Discovery Learning: The Story of the Rubik’s Cube

Starring the inimitable Bodil Isaksen, the amazing Sarah Clear, the redoubtable Katie Ashford, and the wonderful geeks of Michaela Community School

In a bid to make my lengthy commute more enjoyable, I have been experimenting with a range of pastimes on the tube: listening to audiobooks; playing (losing) chess against my phone; ensuring a liberal distribution of croissant crumbs about my person.

I found a new activity a week ago.  While talking to the excellent Ms Isaksen in her classroom, I noticed the small pile of Rubik’s cubes she keeps there as prizes for exceptional performance in Maths.  She lent me one to play with, and a new obsession was born.  I had played with Rubik’s cubes in my early teens, although I had never learned to solve one.

In the following week, I muddled and fiddled and shuffled my way around the cube.  I got really good at solving one side, but was utterly flummoxed after that point.  I thought that either it was a matter of time until I cracked it, or that I just wasn’t Rubik’s cube material.  Meanwhile, my colleague Ms Clear solved one in fewer than 3 minutes in front of my form, to the awe and applause of the kids.

It was then that I bit the bullet and looked up the solution online.  I figured that if I wasn’t making any headway in solving one myself, I could learn from the experts.  So, I wrote down the algorithms and, lo and behold, I solved the cube.  And then I solved it again.  I started to see the interrelation of the movements to the positions of the pieces, and the first few steps at least became completely automatic.  I was soon able, with the help of the algorithms, to solve a cube in less than 6 minutes.  It felt like a real triumph.

A lovely side-effect of my determination was that a group of about 15 pupils would ask to play with the cube every break time, and huddle together helping one another to put certain pieces in certain places.  They were all wonderfully confident in their ability to solve the cube, even though they never had before.  This confidence usually wore off after about 20 minutes of play.

I realised that my pupils, Ms Clear and I fell into three distinct categories.

Ms Clear has a well-developed understanding of the interrelation of the pieces on the cube, and a seemingly innate sense of how to solve one. She can solve a cube with ease.

The pupils have boundless enthusiasm, but no real understanding of how the cube works or how to solve one.  Without guidance, they become quickly disenchanted when their efforts go unrewarded.

I had no real understanding of how the cube worked, but I was shown the answer by somebody with expertise, and as a result came to understand and be able to solve the cube.  I was then able to practice until the steps became embedded and automatic.

While showing off my new skills to my fellow teachers, I explained that I was ‘cheating’ – that I’d looked up the algorithms and followed them, because I was fed up of not knowing how to do it.  Ms Ashford chimed in that this was an amazing analogy for discovery learning, something that we have quite strong feelings about at Michaela.  She had, in just a few words, summarised exactly what was going on.

In a discovery learning classroom, you have two kinds of pupil – the pupils who get it (Ms Clear) and the pupils who don’t (me).  The pupils who get it feel clever; the pupils who don’t feel stupid.  This is hugely damaging.  It lulls the pupils who get it into a false sense of security (“I got it on my own because I’m smart”) and reinforces to the pupils who don’t get it that they never will (“I don’t get it because I’m stupid”).

Neither of these states are necessary.  I chose the alternative: learn how to do it from people who know how.  I found (was given) the necessary information to complete the task and to be, and feel, successful.  It had nothing to do with ability, and everything to do with practice and assimilation of the new material.  Now, no layperson would be able to tell the difference between me and somebody who intuitively ‘gets’ how to solve a Rubik’s cube.

My housemate, when I related this story, said that I was cheating – that I couldn’t really solve the cube by myself because I’d learned using the algorithms.  This is arrant nonsense.  The end result is the same: I can solve a Rubik’s cube.  I got there with far less pain and frustration than if I’d tried without guidance.  I don’t feel any less smart for not being able to intuitively solve the cube: I feel accomplished because I’ve gone some way to mastering the tried-and-tested technique.

If we give the kids who don’t get it the algorithm, we give them the key to success.  If we give the kids who do get it the algorithm, they get to practise and make it automatic.  Tell the kids everything they need to know, and then give them lots of opportunities to practise.  Only then will everybody be able to ‘solve the cube’.

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Spring Clean

Once in a blue moon, I’m moved to rid myself of the clutter that accumulates over the course of term time.  While I was busy having one of the greatest summers I’ve ever had, the heaps of paper and stationery and books and shoes and so on languished in piles around my room.  The piles became mountains. This morning, as I knocked over a mountain on the way to brush my teeth, I thought it time for a spring clean. Yes, it’s autumn, but hang the orthodoxy.

You know the kind of purge I’m talking about.  Summer clothes are banished to the bottom drawer, items are dragged out for re-heeling/mending/taking to the charity shop, hours pass in a haze of ‘what on EARTH was I thinking?!’ It was a morning of cathartic entertainment.

By mid-afternoon I had filled three bin bags.  Now, while this sounds utterly slovenly on my part – and, to some extent, it is – the contents of those bags were different.  They weren’t bags of clothes or shoes.  They were reams and reams of paper.  Paper that had gathered in my room since September 2013, or the day I started my teacher training.

Since I started my training year, I’ve kept every single sheet.  Every booklet, every inset pack, and every set of notes from the many seminars I attended on the various facets of teaching.  I found ‘outstanding teaching toolkits’, guides to various kinds of lesson, data analysis packs.  Over the course of two years, including my NQT year, I’ve amassed close to 3,000 sheets of paper – resources, lesson plans, training notes, advice, photocopies of god knows what…  I kept it all, in the naïve expectation that, at some point, I might need them.

Today I threw them all away.

I figure that the following is true:

  • If I haven’t revisited this stuff in the last two years, I won’t.
  • If I found it useful, I would have in some way assimilated it into my teaching. If I didn’t, I don’t need it.
  • There may have been a huge amount of wisdom contained in that paper, but nothing compares to the wisdom you gain by seeking advice from good people about real life classroom experiences.