On learning how to solve the Rubik’s Cube

Watching my 9-year-old son, O, teach himself how to solve the Rubik’s cube this Summer has been one of the most instructive and thought-provoking experiences I have had as a teacher. It has been like a mini-distillation of going from novice to expert and of how we learn. He decided he wanted to be able to solve the cube back in August after finding some internet instructions for making a Lego Mindstorms robot cube-solver – I think he was fascinated by the way it took 25 seconds to scan the cube from all angles before then following a set of algorithms to solve reliably solve it every time.

He then found a YouTube video showing an easy solving method, and we watched it together. It was here that I found that both of us started to form a new “schema” of the cube and start to see it in an entirely different way. Despite being a child of the ‘80s, I had never really got into the Rubik’s Cube in my youth and initially saw it as 6 different coloured faces. It had never occurred to me before that the middle squares of each face “fixed” the colour of the face and I then began to see the cube not as being made up of faces, but as being made up of centres, edge pieces and corner pieces. (I should have spotted this before given the number of times I did the Painted Cube investigation with my classes back in my early days of teaching!) O and I managed to follow the video’s instructions to make the White Cross, then solve the White Face. At this point I was already finding I had too much to hold in my working memory, so we got an old exercise book and I (in true teacher fashion) got O to draw some reference diagrams of the moves we were following and write some notes on the algorithms we were learning. We spent most of a day of the Summer holidays working through this video (whilst I simultaneously attempted to help my younger boy build some Lego) and although we had the first two layers sorted, we were struggling to get to the final solution. Note here that our schema of the cube had changed again: now we saw it as three layers, with white on top and yellow on the bottom, with the edges and corners belonging to particular layers depending on their colours. My initial “faces” schema had disappeared.

After a lot of huffing and puffing (mostly on my part) and re-watching of the video we finally managed to get it solved. This was the only part where O was not fully engaged, and maybe he would have called it a day at this point if we’d not managed to work out the last steps of the video. I just had to finish a job I’d started, but once I did that was enough for me. I could solve the cube (as long as I had our handwritten book of move diagrams and algorithms to refer to and could have a good 10 minutes to do it). But it was here that things really started to get interesting.

Over the next few days O fiddled about with his cube, very quickly dispensing with our notes. He could reliably solve the first two layers, and told me about how he had memorised the algorithms needed – by making up words or chants using the names of the moves: “Front Inverse Right Front Right Inverse” became “FIRFRI” etc. He used his pocket money to buy himself a “speed cube” and decided he wanted to be able to solve it in under 2 minutes. He wanted to watch a YouTube video of the F2L (“First 2 Layers”) method of “inserting the corners” two layers at a time and was now using all the jargon of the YouTubers. He struggled with this though, and it made him cross, as despite his speed cube he thought it was taking him too long to do the first steps and this was stopping him from becoming as quick as he wanted. At this point I had nothing more really to do with his solving, apart from being asked to time him occasionally, and trying to remind him that in order to get really fast I thought he should probably just get really really good at the steps he knew so that he could do them without thinking.

And very soon he could. And this is where things really seemed to change again. Now he was no longer thinking in algorithms. “If this edge piece is here, and I want it here, I know that I just have to do this and this and that will move it” he was saying to me. He had started by learning a set of instructions that had no real meaning, but now he was really good at these instructions he was finding the meaning in them. He was intuitively using properties of the cube to make things quicker: “I know because this corner piece is here I’ll have to do those two moves 5 times, but if I do them in reverse I’ll only need to do them once”. I asked him about how he was seeing the cube differently compared to when he first started learning, he told me that he could now pick up the cube and by looking at the positions of the pieces see if it was going to be an easy or difficult solve. He was using the positions of the pieces to work out what to do, rather than the standard algorithms: “If I want this edge on this opposite side, I know I turn this layer away from where I want it, this layer towards, then this section away twice again” (or something similar). And he was coming to terms with the F2L method: “I can do it, but sometimes if I see the white pieces are in a particular pattern then I know actually it is going to be quicker to do the other method anyway”. He now wants to explain his methods and thinking to me, which led me to talk to him about metacognition and try to get him to think explicitly about his reasoning. When he tried to walk me through one particular step he found he couldn’t do it slowly. He had become so fluent in that particular move that he was now having trouble unpicking it himself – thinking too hard about it caused him to mess it up.

He can now solve the cube in easily under 2 minutes on most occasions which I am incredibly impressed by, and a lot of the time he doesn’t even have to look. He has shown real dedication and it has been so interesting watching him along his journey. He now wants to buy a “better” speed cube. And of course we now have a great personal analogy for successful learning and for overcoming hurdles: “You didn’t do so well in that last TTRockstars gig, but think back to when you were struggling with the F2L method and you practised, and now look at you! You can do the same on TTRockstars…”

The perils of having a mum who is a teacher….

By Deb Friis

 

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