 Karvol:I'd prefer it if you gave examples of the 70's pedagogical gems and the non-teacher led and independently discovered thereoms and the mathematical insights made by your pupil.
Okay, so in the 70s two interesting things happened for me. The first was that my mother (previously a university lecturer who'd had a career break for four children) retrained as a primary school teacher. Because of all the strikes my school was shut a lot when she did this so I went to her lectures with her. Of course the educational psychology taught was a mess, but what it did do was it started her and me talking about everything. So my school introduced Scottish Maths (I've got the foundation stage book here beside me now), which was a very different scheme to what had come before in England. From year 3 it was teach yourself. It worked brilliantly in my school because we were all literate and because the teachers kept some lessons each week for drill, so that wasn't lost. The way Scottish Maths is written is contructivist in style so it, and the way it was introduced, was an interesting basis for discussion. It certainly wasn't perfect, but it did have key benefits, the most obviously being that it took the cap of what students could achieve. By the time I was in year 4 I was doing year 7 work. During the rest of my schooling I seemed to find myself on the Forrest Gump end of every random initiative & I just discussed it all with mum at this stage, trying to make sense of what was good and what was bad and why. For example I went through the introduction of GCSE. We had to do 6 projects, topics chosen by us. Now this was a very powerful thing to do. It challenged and stretched me as a mathematician in many unfamiliar and valuable ways. But of course I was looking at the admin and logistics for my teachers and realising that the way the whole thing had been implemented was insane and unsustainable. Meanwhile over in Cumbria, where I was to come to teach, a great deal was going on. You had schools like Stainburn - really well respected for maths - running the 100% coursework GCSE. Then you had the likes of Wyndham, also very highly respected, teaching mixed ability up to year 9. There were rural general schools and then there were schools like Ehenside, which developed vocational mathematics courses which they assessed themselves for their students . All the teachers here were so deeply intelligent because they were used to developing, explaining and justifying their own curricula, modes of assessment and core purposes. Many key characters came from here, for example Eric Love who went on to head up maths at the OU was head of maths at Wyndham. These schools were not chaotic hippyfests Karvol. They were very well organised, effective and highly respected school.
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