Julie Arrol asked me this question yesterday on Twitter:
What are your views about amount of time to spend whole class teaching in maths vs. individual/group work etc.?
I told Julie I’d get back to her, but my response needs more than 140 characters – hence this short blog post.
The short answer is that there is no answer! All three modes are useful, and an effective teacher will use all three, but it is not useful to attempt to prescribe an ideal mix. At the risk of setting up a straw man, I think it’s important to remember that there is no such thing as a perfect lesson, and that a lesson which suits one learner very well may fail completely to meet the needs of another member of the class.
Having said that, the reality is that learners still spend the majority of their time in secondary maths classrooms either being taught from the front or doing individual work. This is especially true for the more academically successful learners in S3-S6. One could argue, therefore, that there is room for more group work! I think the work on cooperative learning in maths is very interesting, as is the critical skills model of group working. But we mustn’t throw the baby out with the bath water – those of us old enough to have used the SMP individualised maths program remember students who could pass a test on ratio, but pronounced it “rat-ee-o” because they had never heard anyone say the word!
I suppose the bottom line is that teachers and departments need to find their own answers to this question – guided by discussion with colleagues and learners, and by honest reflection on their own practice.
I’ve been asked via a DM on Twitter for advice about purchasing a first mandolin for a beginner. A proper response will need more than 140 characters, so here I am!
Firstly, I should congratulate you on having the good sense to consider learning to play the mandolin! It is a fabulously versatile instrument, and is relatively easy to learn.
There’s a popular saying among mandolin players: “life’s too short to play a cheap mandolin.” As a beginner, you won’t want to spend too much, of course, but it’s definitely worth spending enough to get a real instrument rather than a toy. My first mandolin was a Tanglewood which cost about £160. It made a pleasing sound and had decent intonation. Before that, I did initially buy an Ozark mandolin for about £70, but it was pretty much unplayable and sounded like a toy – I returned it to the shop.
I can’t overstate how important it is to buy a mandolin that will produce a decent tone – it is really motivating! What constitutes a decent tone is, of course, subjective, so I would recommend that you go into music shops and pluck a few. If you feel self conscious about doing that, ask someone in the shop to play them for you.
After 18 months learning the mandolin, I invested in an Eastman 515 mandolin. At the time I felt very uncertain about spending so much on an instrument, but it was SO worth it. The pleasure I get from it is hard to put into words. You develop a real relationship with a quality instrument as you play it over time.
If you just want a cheap instrument, go for a ukelele instead
I observed the class of an experienced colleague today, at the invitation of my colleague. He is very pleased with the way the class is getting on, and wanted me to come in and give the class a boost.
It was fascinating, as always, to observe a lesson, and I was indeed very impressed by how engaged and enthusiastic the youngsters were.
After the lesson, I recalled how, as a probationer, I was frustrated by the fact that some teachers seemed to have excellent behaviour in their classes effortlessly, whilst I had to work hard managing behaviour.
18 years later, I know that the effortlessness I thought I saw was just an illusion. Experienced teachers are constantly managing the behaviour of their classes – principally by planning interesting, appropriately challenging lessons and by maintaining positive warm relationships with their students, but also by nudging youngsters towards positive behaviour and away from misbehaviour during lessons by the subtle use of body language, tone of voice, humour, praise, chastisement, physical proximity and so on.
For most of us it takes years to develop these skills, and we never stop working on them. As a probationer it can seem like a massive mountain to climb, but over the course of a career it’s part of what keeps the job interesting!
There isn’t really a moral to this story: it was just a wee bit too long for a tweet
Sometimes we just don’t know the effect we have on youngsters.
On Monday I was sitting in the maths base at break time chatting to my colleagues when a sheepish face appeared at the door. It was boy A (who appeared in a previous magic moment), a pupil of mine last session. When he arrived at high school two years ago there were serious questions about whether he would cope in mainstream secondary education, and he has struggled at times.
“Erm, I’m wanting to speak to Mr Jones” he mumbled, so I went out into the corridor to see him. He asked me if I remembered showing Google Sketchup to him and his classmates last year (I did). He told me that he had been playing with it, and wondered if I would like to see the models he had created. I said yes, of course, and he said he would bring them in.
At lunchtime today he turned up with a heavy bag over his shoulder. He unloaded his old laptop and proceeded to show me his work. He has made a brilliant model of an Xbox console and some really intricate houses – and has uploaded his work to the 3D Warehouse.
He was so proud of what he had achieved and I was so proud of him – proud and honoured that he wanted to show his work to me. I called in Craig, who teaches him this year – - “You must see this stuff!” and we all had a play with the models in Sketchup.
A magic moment
I’m currently reading Mindset, by Carol S Dweck (soon to be appearing at the Scottish Learning Festival!). In a nutshell, her thesis is this:
Everyone has one of two basic mindsets. If you have the fixed mindset, you believe that your talents and abilities are set in stone – either you have them or you don’t. You must prove yourself over and over, trying to look smart and talented at all costs. This is the path of stagnation. If you have a growth mindset, however, you know that talents can be developed at that great abilities are built over time. This is the path of opportunity and success.
This makes a lot of sense to me. I have inevitably been wondering about the mindsets of those around me, and about my own mindset. It would be indiscreet to try to judge others here, so I’ll do a bit of navel gazing!
I most definitely grew up with the fixed mindset. I caught it from my Mum (notice that those with the fixed mindset tend to look outside themselves for things to blame!). She constantly told me how clever I was. Not how hard I was trying, but how clever I was. And she still does, bless her.
Fixed mindset people tend to shun hard work, because it exposes them to the risk of failing without the get-out clause of “well I didn’t really try very hard anyway.” In their world-view, such a failure demonstrates an intrinsic weakness in themselves, rather than just a temporary setback.
I can see clearly how the fixed mindset let me down at various stages in my education. I applied to Cambridge to study maths, but when they gave me an offer which I doubted I would be able to achieve, I turned down the offer rather than accepting the challenge. And when I was told by a tutor at Edinburgh University that I was doing well but would have to work harder in final year in order to achieve a first class honours degree, I chose to relax and “settle” for a 2:1 (not that the 2:1 came easily, but I consciously chose not to do the work required to be in with a chance of a first).
I can also see how one’s mindset can change.
At school I was a very low achiever in PE – a report card comment said (and I quote verbatim) “Tries hard but achieves little success” (the fact that I remember that after 30 years says something about how it made me feel, by the way). But I clearly remember the one time that I enjoyed PE . We had an 8 week block of circuit training, in which we kept records of timings and monitored progress. I saw myself improve, and was delighted. For a brief moment I had a growth mindset towards PE. But then we went back to high jump, and the usual raised eyebrows from the PE teacher as I failed to reach the lowest height setting of the bar.
I think teaching changed my mindset for good. I came into teaching thinking that I could change education, and pretty soon discovered that I wasn’t even a very good teacher! I was left with a stark choice – quit, or start working as hard as I could to master the craft of teaching. For once, I rose to the challenge, and here I am 18 years later. I don’t have to work as hard now as I did in those first few years, but I am acutely aware of the fact that my competence as a teacher has little to do with innate ability and a lot to do with hard work, perseverance and a willingness to learn from my mistakes (which continue to happen on a daily basis!).
I have not finished Mindset, and have not begun to reflect in any depth upon the extent to which my classroom practice fosters either the fixed or the growth mindsets. But I shall endeavour to undertake that reflection in the growth mindset.
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