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?




The Quotient ~ 2.9.15

0. The only true wisdom is in knowing that you know nothing. ~Socrates

1. That is probably my favorite quote of all time. It resonates with me so deeply because I’ve realized that every thing I read, write, watch, speak, do, and listen to is but a mere spec on the number line of infinity.

2. Despite confidence in myself and in my abilities in whatever the task at hand is, whether it be teaching complex numbers or overhauling a bottom bracket, inside I always understand that I can be better. There’s always someone or something with knowledge that I don’t have.

3. I have finally begun using exit tickets as they should be used. In other words, I understand their assessment value.

4. I once heard someone say that true innovators and learners engage with people and things that go beyond their area of expertise.

5. Real learners can take a seemingly meaningless or unrelated moment and relate it directly to something that is meaningful to them.

6. Quality over quantity. Always.

7. Being open and willing to accept criticism has taught me that I can be always be better.

8. I’m very excited to begin my (voluntary) intervisitations. I sense an immense amount of growth on the way.

9. Math teachers are always asked to incorporate more reading and writing into their classes. Why aren’t ELA teachers asked to include more mathematics in theirs?

10. If I pray for rain, I better be prepared to deal with the mud too.

11. I need to walk around with small slips of paper (or Post-its) and provide random instant feedback to my students.

12. Video in my classroom. Transparency. Vulnerability. Growth.

13. My standards-based grading has opened up areas of assessment that were simply not available to me before.

14. You have a dream, a goal. Each day, lay down a single brick. Work towards that goal. One at a time, work on perfecting how you lay them. Get better. Eventually you’ll have a great wall. Your goal will be achieved.

15. The wind howls, but the mountain remains still. Stop talking so much. Observe. Listen.

16. Don’t eat the marshmallow.


The Quotient ~ 11.14.14


What an incredible few weeks it has been. A school year of four preps, among other things, has finally caught up to me. Yes, four preps. Here are the things that having running around in my head over the last several weeks.

1. Student questions. When I get a lot of them, I’m pleased because I know my students mind’s are stimulated. But how to handle all those questions can be a challenge at times. What about when there are no questions?

2. Checking for student understanding during the lesson and adjusting on the fly. Basing the direction of my lesson on their level of mastery on any given day.

3. Relations with administrators, new and old. I’m learning a great deal about this dynamic and it’s impact on me and the overall school community.

4. Listening is a very underrated skill.

5. Including the proper scaffolding into each lesson. Specifically, having multiple entry points for students at the onset of learning.

6. After an assessment, the value of data analysis. Numbers never lie. Also, how structured analysis (time and protocol) can really help reveal the story behind the numbers.

7. Related to above: point biserial.

8. Always remember that kids are kids. Relate to them, laugh with them, have fun. They’ll enjoy your lessons a lot more – and work harder for you too.

9. I let one of my students borrow one of my ties to wear at his interview with Harvard University. Very cool. Awesome kid.

10. How much my use of Desmos has increased. I’m literally using it every day.

11. Reflect as much as possible. You’ll grow in ways that you otherwise cannot. Even just 10-15 minutes of concentrated reflection is substantial.


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