Continuous formation

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 C...

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 ...

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 c...

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 ...

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'v e 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 lit...

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...

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 de...

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...

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 spri...

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 a...

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 com...

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: P...

The English language continues to evolve -- jing is now a noun and a verb as far as my students are concer ned. 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 ...

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 ...

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 ...

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 recei...

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...

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 con...

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...

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 listen...

Well, my public challenge to my students two months ago worked... I got hooked on dr inking 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...

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 th...

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 t...

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 ...

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. S...

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 ...

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-choi...

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 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 wi...

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 pointe...

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 :)

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...

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...