• 3-4 divergers per converger:
  arts subjects - history, English literature, modern languages.

• equal divergers and convergers:
  biology, geography, economics.

• 3-4 convergers per diverger:
  physical sciences - mathematics, physics, chemistry, classics(!)

From Hudson (1966) quoted in Orton (1992, pp.112-113)

(Biology context - Mayr (1999) argues that the methodology of biology should look more towards history and less towards physics. On the other hand, Ho (1998) argues that physical methods have extended our understanding of the cell.)

DUALIST & NON-DUALIST (Relativist)

National Curriculum (1991) Closed (single fixed answer) and non-closed (multiple answer) tasks.

Find which areas of biology and mathematics are closed or non-closed.

Possibilities: (non-closed)

• Population thinking - Mayr
• Cantorian set theory
• Chaotic systems
• Cyclic graphs

Set Theory

(exploring ideas of transitivity)

Defn. 6 = s(s(s(s(s(1)))))

S1 = 1, 2, 3, 4, 5, 6, 7, ...
S2 = 3, 9, 27, 81, 243, ...

S2 is a subset of S1

S3 = 5, 25, 125, 625, 3125, ...

S4 = S1 intersection not(S2)

S5 = S1 intersection not(S3)

S6 = S4 intersection S5

S6 is a subset of S4 is a subset of S1

S6 is a subset of S5 is a subset of S1

??????

• References and further reading.
• Convergence and Divergence
• PLM - Notes - 16/1/00