Summation notation, but way more

I’ve been rethinking all of my lessons this year. My hope has been to get my students to reason more. To think independently. To not be sponges. I’d like to think it’s been working. Here’s a recent lesson on summation notation that showcases this shift.

To open things up, I gave them this.

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Super accessible and relevant to summation notation. In the past, I would have chosen a bell ringer that was closely connected to a prior lesson (i.e. review) than the current one. I wanted to provide remediation. I’ve learned this year that a relevant bell ringer is pivotal to any lesson.

Here’s what came next.
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Again, very accessible. Last year Jennifer Preissel mentioned the “Stop & Jot” idea as a simple way of getting kids to write and reflect more during a lesson. Here, I gave them five minutes to express, on their own, what they wondered and noticed about the expression. After, they shared with their groups and we discussed as a class. By including “left side” and “right side,” I wanted to focus student responses. There were comments like “the +2 happens in every parenthesis” and “the number next to the +2 is going up by one.” Their observations led us to the brink of directly relating sigma notation to its expanded sum. In the past, I would jump right into defining sigma, the upper and lower limits, argument, etc. There would have been no exploring or thinking on their own.

Next, I ask them to move on to another example with the hope of finding a relationship.

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It worked like magic. They see the same pattern from the Stop & Jot and they start to generalize. They have no idea what the “E thing” is, but it’s beginning to settle in how the left and right sides relate to one another. They discuss all of this in their groups. I float around. Observing. Listening. In the past, I would show them how to find this sum and answer their questions. Again, no self-exploration and making meaning of what they see.

Now they are to dissect and interpret.

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This lacks clarity. Some students knew to write their interpretation next to the arrows, but many did not. As a checkpoint, we came back together and discussed.

Next: remove the right side.

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Things are flowing now. The scaffolds are working. They know the relationship and successfully express the sum. In the past: The students would probably be completing this problem, but instead of using their own insight to drive the work, they’d be following what I said was the correct procedure.

Finish it off.

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We come back together one more time to debrief and to address any questions the groups haven’t already. To bring things full circle, I mention the task from the bell ringer. “Ohhh!”

Lastly, on the next page, the proper names are reveled.

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We then have just enough time for an exit slip.

This lesson is heavy on notation and I didn’t want to bog them down with symbols. The goal was to find meaning first, then discuss representation. It succeeded. What I miss out on is working in reverse. Namely, using sigma notation to represent a given sum.

What I love most about this lesson has little to do with summation notation. It’s much bigger. It stems from the approach. Bottom up. Using their own insights to help them find meaning. Doing less and allowing them to put the pieces of the puzzle together. This lesson is a microcosm of how I try to teach nowadays, which is much different than in the past. It symbolizes my growth as a teacher, as a learner.

Here is the handout.

 

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Why I stopped flipping

Flip Flops

Four years ago, just before it became heavily commercialized, I flipped my classroom. I created video lessons that my students watched for homework. Class time was used for enrichment, reflection, and collaborative work. I ran with the model for a year and a half.

The other day, out of the blue, I was asked why I stopped. That made me think: back when I stopped flipping, I didn’t have this blog and never wrote about why I stopped. Here goes. Four years later.

Before flipping, I usually lectured. Sure, I disguised it with an enthusiastic and energetic delivery, but I lectured nonetheless. I wasn’t critical of my own teaching at the time, so I didn’t really think twice about it.

After I flipped, I had significantly more facetime with my kids and they had more time to reinforce new concepts. I was really happy about this. My students sat back absorbing new content like sponges, this time from a video embedded with summary questions. After all, a video lecture, however dressed up, is still a lecture.

The problem was that students weren’t discovering mathematics from my lessons. They weren’t interacting with mathematics or each other during the learning process. They weren’t debating with one another while learning something new. They weren’t being asked to find patterns and discuss them with a partner. They weren’t being challenged to make connections and develop understanding. They were using technology for learning, but not to learn. Their first impressions of so many beautiful mathematical ideas included pausing and rewinding a video that contained my face. In short, they didn’t construct their own learning. I did all of that for them.

I stopped flipping my classroom because I realized that I wasn’t flipping student learning, I was simply flipping my teaching.

I discovered that I needed them to take ownership and discover how and what they learned. What’s ironic is that I actually had to flip my classroom in order to realize this. Flipping allowed me to see my lessons through a more concentrated lens that highlighted my teacher-centered approach. More on this.

Four years later, do I regret flipping my classroom? Not a chance.

 

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Summer 2015: An Immersive Research Experience…The After Party

Earlier this summer I wrote about a research experience that I was taking part in: SMARTER, an RET instituted by NYU Polytechnic School of Engineering. The experience was profound. Here’s a recap of my takeaways.

Composite material

  • Firstly, a learned a good deal about composite materials. Going into the program, I had the slightest idea what a composite material even was. During orientation my curiosity was stoked by Nikhil Gupta, my research mentor, about his area of expertise (primarily because he mentioned that his research impacts the U.S. military). But other than that spark, I had no real foundation for where to start the research. Naturally, this equates to an information overload and, in the end, a substantial amount of learning on my end. Part of me wished my research tied in closer to what I teach everyday, but the other part of me understands that being forced into foreign territory was exactly what I needed.

Research Results Chart

  • My partner and I decided to make repurposing waste materials the centerpiece of the research. Specifically, we were interested in the impact that fly ash, human hair, and glass microspheres have when integrated with cement. What did we learn? The results were somewhat inconclusive, but we did discover an ideal proportion of fly ash to glass microspheres that would optimize the peak stress (i.e. the point at which the material begins to break down) of the composition. We expected that the human hair would have a greater impact on the overall strength of all the composites, but the results were fairly mixed.
  • A facet of the experience that surprised me was the collaboration that it involved. When you work with a perfect stranger for an extended period of time, things can get rocky. I didn’t learn to appreciate my partner’s perspective until later in the research; she taught me a ton about seeing things with a starkly different outlook and how this is necessary for the team to succeed. It also pushed me to open my mind and connect with ideas that I initially found hard to accept. I was reminded that everyone has strengths that are both unique and amazing…and that productivity sometimes hinges on the ability to focus on those strengths.
  •  The most significant impact of the experience was the uplifting inspiration it provided me. Before SMARTER, I had a deep-rooted desire to grow as a professional, but I had no ambition to further my education or seek a higher level of certification. But after a brief conversation with a Ph.D candidate who was aiding in our analysis, I left with an unexpected desire to push myself further than I ever thought I would. It was his laudable attitude coupled with the overall atmosphere at the university that left me wanting much more than just to complete my research and get back to teaching.
  • What does this mean? It means that one day I will 1) earn National Board Certification and 2) obtain a doctorate in mathematics education. Yup. I am now eagerly awaiting these immense challenges in the years to come. Thanks Eduardo.

This is my evolution thanks to SMARTER. My students, school community and myself are all much better because of it.

 

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Summer 2015: An immersive research experience

NYU Logo

This past week I began a summer-long professional development with NYU Polytechnic School of Engineering called RET (Research Experience for Teachers).

The RET program pairs up STEM teachers and engineers for a six-week collaboration experience during the summer. The engineers at NYU-Poly work hand-in-hand with K-12 teachers (like me) to conduct ongoing research in their discipline. I will write a paper summarizing my research, present my findings, and create a Teach Engineering lesson plan related to my RET experience [UPDATE 3/31/16: My lesson has been published.]. In other words, I will do everything a full-blown researcher would do (minus the lesson plan).

I haven’t finalized my research topic just yet, but I do know that I am partnering with Dr. Nikhil Gupta. He is well-known in the United States for his work with composite materials.

I’ve met Phil Cook, an awesome dude, through the program. Here’s his reflection on his experience thus far.

I’ll get another post up after RET is complete, but here are a few things that I’m most looking forward to:

  1. Can-Do. The director of the program mentioned that he is regularly inspired by what he calls the “can-do” attitude that all engineers embody as part of their ongoing work. I can relate to this. There will be countless setbacks and obstacles that arise, but the objective never changes: understand the problem, focus on solutions, learn. I’m expecting to struggle quite a bit during RET, so I hope to stay motivated and maintain a “can-do” attitude throughout. I remember my UBI experience.
  2. Research. Other than some minimal, unstructured research that was mandated for graduate school, I’ve conducted no formalized research. For this reason, I’m especially intrigued by this opportunity to not only learn about Dr. Gupta’s research, but to experience the process personally. I hear and read about research all the time, but this time I’ll actually be the one conducting it. I find that incredibly empowering. I am fully anticipating the roller coaster that will be investigation, frustration, and discovery.
  3. Impact. RET is actually intimidating and even scary on a certain level. The workload will be serious. The hours long. But I feel like this is what professional development should be. It should push me out of my comfort zone. How else will I improve? The breadth and depth of this immersive experience promises to provide high levels of enrichment, of which I’ve never experienced before. It will be interesting to see how all this work manifests itself in my career and what I do with my students.

With all that said, there is a bigger picture.

Before I was accepted into RET, I have taken more and more interest in research. I realized this because I have so many questions. Those questions cause me to want answers, even if they’re partial or incomplete. Research is a structured, unbiased way to do that. Anyways, I have a lofty goal to be part of a team of teachers and/or educational team that researches teaching, learning, and/or schools. It’s just a dream at this point and I have the slightest idea of how I would make it happen. I’m sure I’ll pick up some cues from this experience with NYU. Maybe I can use MfA as an outlet for this? Maybe I can find a some sort of RET related to education?

To be continued…

 

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End of the 2014-15 school year

Classroom Spring 2015

-1. Several weeks ago I began thinking about the end of the school year. I suddenly realized the startlingly amount of reflection that awaited me. Today is the last day of school and the only way for me to systematically get it all out is in a list. Here goes.

0. Leading up to this year, my school had a solid four-year stretch of low-turnover and highly stable school atmosphere. 2014-15 not only broke that streak…it was shattered and thrown it under a bus. Things were quite eventful.

1. With any change in leadership, one should expect adjustment in the day-to-day happenings. I found that I had grown too comfortable under previous leadership. Things and people change and I need to evolve with these changes so my productivity doesn’t stagger.

2. During and after vast transformations this year, my optimism was put to the test several times and, in some cases, folded. After scarring disappointments early on, it took a good amount of time to rededicate myself to the school’s mission. I let my frustration get the best of me at times – which I don’t regret. Live and learn.

3. What kept me going? What kept me from completely disconnecting from my school community?

4. The incredibly inspirational people around me. My students. My colleagues (in and out of my school). People I’ve never met. My family.

5. Teachers at my school are an awesome bunch. Despite the disarray abound, somehow they found a way to use their collective strength to keep us moving forward.

6. This was also my first school year blogging, which had a great deal to do with my naturally reflective nature this year. It framed my teaching like nothing I’ve ever experienced. I gained serious perspective by reflecting on my own practices via my blog.

7. I implemented standards-based grading. In terms of assessment, it’s one of the best moves I’ve ever made. I committed to it mid-year, which was tough, but it worked pretty much as planned. I had students assess their own retake exams, which was great, but I need to make a stronger push for retakes next year.

8. I helped plan weekly district-mandated professional development sessions for colleagues at my school. I found it both more engaging and challenging than I imagined before the year began. Professionally, this was an area of growth I didn’t expect. Thanks to MfA, I’ll be taking that a step further next year with my video club.

9. I absolutely struggled with four preps in the fall. The quality of my teaching was stretched thin and my students were shortchanged immensely.

10. I was entitled department chair in the spring. The math department had a tough year and we have a long journey ahead. I hope I am able to provide whatever leadership we need. That said, I passionately hate titles and the connotation that often comes along with them. They are hollow and irrelevant. I just want my work to be meaningful, collaborate, and help all of us reach another level.

11. Our robotics team made progress this year. We performed noticeably better than during the last two years of the program. Next year I hope to use class time (versus after-school) for competition preparation. This should afford the kids more time to build and tweak the robot. My robotics class expanded to include introductory arduinos along with the usual Lego Mindstorms.

12. My students did rather poorly on state exams. This is very disappointing given the amount of work both the students and myself have put in this year. So much so that I began questioning myself. How can I adjust to improve this result?

13. A woman leading a PD once told me “When my students don’t succeed, I look in the mirror and ask What could I have done differently?” This has stuck with me all year. It’s not about all the issues, setbacks, and lack of prerequisite skills that students bring into the classroom that hinders their learning. Instead, all that matters is what I do to meet their needs and get them to succeed. It’s a hard pill to swallow. But this perspective is key for me in my hopes of one day becoming a great teacher.

14. I could have been a better mentor. Despite many shortcomings, I have experience and insight that is conducive to the growth of colleagues new to this profession. I did a poor job this year mentoring a new teacher. She is wonderful and would never tell me so, but inside I know I could have had a much better impact on her.

15. I tried many new approaches this year to teach my kids. Just as importantly, I also implemented new ways to reach them. Whether it was friday letterspersonal notestwo stage exams, plickers, speed dating, problem-based learning, exit slips, or others, I can say that I have definitely made an effort to improve the happenings in my classroom.

16. Following up on a new year’s resolutionintervisitations played a significant role in my development this year. I discovered the need to not only get outside my classroom, but outside of my building, and explore the work of others. It helped motivate a colleague and me to apply for the 2015-16 NYCDOE Learning Partners program, which we were accepted. More to come!

17. I relearned how to be patient with my students. Big ups to my AP for pushing me to slow down the pace of the class and remind me to provide more scaffolding.

18. Goal for 2015-16: highly effective. Focus for 2015-16: to be better than I was in 2014-15.

20. Every school year seems to fly by when you’re at the end of it. This one was no different. It was a bumpy flight, but it was over before I knew it. Another one in the books.

Until June 2016.

 

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