Scalable and non-scalable subjects

There is a way to consider mastering a skill as a series of three stages. Take the example of learning the piano. When you first sit in front of those keys every one of them is much the same as another. Sure, some are white and some are black, and you might notice that the black keys have a slightly irregular pattern to them, but you could probably pick your way towards a simple, delightful tune with a few minutes of pecking around. A note is just a note. Spend some real-time getting to know things however, and you discover that the notes can be grouped together into scales, and that some notes sound better in some combination than others, some seem to follow others, and that there is a whole set of rules regarding which note goes where and when in order to build up into incredible moments of grandeur and magic. The musical rules of modes and scales are the framework upon which you construct your music. Go further however, and something more profound happens. Scales and modes begin to dissolve, you find out which rules can be bent and which rules can be broken. Perhaps there were no rules to begin with. Any note is still just a note.

Students are on this never-ending journey too, not necessarily as potential pianists but in whatever skill or subject they turn their minds towards. Our role as teachers may occur at any point along the journey, whether we be the first person to introduce a child to a subject or salute as they surpass anything we ever achieved. But we still have to get them there.

I have spent a lot of time observing, supporting and working with teachers from different subjects. Its usually a very useful experience, but I’ve found that once you are away from the comfort of your own specialism different circumstances come into play. The underlying thinking, structures and ideologies of different subjects can vary hugely. It’s very easy to man the barricades of your own subject and blindly throw accusatory grenades over the top that essentially boil down to ‘in order to improve your lesson you should do it like we do in subject X!’ Good luck with that strategy.

Something I think is useful to consider here is the scalability of a subject. A scalable subject works at both a simple and an advanced level, whereas a non-scalable subject tends towards having fixed limits. Before you raise the objection that there are no limits to any subject, let me assure you I think all subjects have elements of both, but allow me an example.

I would consider English to be essentially a scalable subject. The level of entry is fairly low (excepting young students with genuine language difficulties) because students are (hopefully) familiar with speaking to people, listening, story structure and so on. Yes there are differences and EAL and and and but for the bulk of students the essential ‘elements’ necessary to access the subject are already present: language knowledge. But where does English lead to – there is no end. It can be scaled up from the ability to write ‘what I did at the weekend’ to a Pulitzer Prize winning piece, to get from a ‘It was a dark and stormy night’ to ‘Happy families are all alike…’ is not one that can be done by methodical steps but by an unbounded leap.

So what would a non-scalable subject look like? Well, of course we’re going to science as a prime example. As a taught subject at GCSE and A level (and most of degree level to be honest) it doesn’t really scale up. Compare how many students at your school excel at county or even national level in sports or the arts and compare that to the number of students excelling in the field of science at a national level. I’ll set the class timer for 10 seconds. Science, as we teach it, is non-scalable at this level. There is a a clearly defined set of statements that are assessed and if you know them well enough to apply them to an unfamiliar situation, well, congratulations, achievement unlocked and move onto the next level. Students in non-scalable subjects are like people at the beginning of learning something, they simply don’t understand the ‘elements’ (or as science teachers would call it the content) to start doing anything with it. This is why there is often such a s heavy emphasis on leaning basic content because most students can’t build to anything more complex until they have got past those first mastery stages. There is a high entrance level to access non-scalable subjects, but once you’ve got it the end point is pretty clear. MFL is a clear counterpoint here – how much story writing and poetry analysis goes on at GCSE level in MFL? I don’t actually know, but I’d take a stab in the dark at ‘not much’. Without the ‘content’ of Spanish linguistics, grammar and culture you’re Don Qixote studies won’t get too far.

In the long run you could argue any subject becomes scalable but school students are rarely at that point in their school life for them to have the grounding in content necessary for them to excel in a non-scalable subject. There are non-scalable elements to be found in all subjects of course (there aren’t too many proponents of encouraging creativity in grammar and spelling). If you are working with colleagues in other subject areas go in with an awareness of differences and work with the other teacher. Scalable subjects tend to be much easier to access but there is the trap of staying at the lower levels and being satisfied. Our job often involves taking the students through the less exciting middle level of mastery, not the thrill of first discovery or the incredible heights but the grind of familiarity and fluency. Not all subjects start in the same place nor end in the same place. Don’t assume your experience or subject is Universal.

 

 

 

 

Teacher heuristics

Like the stinking bloom of titan arum, the rarely flowering giant plant that stinks of rotting human flesh, the garish rosettes of election season have reappeared. My knowledge of American politics is currently far better than my understanding of the British scene and it’s interesting to see how much of last year’s elect-u-geddon tactics from across the pond get repeated by our own politicians. The race is on to plant the seeds early in people’s minds, letting the memes flourish and spread like the red weed, until come election time all that will be required is the mere glimpse of a politician to cause people to spurt out “That Theresa May, she’s so strong and stable in her leadership, I’ve always said so, said it years ago, strong and stable I said.” Ho hum.

One of the (many) disturbing things to come from the US was how many people appeared to base their vote not in terms of what they wanted but in order to cause perceived damage to the ‘other side’. Commentators [citation needed…] made the comparison with sports, where the delight in the opposition’s downfall and misery becomes the primary motivation, even over one’s own self-interest. American floors were strewn with self-inflicted nose amputations. Some voters chose harm above self-interest. All of this is interesting from the perspective of decision making and influence, yet this is a blog that tenuously holds on to an educational slant, so what’s the thread I’m trying to weave?

I’m interested in why people make particular decisions. I’ve written before about the affect on option choices, but of course students are constantly making decisions with less long lasting importance, such as behavioural and social choices in lessons. These decisions are based absolutely on their prior experiences and biases. And once the tide of hormones, peer pressure and snapchat has breached the walls of Year 8, the decisions become infinitely more complex. Students are forced to rely on their newly formed heuristics, the mental shortcuts needed to make rapid choices in the everyday world to save ourselves from spending too long evaluating the best course of action. Unsurprisingly, part of the learning process of fine tuning these heuristics into something useful involves a lot of mistakes along the way. Unfortunately for teachers, these mistakes have a habit of manifesting during the penultimate lesson of a full-dayer. So it goes.

It strikes me how many times students will define themselves not by what they are, but what they are not. This is no revelation; the familiar push-back of young people in order to find their own personalities is familiar to any teacher who has asked for a student for the thirteenth time in two minutes to tuck their shirt in, put shoes on that they ‘forgot’ to change back into after lunch or not to lean back on their chairs (4,129 students broke their necks in British schools last year after leaning too far back on their chairs, possibly). The active rejection of cultures and acceptance of others helps develop personalities. If the rejection is one of school culture in general you may have some problems. One solution is to make sure you only select students who already buy into the culture so there is less chance of push-back. You will have your own opinions on the rights and wrongs of that particular issue. But there is another issue in the school: the staff. If you are in any position that seeks to change staff practice or opinions you are in the same position as politicians seeking influence and dealing with the same issues that affect students. The shortcut here involves a top down approach of regulation and ‘selecting out’ staff who do not fit with the culture. You’ll doubtless have an opinion on that too. Yet teachers have their own heuristics and biases that are in play, constantly influencing their decisions not only in the classroom but at strategic levels right to the very top of Government and Ofsted. Perhaps we need to start looking at picking the scab of how much our own decision making processes.

Many people are familiar with the idea of confirmation bias, the tendency to only look for information that confirms what we (think) we already know and favour that information. But there is a counter bias too, disconfirmation bias, where more time is spent attacking and resisting an unfavourable position rather than examining the benefits of your own. Ideas do not float around in an ethereal haze waiting to flourish in a receptive mind, they are hugely influenced, if not formed entirely from, our emotional responses. The ideas we hold to or reject are far more heavily dependent on our positive or negative feelings towards them than we may like to accept.

Take the example of the current progressive/traditional argument. Ignoring for the moment people who are not particularly bothered either way, the more vocal proponents on either side not only have a preference for one side, they have an active dislike for the other side. This isn’t to say either side is necessarily wrong, just that the methods used to approve or dismiss a viewpoint may be more influenced by an emotional response for or against than by a dispassionate response. The phonics ‘discussion’ bleeds raw with this; each side seems to perceive the other in terms of the damage that they will do to students rather than starting from the perspective that both sides do actually want the best for students but differ in the methods of achieving that aim. Even accepting that as a starting point I doubt the opposing sides would come to a conclusion. Cards on the table, as essentially an empiricist I’d prefer the use of evidence though I accept it’s not always applicable, but you could argue that’s due to my positive feelings towards the scientific method. Am I biased towards certain outcomes? Are at least some of my heuristics faulty? Can I be convinced that ideas or right or wrong based on duff information? Most probably, yeah. There will be ideas and positions I hold that would benefit from a closer look and some recalibration. It’s just not always easy to detect your own biases and to be sure that decisions are not based on rejection rather than a clear positive affect. My views are definitely influenced by my educational background in science; it influences so many of my perspectives on pedagogy. As much as I respect science that doesn’t necessarily mean I will always make optimal decisions based on it, particularly if I’m overly influenced by personal preferences, or more uncomfortably, what I reject. None of us are completely rational decision makers (sorry, neo-liberal capitalists…no wait I’m not sorry, screw ‘em). If you genuinely want to change a person’s perspective, whether student, teacher or voter, you’re going to have start accepting that we can all approach the same situation with personal heuristics that we’re already pretty attached to.

Diff’rent Strokes

Every now and then I find I come across a comment or idea in education, usually expressed in an off-hand way, which reminds me of the shallowness of my educational knowledge. At last September’s researchED for example, Phillippa Cordingley at last September’s researchED fielded a question from the audience about something to do with fire-fighting in year 11 and made a quick remark about the emotional boost that you teachers can get from the process. I thought there was a fascinating insight there into why some school level policies become favoured or entrenched, but she had already moved on to the next part of the question and didn’t expand further. Likewise, last Continue reading “Diff’rent Strokes”

And what exactly do you mean by “critical thinking”?

There’s been an interesting shift in the tactics of the online grumbling-community in the past few years. Not in the general tenor of online debate (which continues to sink like Arnie at the end of Terminator 2 but leaving a raised middle finger instead of a thumbs-up) but rather in the tactics employed by people presenting their arguments. There has been a definite increase in people deploying the twin techniques of demanding evidence and calling out fallacies. Or at least it would appear so on the surface.

Take the use of evidence in arguments. Initially it would seem to be a good thing that people are asking for sources of Continue reading “And what exactly do you mean by “critical thinking”?”

Panning for gold in Excel: how do you know what the data is telling you?

For better or worse, schools are currently awash with data. Personally I like the stuff; when I look at the columns of figures, percentages and raw values in the January DfE release of secondary school data it is literally (and I mean that literally) the same as Neo seeing the background code of the matrix rolling down before his eyes. It’s an antidote to the January blues to comb all those juicy number columns for patterns Continue reading “Panning for gold in Excel: how do you know what the data is telling you?”

Don’t get me wrong – the problem of negative results and answers

Abstract: thoughts about the difficulties and benefits of negative questions and experimental results relating to anchoring, cognitive load, age and ability and curiously not squeezing in any references to Rogue One which is out TOMORROW

Last week I delivered some CPD which partly involved the uses of multiple-choice quizzes to reinforce content. I use multiple-choice quite regularly as homeworks (and of course it is now a part of the A level testing regime so students need to be familiar with the style), constructing them myself to Continue reading “Don’t get me wrong – the problem of negative results and answers”

Is it okay to criticise other schools?

“No-one would have believed, in the first years of the twenty-first century, that educational affairs would be eventually watched from the timeless worlds of Twitter. No-one could have dreamed that schools were being scrutinized, as someone with a microscope studies creatures that swarm and multiply in a drop of water. Few men even considered the possibility of education being any other way in different schools. And yet, across the gulf of Twitter, minds immeasurably superior to ours regarded education with envious eyes, and slowly and surely, they drew their plans against them…”

 

Nothing wrong with a little hyperbole-injection to get the tank purring. Perhaps it’s just end of term fever running amok through Continue reading “Is it okay to criticise other schools?”