heart - I began my teacher career as the only math teacher in the school -- 100 kids 7-12. For five years, I did the senior math courses while the rest were picked up by the science teachers. We were the only independent school in the province and it took considerable time and money to get to PD opportunities elsewhere. Isolated geographically and socially (most public school organizations would have no truck with us) I used gopher (does that date me?) and the web (which eventually includes pictures!) to communicate with digital colleagues. However, protracted discussions were slow, it was difficult to share content and the people involved were few and far between. The first ten years of my teaching found me isolated geographically, linguistically (teaching in France & Switzerland) and professionally (most math teachers wanted to teach from the textbook, emphasizing on algorithms. Most still do, unfortunately).
Nowadays, the situation is much changed -- the venues in which we can communicate are legion. There are so many bright and inspiring people out there posting opinions, content and ideas. I regularly do Skype conversations with colleagues in the States, I read and engage in discussions on mathematics and technology from people (friends?) from around the world. The professional isolation I so clearly felt during my first decade is evaporating as I progress through my second. While there are still closed communities, there are so many open ones that you can always find someone to hash out ideas with. With twitter, you have opinion-polling on ideas that can branch out into larger discussions through blogs or online meetings. And I'm loving the regularly-scheduled podcasts/videocasts available through resources such as EdTech Talk, Classroom 2.0 and the growing Ontario Educators Meetup. While my department colleagues are excellent (they are truly amazing) they are not always present and not always interested in what I'm after. There are many people "out there", though, who are!
While I'm not a fan of avatar-based technologies (I'm me and I like me), Second Life and other sim-programs are bringing a virtual-world aspect to these conversations. I'm waiting for the web-based holodeck based on technology like FaceGen that will let me be me and engage in real-time conversations involving digital content in a CoolIris-like environment. Why not video-conferencing? Well, for one, it doesn't let you easily bring in the digital content of an applet or a video. It's a medium not an environment in the same way that chalkboard is a medium, classroom is an environment. But more on this later. For now, I want my PLN! (okay, that 80s metaphor likely dates me too.)

MapleTA

2009-03-06T22:18:00.003-05:00

With the conclusion of the algebraic portion of the MPM2D course (we only have the trigonometric unit yet to cover) the students are looking forward to their summative evaluation. We've been doing review for the past week or so through the application of what we learned in linear systems and quadratics to do the intersection of lines & parabolas and lines & circles. It's a good way to combine the substitution method, and all the aspects of factoring, quadratic formula, discriminant and using graphical methods. I've been pleased that the students transitioned to the linear-quadratic system without difficulty; they were able to anticipate the process.
As part of their preparation I've added on to our MapleTA question banks. While we have a lot of algebraic questions (factor this, CTS that, find the axis of symmetry, etc) at the suggestion of one of my students I've added on questions of the type "when you see..." Students do get confused by all the algorithms and when they need to be used. While we always stress understanding, for many of them a little bit of repetition can be helpful.

Let's pour oil on a fire

2009-03-05T12:34:00.004-05:00

Okay, so I built an assignment around this blog post: http://blog.dotphys.net/2009/02/the-price-of-a-piece-of-lego/ (as my mentor once shared: teachers are great thieves) since we were coming to March Break and just finishing up a unit on lines and data analysis. (Off topic: I use median-median lines with Grade 9 students; using the black box of LinReg just isn't in me.) They'd already written their tests and we had some time to kill. In fact, we already have students leaving for March Break today so I can't really start the Geometry unit.
I set the assignment up so that they used 4 different websites (Lego Canada, Lego US, eBay Buy-it-now and Toys-R-Us Canada) and in their groups created a shared Google Spreadsheet to put in their data. They had to find a way to organize their group so that they didn't overwrite or duplicate. From there they had to analyze the situation and come to some conclusions.
What all my wonderful planning forgot was that these were Grade 8 students (they take Grade 9 math). And I was asking them to look up Lego. Toys. Whose website is designed to bring children in. And entertain them. Chaos ensued for 10 minutes. I could have pushed on water but what is the point? I let them run amok, reliving their halcyon days when their biggest problem was when they were out of white Lego bricks... and then returned them to the work at hand.
I look forward to their results... they tend to be an imaginative group and it's been nice to post their work around our classroom. We don't get our own classrooms at the school so not many people post work up -- so, as my colleague said "You just walk in a classroom and take it over." The bare walls made things so austere and uninviting.

We're yammer'ing

2009-03-05T08:28:00.006-05:00

Well, here's hoping this works out... the IT department (unbeknownst to all of us) has had their own private twitter going on for the past couple of months using www.yammer.com. I serendipitously (maybe?) found out about it and started to invite my colleagues like mad. Hopefully this will provide the school with a conversation space in which to go over some things. Unlike most schools I've been at, this one doesn't have discussions. I mean, like, never. We have meetings, to be sure, but they are almost always uni-directional; we're told what's going on and questions are kept to a minimum as the time in which the information is pushed out to us is relatively short (yes, it's a poor model for us teachers, especially with some beginning educators in the audience). If you want to provide input to the administration, you have to make an individual appointment with the appropriate person; there is no opportunity for us to meet and talk together as a faculty. So, any discussions of instruction, assessment, technology has had to occur very slowly, incrementally, from person to person, from office to office.
Unfortunately, using tools like yammer does restrict the conversation to those willing to participate in the online environment. Like many of our classroom, there's now a discussion going on that many are unaware of. And decisions are made without hearing all the voices. Twas ever thus, I suppose.

Voicethreads

2009-03-03T22:35:00.004-05:00

Well, I think Voicethreads is a great way of offering peer feedback to student work. I used it to distribute their responses to my summative assignment on slopes & equations of lines; the final requirement in that assignment was to provide their conclusions in a creative way. Some did a very simple document, others wrote newscasts and radio interviews, there were the usual powerpoints and three students did animations.
A Voicethread lets me post them all together in a stream. Viewers can then comment on the student's work by clicking on the comment button and providing feedback (text, audio, or video). The example above shows six comments on one slide of a student's work.
Voicethreads really pulled it all together. While I do have to spend some time with the students on how to provide valuable feedback ("Good job" isn't particularly helpful) they did find few problems with the interface and were quick to notice which students had met the demands of the exercise (and the rubric) and which hadn't.
I think this is a great resource for other courses... obviously visual & dramatic arts (since it accomodates video) but also languages and the socials. I'm also thinking that importing speeches on UN topics and then having Voicethreads to critique the arguments might be useful.

Classroom Presenter

2009-03-01T21:28:00.004-05:00

One of the applications I use a lot in my Calculus class is Classroom Presenter (CP3) from the University of Washington. While my teaching style is not typically lecture oriented, because of the time constraints (I have to do PreCalculus & AP Calculus from September->April) it's a pretty teacher-centric class. To make it a bit more interactive, I use CP3.
CP3 takes your powerpoint lecture and makes it interactive with the students. While you have control over the projected image, the students can simultaneously mark up on their tablet their version of what is being projected. You can also ask them to submit their marked-up screens back to you. So, when you ask a question to the class, they can write their solutions, you can collect them all and then project the various solutions and discuss them.
How does it work? Well, it starts with a Powerpoint. I make it up to include the structure of the lecture, each slide with an idea or a question or a link or a multiple-choice task. Then, I load it in to CP3 and initiate sharing. We go through the lecture, I write notes & draw diagrams and they scribble what they find useful on their slides. Then, one slide will be a question for them to do -- they fill it in and submit it back to me for discussion. It lets me pick up on common misunderstandings or great progress. It also has a polling function which is nice for all the multiple choice questions we need for AP Calculus. The newest version now provides cut-and-paste from both my and student laptops so we can bring snapshots from other programs (and from the students' homework). There's no animation, of course -- for that I include links in CP3 to go out into the web or on to Maple.
It's a great improvement over just a powerpoint. I have used it with my Grade 9 students but I so rarely lecture that I haven't found a need for it.

I am an impatient man

2009-02-27T10:40:00.006-05:00

I admit it. I harass people who put on conferences, seminars and talks on mathematics, education and technology and then don't stream or video-archive them. Given the size of our country and the cost of travel between major and minor centres (not to mention the whole green aspect of the issue), I think it's imperative that we use video to make the audience as large as possible. For example, there's a math-education group in Canada -- they advertise really interesting seminars. To everyone in Canada. They're held over a lunch hour or in the late afternoon. So they get, what, 20 people in a room in Ottawa or Edmonton. This is so wasteful. How many more could they reach if they stuck a FlipVideo in the room with them and plunked the video down on their website?
It can't be hard to do; I've done it. NCTM in 04, MAA in 05. I didn't do it at the OAME last year because the room was so small and crowded with people there was no camera angle ... but then I also posted everything on my conference wiki (which is a whole other issue).
Now, people will say ... what about the cost? Why pay for going to the conference when I can just watch it online? Well... there's a big difference between being there and watching it live or even later. Face-to-face gives us so many opportunities that video just doesn't -- I'd much rather attend in person. But what about using a micro-payment model for the video archives? Heck, even a tip-jar. For live-streams, why not a video-attendee rate?
This issue has always been on the back burner for me (ask the poor administrator of the math-ed group mailing list) but Educon 2.1 really made it clear for me. If I'm going to a conference physically, I want to make sure that people who aren't as lucky as I am can get in on it, too!

Why I hate Sharepoint (reason #3)

2009-02-24T08:26:00.003-05:00

I have given up on Sharepoint but school policy says I have to provide a link to my new resource. As it happens, there is no Webpart that allows me to quickly create a link. I can make an IFRAME and put the webpage inside it but I can't just put up a quick link!
I have to go to ALL SITE CONTENT and then create a Link List. And then in the Link List, I have to create a link entry.
I admit... I'm a self-admitted IT professional. I've been programming for more than 20 years. This process should be dead-obvious for the user. Look! An "add a link" button right on the main page's edit toolbar. But no, I have to dig, dig, dig to do anything.
Funny item: when I introduced our new wiki to the kids, one of them wistfully said "I miss Blackboard." Never thought I'd hear that but Sharepoint has had such a poor implementation that I can't blame them. They promised so much and the potential is certainly there... but someone needs to sit down with teachers. Watch how they use their computers. Watch how they organize information (and why they organize it this way). A course management system is not a business intranet. Or maybe business intranets are poorly organized, too?
As one of my bloglist mentioned about me the other day: Little bitter?

Google Docs and Box.Net

2009-02-20T00:35:00.000-05:00

So far, so good. Fingers crossed. Wood knocked.

I've massaged Google Docs into the Grade 8s and the Model UN club; at this rate I'll have about 20% of the school covered by the end of the month. I'm slowly trying to win the school over. Already one of the social teachers noted my use of it with MUN kids: they are writing scripts/storyboards for some videos so I set up a template and shared a document with each group so they could work simultaneously.

It also helps for evaluation. After working to keep this one student on task ("no, Johnny, watching anime on YouTube is not helping your script on the issues surrounding prosecuting peacekeepers on criminal charges"), I sat him down at the end of club and showed him the history for his group's document. He had made one change compared to the huge list of his teammates.

As for the Grade 8s, I set an assignment in GoogleDocs with links to the rubric which was in another GD. What was nice is that they pointed out a structural error in the assignment that I hadn't noticed (the author is always too close to the object) and I went in, changed it and it was automatically refreshed for them. Once their wiki is finalized this will all fit in quite nicely.

My only problem thus far is where to store the OneNote files for my classes. Teaching math on a tablet is a great environment but it limits me really to OneNote for students' written exercises. And they are not pleasant to move around. They tend to be large files so I'm a little afraid of running up against Box.Net's storage & transfer limits (the school will not be interested in paying for any fees). I really like the way the widget works on the wiki except that when you click the OneNote it defaults to save with no option to just open the thing in OneNote. Sigh. The problems.

Finally

2009-02-18T10:02:00.000-05:00

Okay.. it's taken me since September but this was the first math class of my Grade 9s where I was convinced that they 'got it'. Not in terms of the math content; these kids are pretty bright. But rather in terms of how one learns math, how they collaborate, share, discuss, conjecture, disagree, check, etc. It was amazing. And, as we were closing down, they made commentary that showed they noticed it too. Finally. I'm recording this so that when it doesn't work, I'll remember. And when a parent complains that I'm not "teaching" because I didn't tell them what to do, I'll have a happy place to go to :)

Why Smartboards?

2009-02-16T16:30:00.001-05:00

I really have to question the continued emphasis on Smartboards... if you're a teacher (well, high school teacher at least) I'd strongly recommend you consider investing in a good tablet PC and wireless projector. For the price of the Smartboard, you could likely pick up a couple more tablets or a lot more netbooks and using just the wireless projector you can collaborate with your students. There's also some nice collaborative software out there (I use Classroom Presenter from UWashington).

Much like the over-emphasis on the TI (you could outfit a class with netbooks) the bandwagon that the Smartboards are driving is causing schools to waste a lot of money that could be much better spent. At our school, which have had Smartboards for 8 years, every classroom is outfitted with one. And number of them being used? Maybe 5%. Maybe...

What a beautiful day...

2009-02-10T14:39:00.000-05:00

One thing LiveJournal has is a nice space to automatically put the music you're listening to... here I have to do it manually... U2, Beautiful Day.
Anyways... what makes it s0?
1) 10C, rain in the morning... means riding the motorcycle later this afternoon & tomorrow!
Oh, but then there's the professional part
2) The contractor was late this morning, so I was 5 minutes late arriving to class; my grade 9s were working away. Sure, some of them were discussing soccer's latest news but they were seated with their work open. What kids!
3) The same MPM2D; we're finishing up the unit on parabolas and quadratics and the like. I gave them four different quadratic curves, different concavities, one just with one arm of the parabola, one with a series of parabola. They have to come up with questions involving those graphs and all the content we had this unit. The questions are turning out to be great -- I'll post some up here once they hand them in but for sure they're going to be used in the future. They're pulling everything together and some are even bringing in Linear Systems from the Fall, too.
4) Towards the end of class, I interrupted them and pulled up the graph CalculatedRisk posted about last night - huge discussion ensued about real data, parabolas, economics, politics and the like. And using mathematics to make predictions and provide analysis. Given that these are accelerated Grade 9s, most of whom have trust funds of some kind, they all have considerable interest in the economy. I figure I'll spend Family Day planning some kind of summative with this -- Maple, here we come!
We also discovered that all the recent recession has seen me have a life change (81/82 start high school, 91/92 graduate university, 2001 start at this school).
2) AP Calculus - I will be away in DC for the NCTM conference in April for the entire week. This sucks, of course, for a class that meets 6 times a week. So, having been to Educon and seeing it in action I've begun playing with Mogulus video in my class. Well, the first time live it worked amazingly well! It means I have to have a lot of stuff preplanned and use BBFlashback to create my example videos beforehand but wow, what potential. It's a different style of teaching than what I normally do but it's better than a week of substitutes.

Google Docs

2009-02-05T17:19:00.000-05:00

So I've been playing a bit with Google docs in a few classes...
1) Grade 8s. A communal document for review... I distributed review questions to each student and they wrote out the solutions in OneNote and clipped them into our Google Doc for everyone to see. I used the comment tool to mark it up.
I could have used a wiki, but havent finished the setup yet. Small steps with my kids. But our IT director has made a public statement that we can start using other resources and we're not tied to the (lamentable) Sharepoint.
2) The aforementioned Sharepoint will not allow us to synchronize OneNote notebooks (for reasons no one can figure out) so in order to look at their homework electronically, I had my AP Calculus students clip their hw into a Google Doc. One concerns... it's not a click-click exercise since Google Docs don't allow access to the clipboard. The Grade 8s mentioned this as well. *I should try this with Zoho to see if that'll work!

I've also set up Google Latitude... waiting to see if I have a stalker! :)

Putting MapleTA into Wikispaces

2009-01-30T19:31:00.002-05:00

Having looked through the posts on Maple Primes, I found a suggestion to insert MapleTA assignments into webpages. So, I flipped over to Wikispaces and tried it out. A little bit of detective work on the page locations, I got it to work.

Since you can set MapleTA assignments to be anonymous, MapleTA will merely produced the questions and not record anything in the gradebook. Using the EMBED tool and the code below students can practice at whim:
Remember of course, to change the square brackets to the corresponding angle brackets!

[IFRAME SRC="http://server/mapleta/modules/test.Test?className=classname&testName=testname" TITLE="MapleTA" WIDTH='100%' HEIGHT=600][/IFRAME]

This follows closely on the heels of embedding GeoGebra into Wikispaces:

[applet name="ggbApplet" code="geogebra.GeoGebraApplet" archive="geogebra.jar" codebase="http://www.geogebra.org/webstart/3.2/" width="884" height="612" id="ggbApplet"]
[param name="filename" value="http://wikiname.wikispaces.com/file/view/yourfile.ggb"]
[/applet]

You first have to upload the yourfile.ggb to your Wikispaces, then embed the code using their widget button. You can change the width and height values and you have to change the YOURFILE name but that's about it.

This opens up a lot of interesting possibilities and I'm hoping it will encourage a lot more sharing.
I'm switching everything in my courses to Wikispaces this weekend and we'll see how much I can stuff in!

Opening up things a bit

2009-01-30T19:29:00.001-05:00

Having come back from Educon 2.1 I realize that I have to be (far) more collaborative. Not my nature being an introvert but, having tried to blog every year for the past 10 years, I'll try again. Since I can't always talk about CAS, I've opened this up a bit and we'll just look at anything (mathematics U education U technology) that crosses my desk. It'll also help me avoid filling up my colleagues' mailboxes.

A little off topic

2008-10-27T21:51:00.000-04:00

MathML Strengthens Digital Math Texts
Digital texts are moving beyond simply putting pages on a computer screen.
In Kentucky, a small pilot study is demonstrating the benefits of this textbook technology for students with different learning styles. Instead of re-creating a complex math problem as a static image file, digital texts that use math markup language, or MathML, are able to speak words and equations while highlighting corresponding elements on a computer screen.
MathML-enabled digital texts helped the study's very small cohort of students struggling with printed text outperform peers who used traditional print texts. Many students said that before MathML, they'd see a problem but not know how to say it. Hearing the formula and how to say it was a big help to these students.

From ASCD http://ascd.typepad.com/blog/2008/10/mathml-strengthens-digital-math-texts.html

The fence question

2008-10-22T10:06:00.001-04:00

So I assigned the classic fence-against-the-river question to my group (you have 200m of fencing, what's the largest rectangular area you can contain where one side is not needed against the river). We had just started quadratics so they have no real background in it at all. One student solved it thusly:

1) He made a table of values for a few fences:

Then, he turned to Maple. We had done a unit on linear systems and did a few questions on finding lines of best fit... so he used the Curve Fitting Tool to find the best fit parabola, then found the vertex of the parabola and hence the best area.

Then he found the vertex of the parabola by zooming:

Almost every other student did it the traditional way of setting up the equation, graphing and finding the vertex. I thought it was a nice bit of synthesis from the previous unit to approach it in this fashion!

So a little further

2008-10-20T12:45:00.000-04:00

Well, we're into quadratics now. The one section is doing really well incorporating Maple into their learning process -- they fluidly jump back and forth between Maple & OneNote. The other class more stubbornly holds on to doing everything by hand/calculator. I keep struggling to move this section to a more exploratory model but they will have none of it.

Maple still perplexes us from time-to-time... the switching between independent & dependent variables based upon alphabetical order is one of the more irritating ones. It will graph it in the desired order but as soon as you change the window (axes, zoom, etc) it switches the order! I've gotten around it by choosing my variables appropriately but when they experiment the students don't always think to (nor should they have to).

Variables

2008-10-14T10:35:00.001-04:00

Well, we've used the Curve Fitting Tool for the past couple of classes. Lesson learned: it's best to be descriptive in your variables because using x and y is not conducive to the CFT (it wants to use x as the regression variable).
We're on to quadratics now; I wish the spreadsheet tool was a little more flexible than it is and followed Excel notation ... having to add the tilde before the cell reference is clumsy. I also wonder if there's a way to have the column filled by a list variable?
Oh... and results on the survey coming up.

The test

2008-10-08T08:45:00.000-04:00

Things that immediately pops up....
Having them able to use the TEXT to describe their variables and present their solutions neatly. We focused so much on the math work that I didn't do enough on using the text component to explain the setup and solution. Sigh.... only so many hours in a class is one excuse, but it is an excuse, I should have done it. Goal for the next unit.
And another thing... having them use the HELP function in case they got stuck during a test.
They are also spending a long time (relatively speaking) per question on the Maple as opposed to the written portion. They finished up the written part (3 algebraic solutions, 1 graphical, 2 analysis questions) in about a half hour, then took another half hour to finish up 1 graphical & 1 algebraic question in Maple. Something is up there... going to survey them to see what they thought.

Leading by the nose? Or breaking a path?

2008-10-01T18:58:00.000-04:00

Well, we did a bit of direct instruction (not Direct Instruction, which is completely different... kinda like variables in poorly designed programming languages) where, in order to lead them through using Maple to get a least squares line for a set of data, I had to go through with them step-by-step. For one, I didn't plan enough time to write out instructions & film them ... 2nd, I wanted to be able to discuss WHY we were doing each step with the students.

It went VERY well... in fact, I had a number of students say "I really like using Maple" and most were actively engaged. I did have one student get frustrated and say "I hate Maple" but a caveat: he's not the most focused student and tends to make sloppy errors. His adjacent seatmate helped him make corrections.

They also wanted to experiment a bit... one student didn't want to write all the years 1989-1992 so wanted to write that Year:=1989..1992. I said there was a way to do that so I'll have to work that idea in later.

I'm really hoping that they are open to experimentation... they seem okay with the "button pushing" process but, of course, I really want them to focus on mathematics problem solving.

And they find another one...

2008-09-20T17:26:00.000-04:00

Well, we've been graphing now pretty successfully.... when we get to this simple little example:
d = 230t
d = 200t+170.
Plot the first, drag the second on to the grid, no problem. Then, we try to zoom/translate to approximate the intersection's location.
Well, Maple decides that we aren't going to get it. When you don't use x/y as your independent/dependent variables, then even when you specify an implicit plot of t/d, as soon as you do any manipulation Maple reverts the graph to d/t. In fact, regardless of your initial setting of independent/dependent variables as soon as you use the zoom or translate tool Maple resets the variables in alphabetical order.
So... I was warned through research that using a CAS system would require better understanding of mathematical expressions and their equality. I just didn't expect to have to deal with Maple's idiosyncracies (or is it errors?). In the future, I guess my variables will be in the correct order... I wonder if the students will notice?

2nd foray

2008-09-18T08:28:00.000-04:00

Having done graphing with Maple the other day, we worked a little bit with solving systems of equations by substitution. One of the students mentioned that instead of assigning names by typing "L1:=y=3x+2" you could avoid the first equal sign and just use a colon.
Well, that was okay for graphing, since you just right-clicked and chose plot. However, it doesn't work because the assignment to L1 isn't made, so when you tried to do a substitution into L1, it didn't exist.
Some of the students in the 2nd section had a challenge with the 2nd line they dropped on to the graph only had domain -10 to 10... wasn't sure why that was happening.
The second section does algebra on Friday ... and we'll do more algebra with it next week!

Dipping a toe in...

2008-09-16T11:46:00.000-04:00

Okay... well we made an attempt at Maple 12 today... just a brief introduction to graphing. I deliberately did it by assigning names to the equations
L1:=y=3x+2
Then I chose to have them graph it implicitly. I'm trying to plan ahead here, so that I can use the names of the equations when they start to solve algebraically by elimination.

Unfortunately, Sharepoint requires them to download and save the file and THEN open it ... it won't open directly :(

So it starts...

2008-09-07T23:29:00.000-04:00

It begins tomorrow. Well, actually, it doesn't because the students don't have their laptops tomorrow so we will just do a "welcome back to school, I'm your teacher, here's a little activity" without involving any technology.
So it will actually start on Tuesday. I'm hoping to get the permission forms approved by admin by then so they can get home, signed & returned by next Monday. Then I can formally start recording observations! In the meantime we'll introduce Maple 12 and see how it goes. More, much more, to come.

Out to the students

2008-09-03T09:32:00.000-04:00

We've distributed out to the students instructions on how to install Maple on their laptop before they arrive in class. Normally (and in the future, one hopes) this will be part of the tablet image that goes on to the computer before the student receives it or gets repaired but the IT department has been swamped. The process is easy (agree to everything, basically) but it does take about 20 minutes.
One of the big concerns with Maple is that it is a huge program; it takes about 30 seconds to get up and running. One wishes that there was some kind of staged loading, so that it would pop up immediately and then bring in things over time. The context menu pops up rather slowly, too, but much faster than previous version. If we're going to make the change so that this is the mathematical scratchpad then the faster things are, the less chance the tech gets in the way of student problem solving.

Workshop day

2008-08-25T21:47:00.000-04:00

So we had our workshop today... not bad, six teachers, so that's half the department. Two others were working at school and couldn't make it. A good four hour session with a pro-user who's also a teacher. While he didn't cover a lot of the fundamental stuff or get into all the changes in the user interface that Maple 12 has, he did keep up with most of our teachers (we're an agressive bunch when it comes to learner... doctors making the worst patients and all). There was a nice bit of work done with programming and question construction. Hopefully things will come of it... we discussed a lot of classroom issues while we were learning Maple. Now I have to have some serious stuff ready for next week!

Maple 12 Interface

2008-08-19T15:47:00.001-04:00

One of the reasons we've decided to jump into this CAS process at this point in time is that the new interface is far more student-friendly. We were loath to start with a CAS when the learning curve would be so great. While I know that some would say that the TI is a possibility, it's short-sighted; no one uses the TI software/handhelds beyond highschool. And the hand-helds are a button-intensive, small screen mess. It's a toss-up between Maple and Mathematica - and we have an existing relationship with Maple (it's HQ is down the road an hour).
The interface is now far more point & click with no (okay, few) arcane (to students) commands and it describes the step that has been performs.
Graphing is a lot easier (you can drag an expression onto a grid and it graphs!) and parameters can be automated with a click.
That, of course, is the easy part done. Now, the hard part:

what questions do we ask to develop understanding, concepts, algorithms?
how do we encourage exploration over presentation?
how do we avoid an emphasis on calculation/algorithm/button pushing? This can't be just "better worksheets through CAS"
how do we make the link between paper-pencil and CAS techniques?
how do we strength understanding of equivalence (since CAS' representations differ)?
how do we deal with the time factor? (student-centred takes more time)?
are our teachers ready to deal with the mathematical conversation that will/should occur?

Day -26

2008-08-12T09:54:00.000-04:00

Just doing some preliminary setup for storing and sharing information on our project... the Drexel courses I've been taking on (Action) Research have been helpful in doing a lot of the preliminary readings (see sidebar for some good references). I'm also trying to work on the Sharepoint site... it may already be time to throw in the towel on that and just use a wiki. I'd much prefer the wiki anyways just because of the ease of use (for me and other users), accessibility (are our Sharepoint sites available to outside users?) and my own personal philosophy.