I Flipped My Lesson. Now What?

The following blog post is written by Mrs. Rhona Flaumenhaft, Math Teacher at The Frisch School. I have invited Rhona to cross-post on this space so we can benefit from a master teacher's years of experience in teaching math while at the same time integrating new technologies and research.

For the past six years, in an effort to keep my students more engaged, I have been writing worksheets for the kids to read at home the night before a difficult lesson. I had no idea that what I was attempting was a “flipped classroom”.

I always felt that it was important for my students take more responsibility and be active partners in what they needed to learn. It was a feature of the learning process that seemed to be disappearing from my classroom in recent years. My sheets were carefully designed to start with very simple facts, linking them together in a way that built a solid foundation to support the difficult concept or skill that I hoped to cover the next day, making the lesson more productive. However, many kids still needed me to read the sheets with them in class. The sheets were visual tools and many of my students needed an auditory experience.

Technology, in the form of the iPad and the Explain Everything app, allowed me to turn my worksheets into videos. For the past year, that has been my focus. 

I have been teaching middle school and high school math for almost 40 years and have very definite ideas about how to teach a math lesson. Of course, the graphing calculator and the Smart Board have made significant contributions to certain aspects of my lessons. But the fundamental structure of my lessons hadn’t changed, nor did it ever occur to me that it should.

I came to the recent unConference on the Flipped Classroom looking for new tools to make a better video, but what I came away with a much larger issue to tackle. As those of you who read my previous blog know, what shook up my world was the presentation by the keynote speaker, Julie Schell from Harvard University, who invited us to compare a picture of an operating room in the 1800’s with the operating room of today. They were shockingly different; technology had transformed the OR. Then we were asked to view then and now photos of the classroom; the differences seemed shockingly non-existent. The message was subtle yet clear: medicine had advanced, education had not.

The next idea that captured my imagination was the call for creativity posed by Sir Ken Robinson in a video clip shown during one presentation. Robinson spoke about the need to embrace creativity and prepare the classrooms of the future to equip students to meet the challenges in the new world that technology and globalization will establish. I was energized when I left that conference; convinced that I needed to change the way I taught.

But the more I thought about the comparison of an operating room to a classroom, the less compelling it became. Medicine relies on the discovery of new protocols and new drugs to treat or prevent disease. Technological advances in robotic surgery, for example, have transformed the OR. Teaching, however, is about enabling children and young adults to gain the information and skills they will need to support their future goals. I knew that student expectations had changed; that is what started my journey to “flip” my classroom. But had the fundamental ways in which students acquired knowledge changed?

I began by searching “how the brain learns” and got 81,600,000 results. Yikes; the task seemed impossible but I don’t give up easily; spending six years re-writing worksheets had made me tough! I jumped right in and almost immediately felt like I was drowning. One article claimed that new research into how the brain learns will change the way we teach. Another article claimed that not all scientists agree on how brain research should be applied to education, but many articles made suggestions about how to use brain research to improve education. Some spoke very clearly to the elementary school years and dealt with the issues articulated by Ken Robinson, although I felt that some of the suggestions would benefit the high school classroom as well.

Shifting my focus to math education in the high school years made my job harder (it is fascinating how much educational energy is devoted to math). I found so many articles with so many opinions, some diametrically opposite to each other, that it became impossible to juggle them all. Some articles were backed by research; some were not. Although all the authors felt that math education was important, they were split on what the content of the math curriculum should be. Many articles were devoted to discussions about algebra, but the algebra they were discussing was high school Algebra I in some articles, and College Algebra in others.

In desperation, and to maintain my sanity, I finally had to accept that in whatever way the math curriculum might change in the future, that was not my focus. I still wanted to know if there was a “best way” to teach math in the high school classroom of today. The only mandate I considered non-negotiable was, every student should be offered the opportunity to gain the skills needed to attend college. For now, that makes mastering algebra important.

First, I needed to review a “real world relevant/exploration” approach to structuring a math lesson. It was simple to consult the TED talk that had been part of the Frisch Math Department’s Staff Development program this past year presented by Dan Meyer. He feels strongly that teachers need to make math more palatable by making it more relevant, which is accomplished by finding problems that reflect the real world. He believes it is important to create an environment in the classroom where students are able to feel comfortable having math conversations. Meyer feels that technology is a compelling tool for powering our lessons. He also injects humor to make his lessons more engaging. All of these principles, relevance, visual stimulation, and humor, are mentioned in the brain research I read. At that point I realized that I had used all three to make my worksheets more effective. There is something very appealing in this approach, using relevance to generate excitement. However, I am concerned that there are certain limitations to making this approach a steady diet.

It is not always possible to see the relevance of something you learn at the exact point in time when you learn it. In order to make sense of all the articles I researched, I needed to be able to read and understand what I was reading. That process began with Dick and Jane, and “run Spot run”; yes, I am that old! Luckily for me, it never occurred to me to wonder why it was important whether Spot ran or not.

We cannot limit ourselves to concepts and skills based only on their real world relevance. Some important skills are embedded within a larger question, and the reason for learning them may not be apparent.

Second, as the adult in the room, I feel it is my responsibility to make decisions in my student’s own best interests, whether they understand my reasons or not. It is much more fun to ride a bike without a helmet, and to travel without a seat belt. We don’t allow our kids to do either, whether or not they understand its importance. By attaching too many bells and whistles to a math lesson, we may be sending the message that pure math is boring, or that the legitimacy of what we teach must pass muster with our students.

I feel that one of the biggest shortcomings in today's students is their failure to accept that some of the things they learn can be necessary without being fun in the way they define it, nor instantly rewarding. This is a fact of real life.

Any parent who wants to raise a child (which I think is rewarding) has to change dirty diapers (which may not). While I certainly don’t equate factoring, for example, with dirty diapers, the fact is that many of my students do. At this point, I realized that my concerns had meshed with another key component of the brain research, meaningful practice.

I turned to an article that spoke to this issue, written by John Mighton in Scientific American. Mighton believes that every student is capable of learning math. The key is breaking down each skill or concept into micro steps and then practicing each step. He suggests that the teacher needs to provide guidance and scaffolding to help students master new concepts. According to an American Psychological Association Report, “Practice for Knowledge Acquisition”, student performance is affected by how much they engage in effective practice.

After reading this article, I realized that Mighton’s approach was also a big part of both my sheets and my lessons. I thought back over the hours (and I am not exaggerating) it sometimes took to analyze the steps needed to understand a new concept or skill, in order to present the material in a way my students could absorb.

And, I realized that the whole point of the “flip” was to provide more time in class to practice each new skill.

I agree with Dan Meyer that students need to be able to talk about math and work together; I encourage collaboration and peer instruction. But I also agree with John Migton that kids need guidance and a framework to learn information for its own sake.

My first teaching job was at Hunter College High School and my first chairman was an incredibly talented educator, Dr. Harry D. Ruderman. He always warned his teachers that if a lesson is properly structured our students will be willing to join us on the exploration of new territory. The minute a student asks, “why do we have to know this” what he is really saying is “you lost me”.

Learning is a fascinating activity. The brain loves to learn and that is our ace in the hole. I have found that my passion and love for math influences my students. I don’t teach to their limited vision of what is important; I try to invite them to share mine. 

In the end, I try for a Meyer-supported and Mighton-based classroom. The biggest support I have for continuing to teach this way comes from my students. After accepting that I will not teach what they would secretly call a “joke course”, they very reluctantly accommodate this crazy woman, with the quirky sense of humor, who actually loves math and often thinks math problems are “cute”! And as they see that they can learn the material and be successful, their delight and excitement is its own reward. I often hear, at year’s end, that they are amazed by how much they have learned and understood; they take pride in what they have accomplished. Students often tell me that they feel smarter and they say it with confidence; if they could learn math this year, then why not next year as well? A subject that they had previously written off is now a potential resource. That feeling can open doors and that is the whole point!

(Cross-posted on the The Emperor Can't Do Math)