So this course was announced, it said ‘Calculations on Elliptic Curves,’ which could mean anything.  Didn’t mention Fermat, didn’t mention Taniyama-Shimura, there was no way in the world anyone could have guessed that it was about that, if you didn’t already know.  None of the graduate students knew, and in a few weeks they just drifted off, because it’s impossible to follow stuff if you don’t know what it’s for, pretty much; it’s pretty hard if you do know what it’s for.”
Nick Katz, quoted in Fermat’s Last Theorem

As teachers, we have clear ideas about where our lessons are going, how they build towards the aims of individual schemes of work and an overall vision for our students.  This term, I’ve spent a lot of time thinking about the question:How can we ensure students understand these aims?

This first post discusses why this matters, the second will consider how we can achieve this and the last will reflect on some of the ways I have tried to improve my practice.

## Why does sharing learning intentions matter?

The quotation from Katz offers an illustration, but the point is worth labouring, because I’ve encountered a fair deal of scepticism from teachers as to the importance of a) having learning objectives and b) sharing them with students (this, from Phil Beadle, is a representative example).Dylan Wiliam makes many useful points on this; the most critical of which derives from a study by Gray and Tall (1994):

Higher achieving students were able to work with unresolved ambiguities about what they were doing, while those students seen as lower achieving were struggling because they were trying to do something much more difficult” (Wiliam, 2011, p.53)

Gray and Tall examined how primary school students approach maths problems which can be answered using a variety of tactics.  They noted that higher-attaining students, ‘Make use of flexible strategies which generate more knowledge,’ while lower attaining students follow ‘inventive’ and ‘more tortuous’ routes which succeed ‘only with the greatest effort’ or they fall back on the simplest strategy, laboriously counting (p.17).  Although this can work at lower levels, students struggle to appreciate and manipulate mathematical concepts (p.18).  Being willing to deal with ambiguous ideas in maths ‘gives enormous power to the more able’ and creates a ‘chasm faced by the less able in attempting to grasp what is – for them – the spiralling complexity of the subject (p.24).’Wiliam also cites studies showing that clarifying learning intentions with students helps them to improve.  For example, White and Frederiksen (1998) conducted a study in which, for one period a week, classes either discussed their likes and dislikes about lessons or were introduced to the criteria by which they would be assessed.  All students in the latter group improved their scores significantly; lower-achievers improved the most – helping to close the ‘achievement gap.’

So why wouldn’t you share them?

1) It’s a poor use of time
Beyond the evidence of the studies referred to above, I’d just suggest that I have always felt that prioritising ‘getting on with the learning’ is probably a false economy; a sacrifice of two minutes in order to have clear aims is likely to make the subsequent learning far more effective.

2) They are a tick-box exercise
Like so much of AfL, lesson objectives have gained a bad name because they have been systematically misused by those who understood enough about formative assessment (and what they thought Ofsted wanted) to want their teachers to mimic it, but not enough to engender understanding or mastery of its underlying purposes.  As Joe Kirby put it: “Many senior leadership teams then enforced the letter of the AfL law rather than the spirit of it.”  I’ve never understood how any teacher with a mind of their own either instituted or implemented a policy of copying out lesson objectives.  Hostility to such nonsense is well-founded; it does not follow that sharing the direction of students’ learning with them is in itself a bad thing.

3) They are a terrible to start a lesson
The most common time lesson objectives appear to be used is at the very beginning of the lesson (often as a way to settle students – a ‘starter’ in which they learn nothing).  There are better ways to start lessons (and to unfold learning objectives) than this.  A fabulous article, a dozen years old, called ‘Making history curious,’ (abstract) explored how teachers can use ‘Introductory Stimulus Material’ to arouse students’ interest, establish possible questions to pursue and “outline aims and objectives in a clever, meaningful way.”  It also highlighted how the concrete basis of such material helps students build from the concrete to the conceptual.  As the editorial comment noted, the article threw “a constructively critical light on the fashion for ‘starter activities’ and the emphasis on setting out lesson objectives to pupils…  In our best history classrooms, theorising about the start of lessons is more sophisticated and better integrated into subject practice than this.”  Teachers may, for example, wish to stimulate thinking while retaining surprises as to what actually happened, offering ‘oblique’ introductions which motivate curiosity and encourage students to formulate both historical questions and hypotheses.

Like any aspect of teaching, teachers need to think through how it can work best for their classroom; this is something which I am in no position to judge.  So when teachers question the importance of sharing learning intentions I offer this acid test, that they ask all of their students (as an exit slip), at the end of the lesson, the question:

“What do you think you were supposed to learn from the lesson?”

If teachers can gain coherent, accurate answers from every student to the question, then I would argue that they need not worry about sharing learning intentions further.  If not, perhaps it would be useful for them to look again.In hiding the aim of his lecture course, Andrew Wiles successfully avoided alerting his colleagues to the direction his research was taking.  However, Nick Katz missed a critical flaw in Wiles’ solution to Fermat’s Last Theorem.  Wiles suffered a deeply unpleasant year, trying to amend this flaw, under intense pressure and scrutiny – and almost missed out on the proof.  Perhaps sharing his learning intentions with the audience would have spared him this…

In Part II I reflect on how I had been introducing learning intentions and some of the different approaches available.
In Part III I discuss what I actually did and evaluate how well it worked.

[Originally posted July, 2013]