FEKR! Take that proportionality!

I recently read Doug Lemov’s book and was intrigued by it.  I liked his suggestion to turn anything that has several steps into something more interesting.  I probably should have thought of it myself a long time ago, but there you go, I didn’t.  So, I give you FEKR! The illumination of a light, L, varies inversely with the square of the distance, D.  When L = 100, D=50, find an equation for L in terms of D.

 

F – the fish statement E – form the equation K – find k

R – replace the k

 

Maybe that’ll stick a bit better.  It did make it easier to refer to parts of the argument that were missing and I’m looking for ways to use this in other places.  I don’t want to rob of the higher order thinking though – how do you find the balance?

The summer term begins

I decided to put my chairs back in rows today…

This didn’t come as an easy decision but I figured I have to try it.  I’m struggling through a weird internal conflict at the moment.  Philosophically, I fall down on the constructivist side of things … students will learn better if they discover the mathematics themselves and give it their own meaning.  Dylan Williams says, “The more explicit you are about what you want, the more likely you are to get and the less it is likely to mean.”   I want group work, discovery lessons, cooperative learning and the like.

But I also know that if I have short bursts of 10-15 minutes activities that explore a learning objective, in active and calm ways, with whizzy bits and practice bits, highly directed with room for pseudo-discovery and all delivered in an enthusiastic way, my students will learn.  They like the Me-Us-You structure of traditional transmission teaching and respond well to it.  Their parents expectations are met when lessons are delivered in this way,

Here are my questions:

Is this ‘doing mathematics’ or prepping for a test?

Given that so much of the students’ futures are influenced by their GCSE results, should I just get over my philosophy and teach so they can do it?

Where do these things become mutually exclusive and where do they co-exist in perfect harmony?

I’ve been teaching for a while now and I think I’m quite good at it.  But, I also have long periods of self-doubt and inner reflection – I read something and decide to through the baby out with the bath-water.  I hope I’m not doing that now but we will see.