Teaching without Teaching (an experiment)

I’ve been looking forward to writing this post, having had an exciting/terrifying idea two weeks ago, but had to do a test with the class before I knew if it worked (or not). 

Inspired by a link from @mrpcollins’ blog, inspired in turn by daratodifferentiate’s article on think tac toe boards, I was looking for a way to try something similar in my lessons. 

During the first week back, after a successful lesson on surface area of cuboids and relatively ‘easy’ prisms (e.g. trapezium-based), Y9 ran into a stumbling block in lesson 2 (surface area of cylinders) when it turned out there was a VERY wide range in their knowledge and understanding of circles. I asked them to comment in their books, as part of their end-of-lesson self-assessment, on how much practice on circles they wanted in the next lesson. Predictably, there was a 3-way split amongst

  • “I don’t get circles at all, can we spend a lesson on the basics?”
  • “The basics are fine, but I’d like to do harder ones” and
  • “Everything in circles is easy, and so is surface area of cylinders. I want to do something harder.”
Reading this at 18.30, when the next lesson is in the morning, and you’re rubbish at differentiation…


Assuming that there was no way I could successfully run a ‘normal’ lesson with such a range of knowledge, skill and confidence, it seemed like as good a time as any to try think-tac-toe. I made a ‘step ladder’ (not *quite* a level ladder) showing the different sub-topics in order of difficulty so pupils could decide how much they wanted to challenge themselves (and select the right resources for their objectives), and a 3×4 grid. They had to complete at least one activity from the centre of the grid, and had three lessons to complete 3 activities from the grid. 

Here are the stepladder and grid: 

Think Tac Toe (circles)

[Full disclosure: I should add, at this point, that the class I did this with are very able (although this is still very spread), very motivated and – with rare exceptions – utterly delightful.]

On Tuesday morning I explained how the TTT would work (they chose their objectives and their activities, and could work alone, in pairs or in groups), that there would be ‘red time’ when they weren’t allowed to ask me any questions (as I was teaching a very small number of pupils who were really struggling), green time when they could ask, and ‘amber time’ when I was inspecting pupils’ work at random. I also explained that we would have a test the next Thursday (lesson 6), that on Monday (lesson 4) we would revise as a class/clear up misconceptions and that on Tuesday (lesson 5) they would work independently on revision websites (e.g. Mangahigh/MyMaths/Bitesize). Finally, I set two pieces of homework on mymaths: a compulsory one on surface area and a choice of pieces on circles/volume/cones, etc, of which they should choose one.

They launched into it (totally bizarrely, at least 1/3 – all boys – went for exam questions as their activity of choice! Weirdos), and were quite quick to choose their activities and get going. However, I was disappointed to see that at least 1/3 weren’t really challenging themselves in terms of content/objectives (e.g. making posters on how to find circumference, or what radius/diameter means), and one boy completed little work. That said, at least 10 produced some really fantastic stuff (board games with increasingly difficult questions on mensuration, or independently researching the volume of cones and spheres). 

On Thursday I reiterated that I wouldn’t be teaching them any content directly, and that it was their responsibility to make sure that they were prepared for the test (pointing out that everything on the ‘ladder’ would be on the test). I was quite scathing about some of the activities chosen (saying that anyone who needed to make a poster about what the diameter is shouldn’t be in the top set, or even Y9) and – on the advice of a colleague – warned them that the class had to achieve an average of a C in the test if we were to move on to the next topic. I’ll admit I made the ‘not moving on’ scenario sound really grim (“you’ll have to copy examples from the board, then practise them silently until I’m convinced everyone can do it”…even I was dreading that scenario).

The transformation was amazing: by the end of Friday (lesson 3) at least 1/3 of the class had taught themselves how to find the volume of cones and spheres, and we had a host of ‘products’ from a “Pi in the Sky” boardgame to a “Circles for Dummies” workbook with examples, tips and questions to ‘try at home’, to a rap. The class was asking much more sophisticated questions of me, and were working in productive little groups of their own making (e.g. one group of 5 were doing exam questions together and marking each other, one group of 4 were making ‘instruction books’ and reviewing each others’ work and three pairs were developing board games). 

On Monday (lesson 4), about half the class was absent due to a trip, so the revision lesson was very focused but did miss out half of the pupils. On Tuesday (lesson 5), they worked on Mangahigh challenges and asked questions (6 spent about 20 minutes with a senior maths teacher, who was ‘interviewing’ them about the work they’d produced). I felt quite nervous about them taking the test today as, barring the first two lessons on surface area (the second of which was quite rubbish due to the mixed knowledge), I’d done little direct teaching. There was lots of evidence of progress and work, but many worked almost exclusively on laptops, or in groups, and I had no individual work to look at how they’d been doing. 

We took the test today, with questions starting at ‘this is the radius, find the circumference’ and finishing with ‘find the volume of the frustum’, with some really nasty ‘functional’ questions in the middle. I was so nervous while they were taking it, and had to wait until the evening before there was time to mark them. 

The overall results were: 

1 D+ 

2 C-

1 C

1 C+

7 B-

4 B

5 B+

A- 3 

A 1

A+ 2

A* 0

(3 were absent)

Given that their levels at the end of year 8 were 5a-6a, this represents unbelievable progress for all of them (even the pupil who got a D+ made almost a grade of progress from his end of Y8 level, although it was the least progress). They’ve been making good progress with ‘normal’ lessons, but this was definitely much better. 

So I guess the trick is to stop trying to teach them:)

(jks – this format was well suited to this topic and this group – it wouldn’t work for many parts of the curriculum). 

Next challenge: trial it with a less amenable class… I’ll report on how that goes, assuming I/we survive (and I’m not still cleaning up my classroom).

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Filed under Education, learning to learn, Perceptions of Maths

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