Tag Archives: educational transformation

Creating tesselations with 6th graders and Geometer’s Sketchpad


Katie Hildebrandt (6th grade math teacher) and I just finished a 2-day unit on Tessellations using Geometer’s Sketchpad to rotate an equilateral triangle and translate a parallelogram. I can’t praise Geometer’s Sketchpad (sometimes shortened to Geo Sketchpad, GSP, or simply Sketchpad) enough. It is one of the few pieces of educational software out there that is entirely constructivist. You can actually learn math by using GSP. Just like classical Euclidean Geomtetry breaks down everything in the world to points, lines, and planes, so does GSP; You can quickly learn to construct, animate, and measure a range of sketches, from the simple to the complex.

In this brief unit, we verbally discussed how a vector is a geometric object (in this case, a segment) that has both a direction and distance. They notice the “di” in the beginning of each word. I also tell them that translating is the same as sliding, and both words have an “sl”. We talked about angles of rotation, indications of symmetry, interior angles of a triangle, and reinforced vocabulary: equiangular, equilateral, congruent, parallel lines, etc.

I always start off by showing them works by M.C. Escher. On the site, there is a link to a gallery of his symmetry drawings. I marvel at how Escher painstakingly drew his incredibly intricate and fascinating tesselations component by component. I imagine his pile of pencil stubs and eraser shavings, and reinforce for the kids how we can create infinite variations with GSP in a matter of seconds by clicking and dragging.


I posted something about last year’s activity here.

There is a great PDF with multiple activities put out by Key Curriculum Press (@keypress) embedded below or you can click here to download it. We use pages 7-8 for the translation activity and pages 9-10 for the rotation activity.

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Education Think Tank hosted by @DellEdu today

Google Doc from Education Think Tank
Livestream/photos from Education Think Tank
Eventbrite description of Education Think Tank
#DoMoreEdu Twitter hashtag
So, it was a great experience to be at a roundtable with many people I know and respect from the education world. I felt conspicuous as one of the few teachers in the room (and from an independent school no less). I also felt like a rabble-rouser, as I stated early-ish that in my opinion technology is really about engineering and robotics and programming, whereas much of what we were discussing was social media usage and new media literacies. (Just last week, I presented about this at PNAIS, citing Henry Jenkins‘s new media literacy skills)

However, everyone in the room understood that students need access to a plethora of devices and online resources, teachers need to be enabled to promote sound technology integration, and school leaders need to offer opportunities for collaboration and effective professional development while marketing their best practices/successes for a wider audience. Below are the topics touched upon today:

  •  How can technology serve to transform teaching and learning? When we say “educational transformation”, what does that mean and how do we get there?
  •  How do we increase access to technology and make it a priority in Districts to maximize learning?  Are 1:1 environments attainable?  If so how? Where does equity fit in?
  • What does personalized learning look like and how can it be established? How do we move Districts, educators, and other stakeholders to embrace this concept both in and out of school?
  • What is, or should be, the role of social media in education/the classroom and how can it be utilized for professional development?
  • How do we engage school leaders in a conversation about the important role of technology and social media in education?  How do administrators support innovation in the age of accountability?

At the risk of leaving anyone out, present around the table today were: @NMHS_Principal (moderator), @tomwhitby, @InnovativeEdu, @adambellow, @Edu_Traveler (a parent at @The_School), @kenroyal, @drbpchinni, @erikendress, @timeoutdad, @agarry22, @kishizuka, @kjarrett, @MichLampinen, @teach2connect, @snowwhiteatdell, @paulallison, @susanmcp1 , @PMicheleGlaze, and @SpecialKRB (me).

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