A drama-based approach to calculus

I am in the classroom of Bryce Jandon in Wattson, UA. Before us stands a student wearing a curly wig and plastic, no-lens glasses. His name is Dale and, for today, he is a calculus teacher.

“This is a slope,” Dale explains while holding aloft a string manipulative that he has contorted into a curve.

“Good work,” Bryce smiles, his eyes glistening with pride.

After class, I take Bryce to one side to discuss the innovative calculus program that he has developed in partnership with the Extraordinary Learning Foundation™.  We start with a conversation about Dale.

“It’s not that Dale actually believes he is a calculus teacher,” Bryce explains, “I don’t think we often give kids enough credit. He knows it’s a dynamic drama-based experience.”

I nod sagely in agreement, “Is that a common misconception?”

“Yes,” replies Bryce, “people who don’t understand what we do are like, ‘how can a kid teach calculus?’, ‘doesn’t the kid know he’s not a teacher?’ and so on. It’s kinda like that. But that’s not the purpose. A drama-based pedagogy enables students to empathise themselves into what it would be like if they could do calculus or whatever. That’s a key point. It means that they see it as part of the seascape of potentialities.”

Of course, Bryce is right. I ask if he can explain a little more about the program and how it developed.

Modestly, he suggests, “I owe it all to my mentor, Principal Peters. I was teaching fifth grade social studies when she came to me and suggested I give calculus a go. Naively, I was kinda horrified. I explained that I didn’t think I was up to it; that I didn’t know any calculus. But she put me at ease – using a drama based pedagogy, we could all learn calculus together through co-deliveracy. And anyway, she explained, she couldn’t find a proper calculus teacher.”

I already knew the answer, but I asked Bryce to explain what his pedagogy involves.

“Well, I set the scene. We place it inside a narrative where one of the students has got to teach this class on calculus. This is the set-up, right? We know from cognitive science that narrative is held best in the brain – at the front somewhere – and so that’s the thinking. In Act I, the rest of the students are colleagues of the teacher who help him research his lesson before becoming the students in Act II.”

“Some people would ask how effective this method is for teaching calculus,” I suggested.

“Ah yes,” Bryce nods knowingly, “The guys who want to measure everything and calculate everything: The positivists.”

We both chuckle.

“Look,” Bryce explains, “I’d say to them that we are doing much more important work here than merely developing a student’s ability to regurgitate disconnected facts on a standardised test. The jobs of the future will not even exist. They will require collaborativity, evaluativity and the ability to work together. All of these crucial skills are developed through this unique pedagogical approach. In comparison, the idea of learning how repeat a few algorithms for the purposes of a 19th century test in an airless room is just over.”

‘Exactly,’ I think as I walk to my car at the end of our meeting: Learning calculus is not the point.

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Developing a Thinkiness scale

At the Extraordinary Learning Foundation™ we have developed a number of ways of making Thinkiness visible such as this one:

And also this one:

These express Thinkiness as a provocative verb construct. A doing. However, as we continued to work with the complex and surprising concept of Thinkiness over time, we began to realise that there were different levels, with some tasks and conceptualisations being Thinkier than others.

It was while the team here at West Bay University were contemplating Deleuze’s concept of becoming that we came-up with what has come to be our powerful metaphor for how this kind of development comes about. Rather than going up like a tree does, we decided to express the increasing intensification of Thinkiness as a series of different depths.

I’m guessing you’ve not seen anything like this before and neither had we. The beauty and simplicity of the abyssian metaphor immediately struck us as a close correlate of going deeper and further into our students’ heads; precisely what Thinkiness is all about!

This clearly illustrates that Thinkiness is not dichotomous. The direct teaching of indigestible facts has a role to play in developing Thinkiness, it’s just that it’s not a very important one and is potentially a form of abuse.

Instead, all practitioners in their own myriad ways and using a full spectrum of pedagogical techniques can develop Thinkiness in an authentic and relevant manner that is true to themselves and their students, now that they have this diagram.