Today was a pretty important day in my approach as a teacher of lower sixth mathematics. It was the first time where I can genuinely say I planned for and observed for learning.

I have blogged previously about our approach at Wellington to Sixth Form Maths – following the Harkness philosophy where students come in with questions done and we talk about their solutions in class.

Usually these lessons involve me chairing a discussion and letting student A talk through his/her solution before the odd pupil chimes in. I then proceed to ask some question to try and touch on the conceptual ideas. “Why is it important to write the equation in this way?” “What does this mean we can now do?” “Why do we care how many roots this quadratic has?” etc.

This morning, however, I decided to remove myself from the lesson and watch. I told the class this was my intention and I would only intervene when they had confirmed they were happy with the discussion that took place and I had spotted some mistake.

What then followed was some brilliant student leadership – a couple instantly took it upon themselves to dictate pace and timings of the lesson. They decided to focus on 4 questions and the atmosphere was far less judgmental than it feels when I am involved. The students seemed far happier to interject and offer slight changes to solutions than when I am leading the discussion. I think this was probably because they are waiting for me to jump in sometimes.

I only had to step in on two occasions. One was to be slightly more rigorous with a proof and the other when a conversation was going round and round in circles. The second in particular was a valuable learning point for all about how to bring yourself back to basics when finding a problem with a mathematical question.

The problems with this lesson were that the conversations were very procedural. “I did this and then I did this” “But how have you got from that line to that line?” “Yes I got that answer too” “Did you do that on the calculator?” “Is my answer the same?” and so my challenge for them was that next time I want to listen to some conceptual conversation.

This is something I will almost certainly try with all my classes in the near future. I felt like an empowerment happened and the students surprised me in the quality of the discussion. I have since learnt that “this won’t work in maths – the teacher is too important” was an egotistical feeling more than a fact.

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