Fines told the children about the Roman attack on Syracuse and gradually
drew them into enacting certain roles. At one stage he himself slipped
into the role of Marcellus and bawled out two centurions who were not
springing to attention. The children were spellbound and threw themselves
into the drama. Archimedes ignored the soldier and died a splendidly
protracted death. What was so skillfully original was the way the class
was then asked to reflect on the story that they had enacted. Was it a
plausible account ? What would actually have happened? Whose interests
were satisfied by the story? The children discussed this intelligently.
At one stage, someone suggested that it was hardly likely that anyone
would be so wrapped up in a geometrical problem that he would ignore such
danger; others demurred and referred to their own concentration on
diagrams during the previous weeks. Fines suggested testing this out with
one half of the class trying to solve mentally a problem about squares
while the other half distracted them as much as possible. It was a
memorable lesson for all of us.
I recount this to celebrate a distinguished teacher. But also as a further
comment on some of the points that have been made in the discussion on the
teaching of the history of mathematics. I tend to side with those who have
wanted to invoke the history of mathematics as part of a humanising of
mathematics. I have in my own teaching usually wanted to do this in the
context of teaching some actual mathematics. But I would be loth to make
this a principle - at any rate for those of us whose main interest and
experience lies in teaching youngsters. I was delighted by Fine's lesson
because it raised so many general educational issues. Only a few of the
ten-year-olds would have reached university mathematics classes. All of
them would need to value concentration and the need to be very critical
indeed of any stories about past or present.
Finally, I add a comment on the way some views are often expressed in a way
that cuts out others. The anthropologist Mary Douglas has pointed out that
purity rules tend to be designed to buttress a group feeling. I sense that
some professional historians of mathematics see themselves as an endangered
species and are tempted to adopt very strict purity rules. " .... God and
the devil; inside and outside; purity within, corruption without; here
is the complex of ideas that is associated with small groups with clearly
marked membership and confusion of internal roles." (M Douglas, Natural
Symbols, 1970, p118). .... E T Bell rules OK?
Dick Tahta