[Maths-Education] 0.01 of a national curriculum levelin mathematics?

[Hugh.Burkhardt at nottingham.ac.uk]

Also critical to this discussion** is the accuracy with which 
performance can be measured.

Races, whether of cars or humans, can be timed to small fractions of a second.
The uncertainty in mathematics tests as measures of performance in 
the subject has concentric circles of variations, each larger than 
the previous ones:
   * mark-remark error, between 2 different markers on the same script 
(small for maths)
   * test-retest error between two "equivalent" papers (eg different 
Boards, or years)
   * test-objectives error:  How far does this test sample performance 
in the subject? (not far)

Test-retest error, when measured, is rarely less than half a grade. 
You can find this in research papers (eg "Weighing the Baby") and, 
sometimes, in the fine print of exam providers.  It is rarely 
acknowledged at policy level or in public -- probably because 
removing the certainty that surrounds exam grades would undermine the 
perceived fairness of the important life-affecting decisions 
(from11-plus to a 3Bs university offer) that are taken on that basis. 
Life would become uncomfortable for all concerned.  Such us the  way 
with social constructs.

Ironically, the marking "scandal"/"fiasco" of a few summers ago 
involved far errors smaller than the uncertainties inherent in the 
exams.  Look forward to this year's contribution to feeding the 
media, starving in the Silly Season.

Many years ago, the Research Committee of the Joint Matriculation 
Board discussed reporting on a  20-point scale with a declared error 
band (eg 14+/-2)  It was thought too sophisticated for users who 
would not welcome the ucertainty.

The fact that life has a random element is generally unwelcome, 
notably in areas of risk, where the perception has two elements, 
roughly:
	Risk =  Probability + Outrage
Perception is dominated by Outrage.  The costs, to children in 
overprotection and to us all in civil liberties, are substantial -- 
but it's great for the media.  Anecdote is more powerful than 
evidence for most of us, particularly when seasoned by Outrage.

Minimising the difference between  perceived and real risk 
(probability of the bad event) is a major challenge in making 
secondary mathematics education functional.  (July 6th is not a bad 
day to note this)

All the best

Hugh



** as well as the significance (in the non-technical sense) of any 
difference in scores, which has already been discussed here -- 
clearly, any difference that is much less than the inherent 
imprecision is not significant.  (signal<<noise)