I think we talk too much about lessons. A lesson is usually the wrong unit of time to think about.

@prcollins recently tweeted the following:

I’m doing an ‘inspirational lessons’ training session to our school’s ITTs and NQTs tomorrow (no pressure), what would you include…?

— Paul Raymond Collins (@mrprcollins) January 25, 2015

I replied:

@mrprcollins @Just_Maths The most inspiring thing you can do is teach them to be really good at something really hard.

— Bodil Isaksen (@BodilUK) January 25, 2015

I can’t imagine this going down too well in the training session. It’s not something that can be done in one lesson, after all.

This is true of so many things in teaching.

Thinking about an individual lesson leads us down the wrong path to the wrong solutions.

Inspiration is not something cultivated by a one-off lesson. It is the product of day-in day-out ethos and teaching. You catch them one by one.

Differentiation, too, is something that’s been widely discussed on Twitter over the past few days. Again, it’s best thought of over a longer period of time. Thinking of differentiation as being done within a lesson is a constraining, artificial timeframe. When I think of my most powerful differentiation, I think of catching children at lunch who got their exit ticket wrong to go through it again. I think of whipping out a fantastically difficult problem for the kid who is flying through the work to chew on over multiple lessons and at home. I think of translating the unit’s knowledge grid well ahead of time for our recent Polish arrival. These aren’t things that would go on a lesson plan, but they work.

Our planning is weakened by lesson-based thinking. It makes it too easy to forget about cohesion and natural progression over time.

Thinking about lessons as the unit means one has a tendency to give up too easily. “Surely we can’t spend another lesson on that topic – we’ve got so much we need to cover,” the teacher ruminates guiltily. Lesson objectives need to be covered in a lesson or you’ve failed. You need to show progress in a lesson or you’re inadequate. A familiar narrative. It’s all a nonsense.

If one is thinking about lessons as the unit of learning, teaching children to fluency can seem an insurmountable task. Getting children who add on their fingers to know all their number bonds to automaticity can feel impossible. It’s not: it just requires practice little and often, and heaps of patience. But no-one ever learned it in a single lesson.

The real toxic impact is on retention. Zig Engelmann said “nothing is ever learned in one lesson”. A lesson-by-lesson approach, ticking off an objective at a time, considering it “done” runs counter to our entire understanding of the brain. Interleaving and spacing may not improve performance, but they sure as hell improve learning.

I recently read a quotation I loved: “we overestimate what we can achieve in a day; we underestimate what we can achieve in a year”. I reckon a similar thing applies in teaching. We drastically overestimate what we can achieve in a lesson. But perhaps we underestimate what we can achieve in a term; in a year; in seven years.

*Found yourself nodding along to this? You’d probably be a great fit at Michaela. We’re doubling in size next year, and therefore recruiting in lots of subjects! Take a look at our ads or pop me an email at bisaksen@mcsbrent.co.uk*

The Wing to HeavenAs Aristotle said, ‘For one swallow does not make a summer, nor does one day; and so too one day, or a short time, does not make a man blessed and happy.’ Also Will Durant on Aristotle: ‘We are what we repeatedly do. Excellence, then, is not an act, but a habit.’

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R. CraigenLessons should not exist in isolation, particularly in mathematics though it is true in other disciplines too — the notion that a lesson can be taken in isolation of what else a child knows is a great failing of what in N.A. we call Reform and in U.K. you call Progressive education. It is worked out in horrifying detail in some of the curriculum frameworks I’ve seen that are predicated upon the assumptions of this movement.

I remember entering a discussion amongst educationalists not long about about curriculum and how to teach this or that, and the question arose as to how the so-called “invert and multiply” method of dividing fractions can be taught “with understanding”. Participants bandied about their favourite approaches and seemed to tacitly presume that I didn’t care about the “with understanding” part. As a matter of fact, I am a professional mathematician and am pretty sure that those of my profession actually care more — and understand more precisely what that means — than most educationalists. I certainly do.

Well, it fell to me to contribute, and I did with gusto. But they felt my proposed “lesson plan” was cheating, because it started off “Let us begin by assuming that we have ascertained or already have confidence that all students in the class already know X and have mastered skill Y…” Of course, none of the other proposals contained any such assumptions.

But I insisted (and insist) that this is precisely why my lesson plan was better than any of their clever but misguided ideas. No such lesson can exist in a vacuum. It must be part of a continuum of learning, and if you don’t know where you (and more importantly the students) are along that curriculum it is foolhardy to dive into the teaching and learning of one of the most pivotal and, by reputation, most difficult, cognitive outcomes in the classical mathematical middle-school curriculum.

As a matter of fact, with all the right precursors in place it is a snap to teach “invert and multiply” and to do so “with understanding”. A piece of cake, and you can be confident that even your weaker cohort will “get it”, perhaps with a little bit more help. Math is not hard when properly scaffolded. It is really quite beautiful.

But what the Reform/Progressive Ed folks don’t want to hear about the subject is that mathematics is relentlessly hierarchical. And any sequence of learning outcomes that does not respect this fact about the subject has no business being implemented in the classroom. You don’t build a house from the roof down, and you should not try to teach “higher skills” of mathematics to students for whom foundational skills are not in place.

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BW_2012 (@BW_2012_origin)A chapter is the wrong unit of time; sometimes so is a book.

Take the Lord of the Rings as an example. One might, so easily, give up on Frodo.

As (with the Star Wars books and and films in mind) for little Anakin, Ofsted his learning based on “The Phantom Menace” or “Revenge of the Sith” in isolation and a trick is truly missed.

Einstein: his whole school career was a distraction.

It’s a tricky business with the exceptions; equally, the rules.

To be continued…

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