Free (the) learning

Last Friday April 17th I attended the Thinking Classrooms Experience meeting where Innovamat brought Peter Liljedahl to Madrid and I felt like sharing what i learned. Peter Liljedahl is a doctor in mathematics education who has spent more than 20 years researching how to improve teaching and he discovered that the best way was by getting students to think. He made us think and I learned. If you haven't read his book Building Thinking Classrooms, I highly recommend it.

How many times have we encountered students that used to love maths, who have always been good at them but their grades suddenly dropped to the point of failing?

Peter talked about mimicking and how humans tend to be efficient choosing the least cognitive demanding path when solving something. If the students get good grades by mimicking what the teacher has previously done, we are rewarding them for mimicking and that's what they'll learn, to mimic.

Mimicking is effective in the short term, he continued saying, at the beginning it is possible to do well by mimicking because of the low demand of curriculum, but curriculum demands grow and, eventually, they'll exceed what you can do by mimicking.

So, a possible cause of a significant drop in grades could be that they weren't good at maths, they were just good at mimicking.

He told us that the traditional "I do - We do - You do" scheme promotes learning by mimicking, the same goes for teaching worked examples or problems. And when a student starts to learn by mimicking, it's very difficult to change.

The alternative to mimicking is making them think. But asking students to think won't work if we don't facilitate thinking situations which they won't get over by mimicking.

This reminded me of Carlos Magro's "The way we assess determines their way of learning".

Students don't listen to what we say, they listen to what we do. If we ask them to think but we work out problems that can be solved by mimicking, what they hear is that they have to mimic.

Peter said something that has had me mulling it over: "Liberate them to think", they already have it in them, we just need to make sure that they can do it.

A good thinking task (a rich task) must have a low floor and a high ceiling. The low floor makes it reachable so everyone starts thinking and the high ceiling prevents the highest achievers from finishing fast and getting bored.

He spoke about how natural it is to get frustrated in mathematics, he talked about hopeless frustration and hopeful frustration (a.k.a. productive struggle). Because frustration can either make us abandon the task or roll up our sleeves and fight it.

How can we get the students in the right side of frustration?

When students are on the road of success, they get on the right side. If we pose a reachable path of tasks and they link a number of consecutive successes before a challenge, they will be more likely to fight it. But, if they struggle from the beginning without success, they will be more likely to abandon the task and disconnect from the activity. This justifies the low floors. The high ceilings are to stop them from mimicking.

When students are not thinking, everything is difficult, it takes more time and they don't learn. 

Getting them to think takes time, but when students are thinking, anything is possible. When students are not thinking, everything seems difficult to them, it takes more time and, actually, they don't learn. Instead of drowning them in curricular tasks, it pays off starting with a strictly non-curricular rich task in order to "start" their brain to think, and then shift to a curricular task.