To gain Masters-level credits on his PGCE course at the University of
Brighton, Theo Giann designed and tried out this prompt in one of his
classrooms: Theo wrote an interesting paper on how
to develop student autonomy. In the appendix, he reflected on the prompt:
In one of my higher year 8 classes I
set a very open ended task where students could either “work in their books,
make a poster or complete a worksheet.” The work they did had to investigate
the picture above. That was the extent of the instruction given. One boy, who
usually was unmotivated in my lessons, produced a poster with many different
examples of different inscribed polygons and clear mathematical labelling of
each one. He went on to eloquently explain his work to the rest of the class;
however, he made an error in his work – he deduced that because he had drawn an
irregular inscribed pentagon, |

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