Giving your students free rein

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The need for assessment can often restrict the scope of students' work. Kester Brewin reports on a statistics project that is wide-ranging, student-led, ethical, challenging ― all because it is not going to be marked.

The other day I surprised myself by actually feeling a pang of nostalgia for GCSE maths coursework. 

It is a few years now since it was dropped, but I couldn’t help a wry smile thinking through the opening lines of the first lesson each time it was started: “Sign your name on this piece of blank paper and hand it back to me. Thank you – if you fail to hand your coursework in on time, this is what I’ll be submitting for you.” It always worked a treat.

Getting rid of it was a huge relief, partly because of the constant hassle that was needed to retrieve work, blood-from-stone-like, from students who suddenly became slippery and devious. 

Once it was in, the marking of it was never much fun, but not that horrific. And the moderation, while a total bind, at least gifted the department a chance to drink tea and argue for a few hours. 

But the worst part of it was this: the nagging sense that what was meant to be an open-ended exploration was anything but.

No matter how much we liked to dress it up or pretend otherwise, every student always, miraculously, appeared to drift, in a manner not unlike being dragged by the scruff of the neck, down the road set out in the assessment criteria.

Of course, we all did it for good reason: it was a flawed system, and we weren’t about to let our group’s grades suffer for a point of principle. The pressures of league tables and mark accumulation were triply felt by parents and staff and students, so we did what we could within the bounds of what felt right and allowed them to regurgitate near-identical “explorations”, closed “Open Box” problems, and very fenced in “Fencing Problems” too.

Why, then, the nostalgia? Because, without the marking, without the cycles of moderation, without the pressures of assessments and scores, allowing students time to explore a problem in depth over time really is a wonderful thing. 

We are very keen to tell children when they ask what school is “for” that learning is its own reward, and here, I feel, is an opportunity for them to actually experience that. 

There is something delicious about setting out on a piece of work that will not be formally assessed. Of course, assessment has its rightful place, but are we not constantly complaining that our students are assessed too much? 

Why not practise what we preach and set a task that is simply not going to be marked? Why not wager with them that if they put something into it, then they will actually enjoy it? Any why, if we have set the task up appropriately, shouldn’t they?

So this is precisely what I did. With a group of year 10 students, I presented them with a challenge to do a piece of statistical exploration, and allowed them to have pretty much a free reign in their work. 

First, they had to think of some area of life that they would like to explore through data collection. The only rules were that a) they had to find it interesting, b) I had to find it interesting (which was a euphemism for valid and sufficiently challenging!), and c) it was ethical.

The ethical point provided some excellent opportunities for discussion. We considered various statistical experiments and debated their ethics. 

One boy wanted to explore the effect electric shocks had on short-term memory. His hypothesis that greater shocks would be detrimental to recall of objects on a tray was based on his personal experience of having had a large shock himself, and he was genuinely excited about setting his experiments up, but had to be guided into other lines of enquiry!

Other discussions centred around what was sensibly measurable, and how to collect valid data. One student, whose mother was a psychologist, wanted to explore how happiness among staff changed over the course of the working week. 

Having encouraged him to research some existing methods for measuring something like this, he did pursue this project successfully, though had to admit in his evaluation that a much longer time than two weeks would have been needed to finally conclude that Friday afternoon was the happiest moment of the collective staff’s lives.

It was these sort of moments of genuine interest that I had hoped to find now that the shackles had been thrown off and the opportunity for proper exploratory work was available. 

Importantly, the success of the investigations was, I believe, in no small part due to the relaxed manner in which they felt able to approach the task. Once they realised that the assessment pressure was off, no student, regardless of their mathematical ability, felt unable to come up with a line of statistical enquiry that could sustain their interest for six or eight lessons from inception to completion.

The more academic students may veer towards cerebral studies like those mentioned above, but if we believe in the universal utility of our subject, regardless of ability, then we ought to be brave enough to put our money where our mouths are and risk putting our beliefs to the test. 

The first proper piece of statistics I remember doing was something I was passionate about too: I surveyed the then terrible leisure facilities in my local town for my GCSE geography project, and found that, like me, most people thought they were not good enough. 

Looking back on it a couple of weeks ago after my parents cleared their loft, it is clear that the level of sophistication was barely enough to scrape into the C zone for maths.

Though a very basic project, the work at least had the advantage of being something I was interested in, which could hardly be true of analysis of heights and weights of pupils at Edexcel’s infamous Mayfield High School. Not only that, it felt to me as if it had local relevance. 

I doubt there is a single community that does not have a local issue that would benefit from polling by students. Are there enough youth clubs? Are more people suffering crime? What do local shopkeepers think of school children from different local schools? 

Frustrated by their persistent lateness, and challenging them to back up their excuses with hard facts, I asked a group of A2 statisticians to do a hypothesis test on the frequency of buses, and whether the timetable claim of a service “every eight minutes” was credible. We were all annoyed to find that the bus company appeared to be running a rather short service!

It is these local issues that I will be encouraging my students to think about next year. Is there a piece of market research that a local business would like doing? Or perhaps a parent running a company would like some data collected? 

Again, we insist when questioned in lessons that our subject is relevant, so here is an excellent opportunity for us to show students that it really is useful, in real-life and business.

We so often bemoan the fact that education has become risk-averse these days, but we must own up to our culpability here too: in an education system where league tables and statistics are everything, risky ventures in programmes of study are often discouraged.

Time is not to be wasted on non-syllabus material. This is the short termist corner that we are forced into: better places in league tables are the only way to secure stability for the school and attract “better” students. These “better” students are then predicted to get even better results, so we focus even more closely on the examined syllabus, and so it goes on.

This is particularly true in mathematics, where the question “what is this subject for?” is not straightforward to answer. Yes, students need to be numerate. But we cannot truthfully claim that any significant proportion of pupils will end up using algebraic processes, probabilities or advanced mensuration. 

The nuanced answer is that we are teaching them to think logically, and to be able to break down problems in order to solve them accurately and efficiently. 

If this is the case, then it is even more important that we meet our side of the bargain and provide opportunities for these sorts of skills to be put into practice.

Without the spectre of heavy assessment looming over the projects, my hope is not only that students will genuinely take some risks and do some creative thinking for themselves, but that I will feel free enough to allow them to do so too.

The removal of the coursework component has been a good thing. It was not doing what it purported to do, was open to widespread abuse, and left students with a distorted idea of what investigative mathematics is really about. 

However, rather than fill the time we gained by its removal on syllabus-focused work, why not give students some good experiences of open-ended investigation? 

It will be risky, and it may not initially produce good quality work. But it will at least be honest of us to provide the time, given that it is precisely the skills that they will be using in that time that we claim to be training them in. 

  • Kester Brewin teaches mathematics at a school in south London. His new book Mutiny! Why We Love Pirates and How They Can Save Us is out now.


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