So, after a week away I have an opinion piece… Please give me feedback as I would like to hear other people’s opinions and I am open to mine being changed!
With the new GCSE specification coming in, I often hear how “we need to be teaching more problem solving skills”, “developing independent learners”, “using inquiry based teaching techniques”. This, along with a general focus on child centered learning makes me feel a bit uneasy….
I’m not against these techniques – I use investigations and inquiry type things to promote pupils curiosity about mathematics and give them a flavour of what being a mathematician is about – but I think they need to be used in conjunction with more traditional teaching styles to be effective.
Most of the maths taught in schools is hundreds of years old and required hundreds of years of work to be discovered and perfected. The average child isn’t going to be like Gauss. When asked to add up the first 100 numbers I’m sure most will just add them in turn (I may try this with some of my classes), even if some notice that you can work inwards and pair up the numbers to quickly work out sum with a multiplication, I don’t think even my sixth formers would come up with the algebraic formula for the sum of the integers without any prompts! There are some things which probably just need to be learnt, so that they can be applied. After all, mathematics is advanced by people applying previous knowledge in novel situations.
With some of the more extreme types of independent learning I question the benefit that it brings to the pupils. If they have no clue about something that has been presented to them, then even the most tenacious pupil will become demoralised. I can’t imagine a teacher that wouldn’t provide more guidance in this situation, and steer the class to the desired conclusion. I really like the unpredictability of the inquiry idea and being able to look at some maths that the class stumbles on, but for them to be able to do this they need a sound knowledge base. This is why, for students to be successful at this and other investigations time must be spent building up a good body of knowledge, that all pupils can successfully weild to enable them to make progress.
In terms of problem solving skills, I think these are probably best taught by equipping students with enough knowledge to feel comfortable that when an approach doesn’t work they can try something else. Tenacity and patience I think are the most important problem solving skills.
I guess in conclusion I don’t like the polarised investigative child centered vs didactic teaching debate – there is a place for both approaches and the good teaches will blend the methods to ensure the best progress of their pupils. But I believe a strong knowledge base is key for any success in mathematics.