I have been meaning to write a post about the flipped classroom and its use, particularly, in mathematics classes, for a while.
After a week’s leave in Outback South Australia and then a week dealing with the flu, I have finally found that space in which I can.
I was interested to read of the “Khan Criterati”, as Dan Meyer calls them, in this post.
Apparently a video that addressed the mathematics of negative numbers (which I have not seen) created a bit of a furore.
Dan Coffey, one of the main critics of the Khan Academy videos is described as saying:
But as Dave Coffey explained on his blog, it is the pedagogy of the lecture model and Khan’s emphasis on how to complete the mathematical procedures he’s explaining instead of the conceptual framework behind those procedures (the why of education) that is at the heart of the criticism.
I have a great deal of empathy with this view. I think there is a reason that mathematics was the first discipline to feature videos as part of a flipped classroom…it is seen as a discipline that mainly involves learning procedures and processes and ‘answer getting’. If you learn the process, you learn mathematics. Regular readers would know that this view is anathema to me.
For example: the teaching of solving simultaneous equations. The ‘big idea’ behind simultaneous equations is a strategic problem solving technique, that of breaking down a larger problem into manageable ‘chunks’ by considering one aspect of a problem at a time. That is the transferable idea. To teach to understand that idea, one can introduce it in a number of ways. The aim is not merely to be able to ‘solve’ the two equations in two variables. To teach simultaneous equations as just the technique is to teach ‘answer getting’. This is not mathematics.
My strongly held belief is that the teaching of ideas should be the determining paradigm in the teaching of mathematics. These big ideas are the peaks of the landscape, the things we look out upon, appreciate for their beauty and use to guide our journey forward. Looking at, and placing, where we put our feet are the skills and processes of the discipline. The metaphor can be extended.
One can scale the peaks by following in the footsteps of another, having porters doing the heavy lifting and carrying and setting up camp where others decide. The journey is not easy, even with all of this. Take away the porters, take away those that showed the way, take away the determined paths and put that same person in an unfamiliar landscape. Could that person undertake another journey in the landscape using their previous experience? Is that important?
I happen to think it is.
Education should not just be about learning about the ‘known’. We need to ensure students are educated to deal with the unknown. One recent tweet I read (cannot recall who said it, I’m sorry) indicated that education is not about ‘preparing’ students, it’s more about learning how to ‘be’ in the world. We can no longer educate for particular professions. We need to teach students how to think for themselves and to self-manage…to take control over their own learning.
I think that the non-discriminating use of videos to instruct students in the ‘how to’ of the skills and processes of mathematics contributes to a shallow view of the discipline, reinforces a ‘lecture style’ of instruction that detracts from a more active learning pedagogy and implies that there is one set process that needs to be learnt. It can take away creativity and independence of thinking.
I have kept an open mind with respect to the flipped classroom and tried out a couple of flipped lessons. I gave my Y9 class a video on scientific notation with some associated follow-up questions and it worked very well. I could walk into the following class, check for their understanding of what scientific notation meant and whether they could use it then move onto more important ideas.
I am not saying that the flipped classroom has no place in the mathematics class. What I am saying is that the teacher needs to think very carefully about what the essential learning is that is desired to be engendered and then consider the appropriate pedagogy that will give students the greatest opportunities for them to learn it. Sometimes a video is not going to be appropriate. Students need to have the discussion with each other, they need to make mistakes and learn from them and they need to grind their way through the thinking in order to embed the learning in their own brains by connecting to previous knowledge.
To assign a video lesson to ‘instruct’, without thinking carefully about it, is criminal in my view.