# I wish this game of football would end, I want to play some soccer……

I think that both of the respective articles argue some fascinating points. Meyer highlights a level of impatience amongst pupils and possibly the desire for students to find the easy answer, he also highlights the use of textbooks by most teachers, and the reliance on the pupil to refer to previous questions and map their answers from such onto a newer problem. In essence, I think that this argument is very much shared by Skemp and his opinion on instrumental learning.

As highlighted in task 1 by Sir Ken Robinson, pupils in the modern world have an overriding desire for instantaneous results, and if this becomes a longer activity in duration there is scope for students to lose interest and react with, in most cases, negative behaviour. Meyer argues that teaching should be grouped into shorter “sitcom” segments, however at the same time he emphasises the need for an understanding to address problems. We need to make sure the student understands what is actually required from the problem and then we can use the methods that we know to begin and solve such.

I think that Skemp’s piece raises some significant fundamental points, the concept that children are taught very much on a rational basis unfortunately rings quite true. This can be typified by the processes by which children at infant stage learn multiplication through their times tables, how much understanding do they really gain from what they are doing? Only this morning, I was part of a lesson which explained how trigonometry actually works, now I love Maths but even so I have to say that this particular subject was one of my least favoured. In hindsight, I think that this is so because I didn’t have an understanding of actually how it worked, I simply used the traditional SOHCAHTOA method and punched numbers into my calculator. As of today, I now know and understand and you know what?? I love it!! Out of a typical class of high achievers it would be interesting to see what proportion of children actually understood how the methods they typically learn by repetition actually work. Surely, if they were to have a greater understanding of such they would be able to question their own work with the potential of improved results. It should be noted that in recent years more emphasis has been placed on showing detailed workings, which should imply a greater understanding from pupils.

Meyer’s proposals ultimately puts a great deal of emphasis upon the pupil, asking the questions and formulating their own solutions to the problem, in essence promoting the idea of independent learning. Is this not what Skemp is striving towards with a focus more so on Relational learning? A large part of Mathematics should be exploration and this should be done by the pupil, once we understand how something works we can then use the tools that we have, or even the best tool that we have to do the job. I think teaching can become overcomplicated if everything is taught on a relational basis, but a mixture of this vs instrumental merits thought. The problem is cost and time constraints will apply.

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## aw677

1 March 2016A thought provoking piece Phil, I agree we do need to find a balance between what works best in terms of school policies and politics, but also in terms of cost verses benefit. There is only so much time available to us as teachers and we are faced with a very tangible success criteria. Perhaps we need to reassess the outcome we are striving for and then revalue associated success criteria.

## Charli

7 March 2016I really like your example of learning to love trigonometry more once you had a greater understanding- I think it was a bit of a ‘wow’ moment for quite a few of us. I think that teaching students to become independent learners is so important and can be taken away from students when teacher’s are overly helpful. I agree that a mixture of instrumental and relational understanding would work best from a practical perspective.

## pepsmccrea

8 March 2016Thoughtful response. You make some helpful links with previous thinkpiece ideas and reflects on how Skemp/Meyer’s ideas fit with your own experiences. Good to see you taking a balanced approach in your analysis – looking at both the pros and the cons in striving to reach a considered conclusion.