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Warning: a lot of this post borrows heavily from education theory. I'm in my student teaching semester right now, so a lot of what I explain is taken from research papers and things like that. So how realistic it all is, I don't know.

I've been thinking a lot recently about different ways of running a secondary mathematics classroom. I've heard some teachers have great success with a flipped model, and some teachers hate it. Here is my current understanding how it all works:

Students are expected to go home and watch a video and do some problems as homework a couple times a week. Then when they get to class, the time is reserved for reviewing the videos and homework, and then spending the rest of the time doing projects and applying the knowledge.

In theory, it sounds great. Less lecturing in the classroom, and more project-based instruction. But I see a few drawbacks as well:

I can see students not wanting to do homework that is "new" to them. Students are used to getting problems in class, and very similar problems for homework. This is a problem in mathematics education, but it is probably the most prevalent model used. Come to class, review homework, see new problems, go home, do problems similar to class for homework, rinse and repeat.

Another issue I see with a flipped classroom model is that it doesn't really allow students to discover the math on their own. Sure, they're learning new material on their own at home via some video and some problems, but it's really not that different from an in-class lecture. In my mind, an ideal mathematics education would have students seeing real problems, and create an atmosphere where the students are asking the questions, and "reinventing" the mathematics required to solve the problem. (This concept is known as RME - Realistic Mathematics Education and/or IBL - Inquiry Based Learning).

It almost seems as if the ideal flipped classroom would be backwards. What I mean is that students begin with projects in class, and then their homework is the lecture which "formalizes" what they discovered in class. This borrows from the idea of something called "The Iceberg Model" or "Progressive Formalization".

I would love to hear what you guys think about this backwards flipped classroom idea, and what you think the ideal classroom would be like. How is class time spent? What is for homework? What does the week look like for a student?

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    $\begingroup$ I think the method of implementation will greatly depend on local circumstances. For example, in many places it is simply not realistic to expect students to be able to watch a video at home (e.g., those without a computer at home, which will often be the case in very poor areas). However, I also think one can find "work-arounds" by carefully considering exactly what it is you want the students to do and how you might get this to happen with what you have available. Yes, I know this doesn't help, but I really think that for something like this a local master teacher is who you want to talk to. $\endgroup$ – Dave L Renfro Nov 10 '15 at 20:17
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    $\begingroup$ The title here is WAY too general! If we knew the ideal way to run a class we wouldn't have all he issues we have with maths ed! Your question is really about how you can successfully combine the idea of a flipped classroom with inquiry-based learning -- which is a good question! -- perhaps change your title to reflect the question more. $\endgroup$ – DavidButlerUofA Nov 10 '15 at 21:10
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    $\begingroup$ Flipping is great, but video? Video is a horrible way to learn. This what books are for. $\endgroup$ – Ben Crowell Nov 10 '15 at 21:26
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    $\begingroup$ I'm totally with Ben Crowell on books over videos. I get so bored with videos; they're always too slow, I wind up yelling at them to go faster, they're not searchable to know where to jump forward or back. But my college students don't see it this way and very pro-video; my concern is this will be a crutch that leaves them unable to read dense text when necessary. $\endgroup$ – Daniel R. Collins Nov 10 '15 at 23:00
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    $\begingroup$ Here are thoughts I've blogged before in regards to this question: (1) angrymath.com/2012/06/reading-writing-and-video-watching.html, (2) angrymath.com/2012/08/against-inverted-classrooms.html $\endgroup$ – Daniel R. Collins Nov 10 '15 at 23:01
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From this statement

I've been thinking a lot recently about different ways of running a secondary mathematics classroom.

and that you said you are student-teaching, it sounds like you want to try out a flipped classroom with your students but are hesitant because of your lack of experience. In that sense, I read your question as:

Should I flip my classroom?

Now, I do not know anything about your school, area, student demographics, etc. but the first thing that you need to ask yourself is "Why do I want to flip the classroom?" Maybe your students are completing their work but not performing well on tests. Maybe they are doing well with mechanical tasks but they are struggling with conceptual understandings. Or maybe nothing is working at all. Either way, you should have a justifiable reason for making a major change to your classroom structure and environment. This is both to give motivation to continue with flipping even if it is rocky at first and to cover your butt for administration and parents. Flipping of a classroom will almost surely raise a few eyebrows (unless this is already a part of the culture of the school) and it is in your best interest to be able to "prove" why you decided to flip.

Once you have a reason the next question you need to ask yourself is "Who are my students?". This is crucial because if you don't have a real understanding of the capabilities and resources available to your students, the flipping will almost surely be a fail. Things like having a lack of a computer/internet access, taking care of family members, or having jobs are all things that can complicate flipping, mainly because it means students will probably not do the homework consistently and without that, flipping really doesn't work. However, if you gauge your situation and judge that flipping, i.e. doing substantial work at home each night, is a reasonable expectation then I think that you should absolutely try it out.

As far as my experience goes, the best flipped classrooms are ones where:

  1. Students consistently do the homework
  2. The homework is used to introduce topics and give students a base exposure to working with the concept
  3. Class time is used to review the homework, assess understanding and dig deeper into the more conceptual aspects, usually through projects, activities, and collaboration

As far as running a flipped classroom, here are my tips:

  • Start out slow. Try out 1 or 2 days a week where the class is flipped and see how it goes. Explain to your students exactly what this "new thing" is, why they are doing it, what you hope to achieve from it, and what the expectations are. If it goes well then step it up to 3, 4, 5 days a week as you see fit. However, the more likely outcome is that it will not go well at first, and in that case you should
  • Stick with it. At least for a half-dozen cycles or so. At that point you should definitely either feel it still dragging and not really working or you will start to see things slowly improve. To help things improve, i suggest you regularly
  • Talk with your students. Ask them what they like about it? What they don't like about it? Their ideas to make it more useful/engaging? You don't necessarily have to follow through with everything they say but it is essential to have that dialogue and to know what they are thinking. All that being said, the last tip is to
  • Know when to throw in the towel. If it is the second month of flipping your classroom and you still are having the same problems you were two months ago, it is probably time to stop. Again, you are the ultimate judge of when enough is enough and it will depend on each individual situation. At some point it becomes damaging to your students' educations to continue with consistently ineffective pedagogy.

Without knowing your specific situation, that is about as much as I can say. If you are this interested in flipping, I think you should try it. Especially with teaching, the best way to learn how effective something is is to just try it out and see how it goes. I hope this helps, I hope you decide to try out flipping, and I hope you learn from the experience. Best of luck with your student teaching!

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    $\begingroup$ I'm not sure that "Start out Slow" piece is going to work out. I have tried a flipped classroom on a couple occasions and it went very poorly. I wondered if I might get better results by jumping in with both feet, and providing consistent expectations of what homework meant. Important to note: I never did try a completely flipped classroom, so I don't know if that would help. $\endgroup$ – BBS Nov 12 '15 at 13:30
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    $\begingroup$ In my experience, flipping a classroom is never a comfortable experience for students, at least at first. While I have failed doing it both ways, my biggest fail was when I tried to go all-out, 100% flipped immediately. Students fought back constantly and I gave up within two weeks. By easing them in, you build up the expectations gradually which helps to assuage the discomfort. This is important because flipping is so polar-opposite to everything they have been exposed to in school prior. The only time I think it may work to jump 100% in is if you do it on the first day of school. $\endgroup$ – celeriko Nov 12 '15 at 13:44
  • $\begingroup$ Thank you for your detailed reply, celeriko! I think the homework piece is super important. It can only work if the kids are able to access the homework and if the kids already have developed a culture of doing homework. How did your students constantly fight back when you tried it? I had two flipped classrooms at my university (which usually means students do their homework, so it's different than k-12) and they both ended up being very useful for me as a student. $\endgroup$ – Wmol Nov 12 '15 at 14:43
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    $\begingroup$ @Wmol basically they would give every excuse under the rainbow of why they didn't complete the homework (computer wasn't working, internet down, busy with other work, website was down, etc.) and when we were in class they would just keep saying it didn't make any sense and would want to spend the whole time reteaching the previous night's homework so it made the flipping pointless. That is worst case, and many of my experiences have not been that way but, again, it all depends on your students and the culture at your school. $\endgroup$ – celeriko Nov 12 '15 at 15:02
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While it may be true that sometimes 'backwards' flipping might be effective, sometimes it might rather be preferable to provide some of the low level content in a video watched beforehand. This would allow students to engage with the material at a higher level in class. You could try pre- and post- class videos. It might depend on the level of difficulty of the topic which method works best. Even within a single course, you wouldn't have to do the same thing with every topic.

Personally I'd usually prefer to have the students arriving at class time with some idea of the topic. (I flip some lower level college math classes.)

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  • $\begingroup$ Thanks! Awesome, maybe the combination forwards and backwards flipping is a good way to do things. I was talking to the 7th grade math teacher in my school today and we were talking about how effective homework is. I'm personally finding that in middle school, students won't even try doing homework if it's something they haven't seen in class. The fundamental problem with this is that students can't grow until they try to learn things on their own! I want to be able to give homework that exposes students to new material before we explore it more in class, but I'm not quite sure how to start. $\endgroup$ – Wmol Nov 17 '15 at 4:09

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