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

Posted by
Cal Armstrong

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 ...

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 ...

Labels:
Assessment,
Homework,
Jing,
Video

### I think I want to SMAK my kids

Posted by
Cal Armstrong

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

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.

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.

Labels:
Assessment,
Evaluation,
Grade 10,
Grade 9,
Mathematics,
Video

### Social Technology & Education @ Harvard

Posted by
Cal Armstrong

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.

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

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.

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

### Working Groups

Posted by
Cal Armstrong

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.

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

Posted by
Cal Armstrong

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:

_________

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

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 up

^{1}. 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._________

^{1}I 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

Labels:
Educators,
Math,
Mathematics education,
PCMI,
Pedagogy,
Professional development,
questions

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