Bill Gates dismisses it – this belief that children can construct their own understanding of mathematics. Many educators disagree.

John Van de Walle’s student-centred approach? Marilyn Burns’ insight into how children learn math? The rationale in the WNCP curriculum? The beliefs of the BCAMT? Gates would dismiss them all.

More importantly to me, he would dismiss the successes that Surrey teachers and students experience when teachers let go and give students a chance to do the math. “Letting go” does not mean students are left to discover the Pythagorean Theorem on their own. The role of the constructivist teacher is to get students mentally ready to work on a task, listen, provide hints, and facilitate discussion.

Instead, Gates supports the Khan Academy and the flipped classroom model. In this model, students watch a video at home so that they can get one-on-one homework help at school. Sometimes, flipping proponents claim that this model frees the teacher up to have students do real problem solving. With all the press that the flipped classroom is getting, there is surprisingly little anecdotal evidence of this actually happening.

Gates, Khan, and others have missed the point. Problem solving isn’t something you do *after* you have learned a concept. That’s *practice*. Students should solve problems not to *apply* but to *learn* new mathematics. The flipped classroom model removes teachers from the most important part of teaching – the introduction of new concepts.

Suppose the proverbial teacher across the hall doesn’t buy in to “all that constructivist stuff” and is considering flipping his or her classroom. Here are three questions that I would ask:

1. **Does teaching = telling?** (See how I made that a math question?)

I understand if the general public views teaching as simply delivering content, it’s probably what they experienced as learners. Teaching, like real estate, is one of those careers that everyone thinks they can do. I guess I expect my fellow educators to know better. I thought we no longer viewed children as empty vessels to be filled with knowledge. I thought we were moving away from seeing curriculum as topics to “get through.” I thought we were moving towards an emphasis on the mathematical processes. Earning badges online seems like a giant step backwards to me.

2. **When you are explaining a new concept, is the interaction between you and your students important?**

I have a confession to make. For most of my career, I have used a teacher-centred approach. Still, even in this traditional lecture format, students were given opportunities to ask me clarifying questions or check their understanding with a neighbour. I was able to pick up on subtle non-verbal cues and adapt my lesson on the fly. Throughout my career, all of my attempts to improve my teaching have me moving towards a more student-centred approach, not searching for a more efficient way to deliver a lecture.

3. **How does replacing a one-size-fits-all lecture with a one-size-fits-all video meet the needs of all of your students?**

** **Flipping proponents exclaim, “Kids can pause and rewind videos! They can watch them over and over again!” Yeah. But it’s still the same video. This reminds me of the time I was lost in Naples. I asked a local for directions to the train station. He patiently repeated, in Italian, the directions to me several times. I was still lost. Last year, Dr. Marian Small spoke with almost 100 secondary math teachers from Surrey about differentiating instruction. Surrey teachers are beginning to use her two core strategies: open questions and parallel tasks. The ultimate goal of differentiation is to meet the varied learning needs of all students, not to have students complete a series of videos at their own pace.

My final objection to the flipped model is that it is being held up as revolutionary. Assigning a video lecture for homework, and then working on 1 to 49 odd in class instead of watching a lecture in class, and then working on 1 to 49 odd for homework should not be considered a revolution in math education. (If this flip did result in higher scores on standardized tests, does it matter?) We know that real change is difficult. Flipping a classroom isn’t – all that is needed is a tablet PC.

I would like to redefine what flipping a classroom means. My idea of a flipped classroom would be one in which students, not the teacher, are doing the math. Instead of teacher-created videos, the tools of my flipped classroom would be chart paper, felt markers, and sticky notes.

Technology will also play a role. In Surrey, secondary science/math teacher Blair Miller uses video, in the style of Dan Meyer, to ask engaging questions. His students use Vernier Video Physics, an iPad app, to analyze functions. His students interact with dynamic applets that he has created using GeoGebra.

*These* are effective uses of technology. *This* is a revolution that I can get behind.

*Special thanks to Numeracy Helping Teacher Chris Hunter for this post. You can visit his blog at http://reflectionsinthewhy.wordpress.com/ or reach him at @chrisHunter36.*

Want to learn more? Chris recommends the following:

• The Wrath Against Khan: Why Some Educators Are Questioning Khan Academy by Audrey Watters

• Khan Academy and the Mythical Math Cure by Sylvia Martinez

• Khan Academy: My Final Remarks by Frank Noschese

• Khan Academy Does Not Constitute an Education Revolution, but I’ll Tell You What Does by Steve Miranda

• Khan Academy Is Not the Progressive Model You Are Looking For by Tom Barrett

• It’s a Video Library, Not a Revolution by Diana Senechal

• Content Delivered, Captain. Full Speed Ahead by SD36 Helping Teacher Amy Newman

Chris,

Thanks for this guest post! You present a compelling argument for a true revolution in math education (applicable to ALL fields of study) We used to talk to our student teachers about flipping the mirror —from facing themselves to facing their students — not always easy, but as Bruce Bearisto says, a necessary disruption.

Chris,

First of all, I appreciate your article. You bring up some valid concerns. But, as a teacher that uses a flipped classroom, I wanted to throw a couple of responses out.

1. While much of the media is on Gates and Khan, their stories and articles do not accurately represent well-run flipped classes. I’m not going to pretend “record and deliver” classes do not exist. But, I would argue that many flipped classes do not run that way. Many have students explore and then use the video for remediation or reinforcement rather than initial instruction. Aaron Sams wrote a great post about this here.

2. There are many times where direct instruction are absolutely necessary. I understand your Naples example (and I’ve been in similar situations myself, so I know the frustration you felt) but that is where the teacher is absolutely critical. I can see that frustration and I step in to address misconceptions. Or, students seek me out either online through email or Twitter or they pull me aside in class. I can then adjust what was said in the video and they can continue. I am able to more fully meet their needs.

3. Student-creation is key. I absolutely agree with that and I do work hard to incorporate PBL and student-driven learning. But, not every lesson is best taught that way. So, it is more of an amalgam of tools working together to reach a goal or outcome.

All I am trying to say is that a flipped classroom is much more complex than what you see on the news, much like any other class when viewed at a distance.

Thanks for the thought-provoking post. One statement urged me to comment:

“We know that real change is difficult. Flipping a classroom isn’t – all that is needed is a tablet PC.”

That is a very uniformed opinion. I am in my second year of flipped class implementation and it is the hardest thing I have ever done as a teacher. It is much easier to do the things the way you always have than it is to try something new. It’s about the “learning” not the “teaching.”

I suggest you actually observe a well-run flipped class in action. I don’t think you’ll find a perfect one, but I am pretty sure it will be more impressive than most traditional classes you have observed. There are no incompatibilities between your ideas of a constructivist education and the flipped classroom, when the flip is designed to include a balance of inquiry, learning from mistakes, self-sufficiency and perseverance.

One of the points of my post was that educators should ask some important questions or risk being seduced by technology into thinking that turning math class into a drop-in tutorial is a good thing. So, thanks, Brian, for your thoughtful response.

Although both ‘stand and deliver’ and ‘record and deliver’ classrooms exist, only one of these is celebrated, by media and educators alike. I wouldn’t describe using screencasts to remediate or reinforce to be flipping the classroom. (What has flipped?) I would also think teachers who use video in this way (as just another tool in the toolbox) would want to distance themselves from a term that, like it or not, now implies video lecture at home and homework at school.

I agree there may be times where direct instruction is appropriate, particularly in instances where the goal of the lesson is to learn a procedure. (Synthetic division quickly comes to mind – not a lot of conceptual understanding required there.) Use of video may be worth exploring here.

I think we’d also agree that incorporating PBL (where doing projects leads to student learning) as you try to do is a far cry from Khan saying he’d ‘have them build robots’. Are how-to videos and projects like the latter working together to build a common view of what it means to learn mathematics? Let’s throw Khan aside. Gates, too. If I’m emphasizing how-to instructional videos in my classroom does that make it more difficult to adopt a learning THROUGH problem-solving approach in my classroom?

Philip,

My “Flipping a classroom isn’t” comment is an oversimplification. Brian pointed to different versions of the flipped classroom. Do you see the change that I described in the paragraph containing this comment as being difficult? This version of the flipped classroom certainly exists. I agree that it is much easier to do things the ways you have always done than to try something new – just so long as we don’t confuse moving from a lecture in class to a lecture on video as the something new. It doesn’t sound like I have to convince you of this since you write that implementing a flipped classroom was one of the hardest things you’ve done. One last thing… I think we need to set the bar a little higher than “more impressive than most traditional classes”.

I just want to quickly comment on your first claim:

Bill Gates dismisses it – this belief that children can construct their own understanding of mathematics. Many educators disagree.

John Van de Walle’s student-centred approach? Marilyn Burns’ insight into how children learn math? The rationale in the WNCP curriculum? The beliefs of the BCAMT? Gates would dismiss them all.

The truth is that this is simply not true. First, I should point out the Marilyn Burn’s MRI project is being directly funded by the Gates Foundation. See http://www.impatientoptimists.org/Authors/B/Marilyn-Burns

Also, another constructivist curriculum (based on the latest research in cognitive science) is JUMP math, also being funded by the Gates Foundation. See http://www.ashoka.org/story/bill-melinda-gates-foundation-now-open-visitors …. the curriculum (uses guided discovery) can be accessed here… http://jumpmath1.org/supporting_research

Clearly, a more complicated conclusion is to get reached, isn’t it?