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I flipped my math classroom

I've normally started my classes with a description of what math we will be learning, and a class discussion about what the math means. 

When I first started teaching, I would lecture for 30 minutes, and students would work for 60 minutes (I started in with a double block of math) during double block math classes, and in a 45 minute lesson, I would still lecture for 30 minutes, and students would get 15 minutes to practice and do other activities.

I discovered early on in my teaching that the less time I talked, the more time students had to work on activities and exercises, and this led to improved understanding. I read research suggesting that adolescents could actively pay attention for about 10 - 15 minutes, so I focused on getting the lecture portion of my lesson down to this length, and on embedding more questions and subsequent discussion into my lecture.

Today I tried something new. I found questions (with an emphasis on real world application) related to exponential functions that students had never seen before, and started class by handing them out as a package, and asking students to work on these problems in groups. I then spent class circulating around the room, answering the occasional student question (but being very careful what types of questions I answered) and pushing students to try finding multiple solutions to the problems. When students were completely stuck, I offered support, but by asking them questions, rather than just giving them the solution.

Now, I've definitely had classes where I haven't taught an idea to the entire class before, but this is the first time I've introduced a completely new topic without either presenting a lecture on the topic ahead of time or using some sort of guided instructional aid for the students (like a video prepared in advance of the lesson).

Here are some observations I had while I was circulating around the classroom.

  • Not one student asked me "is this solution right?"
  • Students were actively engaged in the problem solving process.
  • The questions I overheard from students (to each other) were often about the nuances in the problems, rather than "how did you do this?"
  • Every group of students found the most efficient standard solution to the problem, as well as 2 other ways of solving the problem.
  • No one attempted to Google for the solutions, or even open their textbook to see what information it had.
  • My students were thinking.

At the end of class, I asked students to continue working in groups and come up with notes to explain the topic. As the students will be taking an exam in about a year and half on all of the material they are writing, I recommended that they write the notes for their future self that might not remember having worked on these problems. Next class, I plan on having students form new groups, and collaborate to construct meaningful notes for the future, and then work on some more related problems.

I've flipped the classroom. Instead of me presenting the ideas, my students look for solutions, and I help them. Instead of me giving notes to students, they make their own notes. Instead of the classroom being about the content, it's about the process.

There were no videos, no notes in advance, no computer assessed exercises; just a focus on changing who was doing the thinking.

 

About David

David is a Formative Assessment Specialist for Mathematics at New Visions for Public Schools in NYC. He has been teaching since 2002, and has worked in Brooklyn, London, Bangkok, and Vancouver before moving back to the United States. He has his Masters degree in Educational Technology from UBC, and is the co-author of a mathematics textbook. He has been published in ISTE's Leading and Learning, Educational Technology Solutions, The Software Developers Journal, The Bangkok Post and Edutopia. He blogs with the Cooperative Catalyst, and is the Assessment group facilitator for Edutopia. He has also helped organize the first Edcamp in Canada, and TEDxKIDS@BC.

Comments

Thanks for sharing your experience David, it motivates and encourages us in flipping our classrooms too.
Thanks again from Spain!

Xabier

Hi David,

It's always interesting to read about your experiences and experiments. I agree on the power of giving students some interesting problems they haven't seen before and letting them go - I just posted on my blog about doing this in physics and being really pleased with the results. I find it pretty neat to watch them feel like writing down important things and figuring out problems rather than telling them what to do.

I just wonder about whether what you are doing is just flipping or just overall good pedagogy. Don't get me wrong, I love the concept of flipping when it makes sense. I've found it really makes me decide whether a part of a lesson I've done before (especially in Calculus) is worth doing in class, as an exploration, or as a video that preloads students with some basic information before practicing.

Shifting the focus of class time to figuring things out is making your students active learners rather than receivers of information. Asking questions instead of answering them puts the power in the students' hands to figure things out. Giving an assignment and knowing your students well enough to know that they can solve it given the time to get help from one another shows that you believe in their abilities and want them to be challenged.

You are certainly justified in calling this flipping, as it does reverse the traditional roles of student and teacher in the classroom. I just don't think you need the gimmick of the 'flip' brand :)

Hey David,
I love reading your posts because of the thought and process you put into them. Thanks for sharing your ideas.

I do, however, want to stress again that the flipped class is NOT about the videos. Yes, what you've done is a "flipped class" because YOU were not the focus of the content. Video did not need to help with the content building that happened in your room. Video is simply a tool that can help accomplish a goal. If you don't need the video, don't use it.

The "flip" is not a brand, it's not a copyrighted term, and it isn't ONE way or the highway. The flip is an idea that can help you get kids to think and interact in meaningful ways. Video helps some people do it well, others (like yourself) don't need it and don't (shouldn't?) use it. Again, it is a tool that can help teachers do more things like this work.

I'm glad the experiment worked...I would love to be able to do that with my classes someday, but they're just not there right now. Until I'm at that point, I'll be using technology that helps enhance their learning process.

Thanks again-

Interesting post David. Is this not just experiential learning? Similar to what we do at outward bound?

Very interesting.

Your approach sounds a bit like the Moore Method, in which minimal information is given and the students are tasked with figuring it out from there. I do not think that is an approach that is appropriate for middle school, or any other school where the learners have insufficient background and self-confidence to figure things out on their own.

I agree that videos are not necessary. In fact, I think we will soon move beyond the "flipped class" and move more directly into the "self-directed" class. I think you are already doing that, but most 7th graders I know are not yet ready for it.

David Wees's picture

I don't think you could necessarily give them the same kind of problems as I gave my students, but I'm sure there are projects that you can use that help students learn mathematics. I don't see this approach as completely unguided, as I spent my entire class, moving around and giving students assistance. The type of assistance you give would absolutely depend on the classroom of students you have.

I am currently trying the same process. Have you collected any data? Improved grades? Parental support? Etc.

David Wees's picture

I'm finding myself moving in and out of this process depending on what topic we are "supposed to cover." I can see promise, but I find that the restrictions imposed by the final assessment for my course (a pair of tests worth 80% of my student's course marks) and content required for that test influence what I can do. So, when possible, I try more interesting and challenging learning activities. Where it is isn't possibly, I slip back into what I did before (10-15 introduction of idea followed by mini-project and/or practice problems).
Parents haven't really been an issue. Maybe it's because they don't have as many expectations as to what an IB Math course looks like? I don't know.

Hola David,

Very interesting approach. I like that it empowers students tremendously.

I flip my classes, but because I am a foreign language teacher, I find that the videos are important.

Thank you for sharing this.

Emilia
PS: I also teach online and I teach two students from Stratford Hall...small world!

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