The Quotient ~ 4.16.15

0. There are no tough decisions. Really. When you toss a coin in the air, you already know what side you want it to land on.

1. Despite my passion for teaching high school mathematics, my deep understanding of mathematics needs to improve greatly.

2. There are many things I get. Leadership is certainly not one of them. How can I inspire a group of people to be better than they ever thought they could be?

3. No matter how much it is emphasized, planning is still underrated.

4. In conjunction with 3: improvisation and adaptation is aided immensely by effective planning, but both are still incredibly hard to accomplish successfully.

5. If you’re not moving forward, you’re going backwards.

6. I consistently seem disappointed at the end of every school year. I always feel as if I could have done more, or at least something different, to help my kids attain higher levels of success. I sense the same feeling arising now as we approach May. I know why, but why?

7. Could you guys move in a little bit? There’s a lot of people trying to get on. It would be helpful, thanks.

8. Sometimes you win. Sometimes you learn.

9. I’m not sure why, but during the last couple of weeks I have felt like I did during my first few of years of teaching. Hungry, eager, overly energetic.

10. How I respond to a student makes or breaks a situation. Don’t pierce their armor.

11. PD need not be boring to achieve its goals. Teachers expect that. Next time, catch them by surprise.

12. I see complacent and lackadaisical mindsets forming in young teachers. Its all around them. Its easy. It goes with the flow. Its deceptively harmful. And dangerous.

13. How can I help? What do you need from me?

14. I need a write up about the impact of MfA on my teaching.

15. How will this summer play a role in my continuous development as a teacher?




Blind Trust

I attended Math for America’s Master Teachers on Teaching event last night. If you’re not familiar with it, it’s essentially a Ted-ED style event where math teachers give presentations on topics that they are passionate about. One of my biggest takeaways had to deal with technology and how I address how my students use it.

There were some awesome presentations and one that stood out to me was Patrick Honner’s talk about the shortcomings of technology as it relates to teaching and learning. A couple examples that Patrick pointed out were the TI-84’s inability to accurately represent continuity (asymptotes) and Desmos’s failure in representing holes in polynomial functions. Normally, technology allows beautiful, helpful representations of mathematics, but in all of these instances technology utterly fails to do this. Patrick encouraged the audience to embrace these types of pitfalls as teachable moments that could enable deeper understanding of the concepts.

This whole discussion reminded me of something that happened in my class a while back. Once during an exam, I witnessed a (precalculus) student enter “1 + 2” into their calculator as they solved a problem. In the moment, I almost laughed out loud (and afterwards I did). The next day when I handed back the exam, I brought my observation up to the class. The guilty student openly took ownership of the act and said:
“Mr. P, on an exam, you never know!

This example is slightly different than the ones Patrick highlighted, but it nonetheless brings attention to my students’ increasing dependency on technology. This connects with what was Patrick’s concluding point: our students blindly and inherently trust most all technologies they use – more so than they trust their own intuition. Combining this with technology’s pitfalls, and I see a recipe for disaster: students wholeheartedly trusting a flawed tool.

This means that I have a crucial responsibility to transform student reliance on technology into teachable moments that enable deeper understanding. It also means that if my students blindly trust technology and all it’s shortcomings and fail as a result, I have also failed.