I have just returned from San Francisco, where I had the opportunity to interact and collaborate with other amazing teachers over a technology tool that I love - Desmos. It will likely take me quite a while to wrap my head around the ideas that were percolating at Desmos headquarters on Howard Street during that 48 hours. After a nap on my first plane back east, I started to piece together ideas for an activity builder lesson. But then that lesson morphed into some general ideas and half-formed thoughts related to teaching that I will share below.

So, now you may be wondering why use desmos at all? If the shoe doesn't fit, why bother trying to wear it? When a lesson is constructed correctly, it gives students an opportunity to learn mathematics in the way mathematicians create mathematics. Testing conjectures, making mistakes and failing is a natural part of the learning process. We (many of the math classrooms in the United States) have put learning of mathematics in a sterile environment by removing the opportunity for students to experiment and learn from their mistakes. Instead of giving students the opportunity to construct knowledge for themselves, we tell them the big idea and then drill them with repetition, expecting the repetition to somehow compensate for the sterile learning environment that was created. With correctly constructed lessons, students can be given the opportunity to learn from each other and create understanding. With a Desmos lesson, there is an added bonus - the dynamic structure of the learning environment allows students to see his or her mistakes immediately and the computer has the patience needed to let the student learn from the mistakes at his or her own pace.

Getting parents and administrators to understand the importance of constructing knowledge might
be a challenge, because it is not the way they themselves learned mathematics. At my school, if you ask what a parent wants
for their child they would likely say something like, “Good grades to get into a
good college to get into a good grad school to get good paying job.” Although it is not bad to have these
things – good grades, good college, good grad school, and a good paying job - I
would rather have my child have learning experiences to help them deal with
uncertainty, the willingness to be initially stumped by a question but willing to tackle the question,
the ability to construct their own knowledge and understanding about whatever
topics are presented to her.

We have heard the phrase, “I hear I forget, I see I remember, I do I understand”. This has been expounded upon by an American educator named Edgar Dale. His "Cone of Learning" shows what percentage of our learning is remembered after two weeks: 10% of what we read, 20% of what we hear, 30% of what we see, 50% of what we hear and see, 70% of what we say and write and 90% of what we actually participate in. Basically, the more involved students are in the learning, the more they will remember and the deeper the understanding. I find it very ironic that some very basic instructional design ideas for teaching in the 21st century are nearly fifty years old.

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As I finished my reflections on the plane, I thought about how my
understanding of what it means to learn was influenced by memories of my early
learning and how that has shaped the type of educator I am today. I definitely don’t teach in the same way or
have the exact same philosophy of teaching and learning that I had when I was new to teaching in my early
twenties. Throughout the weekend at the Desmos training, I could feel my
thoughts about teaching and learning – both teaching adults and teaching
students – being molded, as if my views were made of malleable clay. As tiring as it was to think and discuss and
explore, it was also invigorating. To
know that there are other like-minded teachers who are a tweet or Slack post
away for support and a collective effervescence on what it means to teach mathematics
is comforting. To know that there are others like me who have taught for many,
many years and still don’t know all the answers is quite freeing.

Over the next few weeks, I’ll be exploring the computational
layer of desmos and looking at ways it can enhance my lessons. My focus will not be on the bells and
whistles of technology that have come to dominate the educational technology market; my focus will be on using the technology to appropriately enhance the student experience
of learning through the construction of knowledge that happens when mistakes
are made.

Special Shout Outs:

Suzanne (@von_Oy) for saving the day with Lyft to get us to the airport at 4:30 AM.

Jonathan (@rawrdimus) for keeping me company on the walk to the Desmos HQ on the arrival day.

Sarah (@mathteacheryork) for sharing her notes with me on Desmos PD.

Kristin (@Fouss) for telling me about her great Desmos PD day in Ohio. I'll be picking your brain about this again in the future.

Stephanie (@welblair) for being a great roommate.