I recently found out that I was accepted to be a presenter at the July 11-12 GAFE conference in Palo Alto. For those not living in the instructional technology acronym world, GAFE stands for Google Apps For Education. I attended a GAFE Conference in Templeton, CA in March and was shocked to learn that there weren’t any sessions on math topics. I immediately contacted the organizers of California GAFE and offered to lead a session on something mathy. I’ve got about a month to decide what ideas will make the cut for the session. Today I learned that I was assigned the final hour of the final day of the conference. I think that’s a bit like giving the new hire the most challenging kids and 4 preps to teach, hoping they won’t notice. Hopefully it won’t also be 100 degrees out at 4pm in Palo Alto in July.
Speaking of weather, today in Berkeley it rained all day. It never rains in June. So on this rainy day, I stopped by my old classroom as the teacher who currently teaches in it took a new job and I wanted to see if there were any of my things still there that I should retrieve. Tucked away on a dusty shelf I found Michael Serra’s Patty Paper Geometry book. I am a big fan of folding patty paper and would never suggest eliminating it from courses which already use it. However, I am also a big fan of instructional technology. When I was a classroom teacher (just a mere 730 days ago) I was a big fan of creating my own activities which strayed from the adopoted curriculum, yet met the same academic goals. But now as I finish my second year as a Teacher on Special Assignment for Instructional Technology, I am an even bigger fan of fan of finding ways to use instructional technology which don’t require writing your own curriculum. My successes in supporting teachers to use more technology have been when they can use the same curriculum they are already using, but find ways to use technology to deepen engagement and understanding. This feels sustainable.
Which is why I was excited to rediscover Serra’s book on paper folding. Nearly every activity can be done using GeoGebra in addition to or instead of using patty paper. So on a given day, you could divide your class and have 1/2 do the paper folding and 1/2 use Geogebra and compare what they came up with. Or if you have only a few computers, you can have kids in groups of 4 where two are paper folding and two are paired up on a computer, discovering the same big ideas and coming together to discuss.
For example, here is an investigation from Serra’s book:
STEP 2: Draw a ray from the dot to an edge of your patty paper. This will be the direction of the translation.
STEP 3: Place a second dot on the ray. The distance from the first dot to the second dot will be the translation distance.
Take a second patty paper over the first, and trace the figure, the interior dot, and the ray. Slide the second patty paper along the path of the ray until the dot on the tracing is over the second dot on the original. In GeoGebra these steps are eliminated as you can use the translate button and complete this in 1 click. You do, though, discover that you have to make a vector, not a ray in order for the computer to know what you are talking about.
STEP 6: Measure the distance between a point in the original shape and its corresponding point in the translated image. Try this with another pair of corresponding points. Write a conjecture about the distance between a point and its image under a translation transformation.
Transformations used to not be introduced until Geometry, but they are now found in CCSS 8. I used a lot of patty paper when I taught geometry, but I also used a lot of GeoGebra. Patty paper allows for more physical discovery and manipulation with your hands lends itself to imprinting ideas in your brain. In GeoGebra, the ease of tinkering with dynamic objects, the precision of your constructions, along with color coding to highlight key concepts is equally as important.
Both Desmos and GeoGebra are now found in the Chrome Store meaning you can get them to appear in your Google Drive. Your technology department can also put them in all students’ drives in a domain. In my district, for example, all students have Desmos and GeoGebra in their drive, even if they have never used them before. However each of these programs save and share work as URLs, which isn’t as work-flow friendly as the standard Google Drive apps. To get around this, having students take screenshots of their work and dump it into Drive allows you to use Google Classroom with these math applications.