Number Crunching
Number Crunching
Number Crunching
Yes, it’s our old friend Steve from Yorkshire again. With the obsessive curiosity of a Maths teacher (chiefly because he is one), he’s been applying some numerical magic to the mystery of Ofqual’s limp explanation for the GCSE fiasco.
He does this because, like so many of us, he’s seen the devastating effect that the so-called Regulator’s (a) ineptness and (b) ineptitude (take your pick, or use both) have had on colleagues in the English Department.
Steve writes:
A mathematical ‘thought experiment’ into the GCSE English grading situation
Let us conduct a step by step thought experiment into the GCSE English grading situation this year.
We will use this approach to try and prove what happened this year (in the same way, but at a much lower level obviously, that Einstein proved the Theory of Special Relativity).
Hypothesis: That units taken in June 2012 were graded accurately
1) Let us begin by assuming the accuracy of OFQUAL’s case:
a) That units taken before June 2012 were graded inaccurately (leniently)
b) That units taken in June 2012 were graded accurately
c) That the overall profile of results matches predictions from the ‘comparable outcomes model’ proving that the ‘grades awarded in June 2012 are right’.
And further we assume that:
d) The number of students taking units before June 2012 is not zero.
2) Statements 1a and 1b imply that students with a mix of units taken in June 2012 and earlier will have had a mix of accurate and lenient grade boundaries applied to their work.
3) Statement 2 implies that these students will have achieved a grade in excess of what is fair (they ‘got lucky’).
4) Award a value of “1” to each such student who ‘got lucky’.
5) Statement 1b implies that students taking all units in June 2012 will have been graded accurately.
6) Statement 5 implies that these students will have achieved an accurate grade overall.
7) Award a value of “0” to each such student who was graded appropriately.
8) Let us define the proportion of students taking some units earlier than June 2012 as N.
9) Statement 8 implies that the proportion of students taking all units in June 2012 is (1-N).
10) Define P as the overall grade profile score.
11) Statements 4,7,8 and 9 give us P = 0x(1-N) + 1(N) which simplifies to P = N.
12) Statement 1c implies P = 0
13) Statements 11 and 12 taken together implies N = 0
14) Statement 1d states N ≠ 0
15) Statements 13 and 14 together give 0 ≠ 0
16) Statement 15 is 'reductio ad absurdum' (a contradiction has occurred) therefore the initial hypothesis must be wrong.
17) We have proved, by contradiction of the opposite, "That units taken in June 2012 were graded inaccurately"
Steve (from Yorkshire)
1 October 2012
21:10
Monday, 1 October 2012