Reflections on EARCOS Teachers Conference 2012 – Friday

I decided to use a few digital tools to record my thoughts at the EARCOS conference. At other workshops, I tend to take notes on paper, leave them in a folder, and possibly go back to them when inspiration hits, if I remember I have them. Since I am on my computer so much of the time (and NOT digging around in a filing cabinet to see what is in there) I think this will keep the ideas from this conference fresh and nearby.

I attended a few fantastic workshops Friday and tweeted extensively about each one as important ideas came up. The #earcos12 archive and search function will be really useful for going back and reminding myself of the ideas that came to mind during those workshops.

Workshop 1 – The Geometer’s Sketchpad Workshop: Beyond Geometry with Nicholas Jackiw

It was really a treat hearing the person that defined dynamic geometry talk about the philosophy of his software that implements the model. Having learned mathematics using GSP back in 9th grade, I’ve always seen the dynamic geometry as a natural lens through which geometric concepts can be viewed. Nick mentioned that mathematicians initially had a problem with the concept because two triangles with vertices A,B, and C that aren’t congruent are not the same. Since dynamic geometry defines triangles in terms of the relationships of vertices, two triangles with the same vertices connected in the same way represent the same geometric object. This means that any triangle ABC can be turned into any other triangle ABC just by dragging vertices around the screen.

We went through the basics of plotting points, lines, and measuring slope using the tools of Geometer’s Sketchpad. I hadn’t used it for a while, but it still remains a great program. Nick is a genuine guy with a love for mathematics and what his software can do for students learning concepts. He has a solid grasp and had some great activities that could be used for students to actively learn concepts through exploration rather than listening to a teacher go through a list of boring definitions.

I had the pleasure of sharing with Nick that I used Geometer’s Sketchpad to use geometry in ninth grade and that I still had print outs of the assignments I did using the software. Back then we printed out computer assignments and turned them in, much different from today when turning things in electronically is quite easy. I was a little star-struck talking to him, but as with most good teachers I meet, he was really friendly and appreciative of my comments.

Workshop 2 – The Harkness Method: The Best Class You Never Taught – Alexis Wiggins

One of the things I want help doing is improving the quality of classroom discussions. The shelf life of the discussions we have isn’t much longer than the class period itself. I have been able to extend that a bit having students create wiki pages, interact onor create videos describing their understanding of problems.

I think this workshop provided a real possibility for restructuring my class to do this far more effectively.

Alexis shared how the Harkness method (originated at Exeter Academy) has transformed her classroom and itneraction with students. Students spend class time discussing, arguing, and critiquing arguments. In the process, they learn extensively how to be good community members, be constructive in their criticism, and communicate their ideas. She shrewdly hooked us math/science teachers at the beginning (why are we always the cynics?) by sharing that Exeter does this in their math department. Alexis also shared that she does need to do direct instruction once in a while – her ratio is around 60% discussion, 40% other methods. She also does not do this for the entire class period, particularly for the younger (9th grade) students. Modeling the process and explicitly teaching students skills that make this successful in her room is a key part of her process. She made clear that it takes time to get them to be good at it.

Alexis posted her materials at

Workshop 3 – Rules of Engagement – Using Technologies to Motivate Rather than Distract – Doug Johnson

We are constantly having discussions at our school (which is 1:1 Macbooks) about how to maximize student time on task during class – I think this is something almost everyone in schools is currently battling. The presence of technology has so many potential positive applications for learning. It is easy, however, to fixate on the negative aspects almost entirely and stall the process of making these potential benefits available to students in the classroom.

Along with having one of the most useful handouts I’ve ever received at a workshop, Doug Johnson made a number of fantastically relevant points about how school communities can think about the issue. The question he posed at the beginning was “How do teachers compete w/ tablets, smart phones, netbooks, mp3 players, portable games, etc?” What I found most interesting throughout was that he showed how it didn’t need to be a competition. Instead teachers can capitalize on the opportunity

His emphasis on the distinction between entertainment and engagement really resonated with me, as I always wonder if the activities I do with my students are actually helping them learn or not. We then worked together to identify ways to make technology an active part of classroom activities, including a lot of modeling using and references to other similar sites such as

Doug’s presentations can all be found at

Workshop 4 – Digital Citizenship: The Forgotten Fundamental Kim Cofino

This workshop from the excellent Kim Cofino was a perfect pairing with Doug’s workshop and a good ending point for the day. She clearly described her process at the Yokohama International School of rolling out (all at once, which she said was the best idea ever) her 1:1 laptop program with students.

The most important takeaway was how much deliberate planning and community collaboration went into not only creating the acceptable use policy but actively sharing that philosophy with the students, teachers, and parents. The school year started with two days of 1:1 boot camp activities – students discussing and debating different aspects of the policy. She also mentioned that the students will soon repeat some elements of this training and discussion now that the community has been through several months of living out the policy.

An important element of this is that students are explicitly taught and engaged in activities that teach them digital citizenship. She made clear that this does not happen by accident, or by hoping that students will know how to act when they are suddenly given the power afforded them by technology. This is one of the key things I will be taking back with me to Hangzhou.

Her presentation and resources can be found at


This has been a really fantastic experience being at the conference this year – I am learning so much at the workshops and through meeting the incredible collection of teachers here. I appreciate that everyone has been so positive and open in sharing their work and ideas with me. I admit it – I’m addicted to this conference atmosphere. Thankfully, I’ll be able to keep in touch with the people I have met here, and continue learning from them well after I have left Bangkok.

EARCOS 2012 Presentation – Using Geogebra for Skill Development

After a late night getting into Bangkok and a couple hours of sleep (though I suppose few good stories start “I had a good long night of sleep when I first arrived in Thailand) I made it to the start of the EARCOS 2012 Teachers’ conference yesterday morning. I’ll have more to say about the details of the conference later on, but I wanted to post briefly about the presentation I gave on Geogebra in the afternoon.

The room was packed with teachers and coaches armed with laptops and interested in seeing how the program works. My focus was on giving feedback, with Geogebra as the medium for that feedback. I did not intend it to be a beginner’s tutorial on Geogebra for a few reasons:

  • There is so much fantastic material out there already that shows how to use the software.
  • I wanted to specifically focus on the philosophy of using software to provide instant feedback to students on mathematical tasks.
  • Nick Jankiw from Geometers Sketchpad was doing a series of workshops on GSP and I didn’t want to engage in the Geometers Sketchpad vs. Geogebra debate. I see them both as excellent pieces of software. I choose to use Geogebra for a number of reasons that I mentioned in my presentation. The truth is that Geometers Sketchpad defined the field of dynamic geometry, and I do think it’s important to acknowledge that fact.
That said, anyone that wants help getting started with Geogebra should feel free to ask me for help. Thanks to a great suggestion from John Burk (@occam98) and Andy Rundquist (@arundquist) I had some screencasts demonstrating more advanced sketches of my own playing on the screen while waiting for the program to download and while figuring out the basics.
I thought the workshop went well  – I wish I had not felt the need to talk so much and had given more time for people to interact with each other. That said, I think there were many that came and left with much more knowledge than when they entered. A few told me that they already plan to use it next week in their classes.

My slides and accompanying notes can be found here: EARCOS presentation – notes pages

The video is below – unfortunately there wasn’t a great place to put the camera to be able to get me and the slides, and the contrast is not great to be able to see what I am doing in the program. I’ll find some time to post some screencasts of the demonstrations I did with the software later on.