Aren’t infinite geometric series cool? If you just shouted “yes”, then you are potentially as geeky as I am. A “proof without words” from MathFail kicked off today’s discussion:
I wasn’t quite sure what sort of observations I would receive from my class. But just enough ideas were generated to get us going:
There are an infinite number of triangles down the right side.
All those triangles on the right add up to the half-triangle on the left.
Both are great starts for what I hope my students will learn today. A video I made in my driveway continued the ideas of geometric series and their infinite terms.
A few students wanted to argue that the sequence in the video was arithmetic, but some meaningful debate yielded agreement that geometric made more sense. Groups then worked through a similar problem involving a Superball being dropped, leading to terms and total distance traveled.
Many groups employed a “brute force” method to find their answers. Using the Desmos calculator (many students chose to use the iPhone app), we found value in developing the equation and using tables and summation symbols to find solutions. This was my first time usign Desmos with this particular lesson, and it was an awesome addition, which added value to the need for writing a clear function to define your situation.
I love checking my blog stats. Above are just some of the many search terms which cause people to end up here on the blog. You search, I listen. Armed with Camtasia (provided by my friend and barbecue savant Jason Valade from TechSmith) here is a tutorial I hope you find helpful as you start your school year. Resolve to make Desmos part of your classroom culture this year, then check out the Desmos File Cabinet of graphs to get you started. Also, check out classroom strategies for using Desmos to explore function inequalities in the second video below.
Last weekend, I had the oppotunity to speak at the Association of Mathematics Teachers of New Jersey Technology Conference on my experiences with Desmos, where I shared a number of the Desmos activities and ideas I have posted here on the blog. Conference speaking and classroom direct instruction are totally different experiences. There a few things I need to think about in preparing for a conference which aren’t part of my daily routine:
How many people will there be? Conference sessions are mini-popularity contests…I may have 5 people in the room, I may have 50. You just never quite know what to prepare for. Small groups are great for encouraging discussions. Larger groups have a difference set of engagement challenges.
What’s the overall background of the room? People who will come to see me could be a mix of veteran and new teachers, with different stories to share, and levels of comfort with my topic. Taking the temperature of a room quickly and finding a baseline comfort zone is key.
Do I really know what the heck I am talking about? I’ve offered to present because I feel I have something to share; but is my message unique or helpful? Could there be someone in the room who knows far more about this topic than I do?
It can be a stressful experience presenting in front of peers, but also highly rewarding and a great way to make professional contacts!
Overall, I feel my session went quite well. After all of the stragglers found their way inside, there was a full house (or lab) of about 35 folks, with a positive vibe in the room. I think I met all of my goals, and I believe many left the session with tangible ideas for their classroom, and ideas to share with colleagues. If I accomplished all that, then I feel successful.
For this speaking opportunity, I borrowed some equipment and recorded my talk, something I had never done before (see video below). Upon review, there is a common theme running through the talk which has cause some post-talk reflection for me. A few times I ask the group about their experiences with online tools, with some (to me) surprising results from the room of 30-35:
Only 1 or 2 had used Desmos before.
Only one had used Geogebra before.
Only one had heard of Edmodo before.
How could this be? Here was a group of enthusiastic educators, concerned enough about their craft that they sought out professional development on a Saturday, and very few knew about these tools. Is this small sample group indicative of all math teachers? Should I be as surprised as I seemed in the video (really…watch my expression when I ask about Edmodo)? The good news is that hopefully some exponential growth occurs, and these teachers tell their colleagues, who then share with their colleagues…and so on….
But what of those teachers who do not seek out conferneces? How do they find new resources? Or are they even looking? Do teachers have a professional responsibility to seek ro revise their ideas and practices? I won’t pretend to have any answers in this blog post; rather I’d be eager to hear some thoughts on these questions from my readers.
And while my session has a clear technology slant, does the variation in learning experiences extend to math pedagogy in general? Can teachers defend their classroom practices, and seek our resources for revision if needed? How many teachers have considered how Common Core shifts will effect their classroom structures? Have teachers considered the Standards for Mathematical Practices and how they apply to their classrooms? Where do teachers go to find professional development opportunities which meet their unique needs?
And, most importantly, what are the responsibilities of classroom teachers, curriculum specialists and administrators in facilitating these reflections? It’s a lot to chew on.
Below is video of my Desmos session. Seeing myself on camera is at the same time cringe-worthy and thrilling…so much to learn from. Man, do I gesture with my hands…. a lot! Feel free to comment, share or heckle!