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

[Boylan, Mark S]

 Dear all

For the last few years we have set out student teachers an assignment
that requires them to critically (hopefully!) analyse performance data
on pupils that they teach.

One reason for this is that we hope that as mathematics teachers in the
future they might be able to counter the worst excesses of the way in
which performance and assessment data is misused in statistically very
dubious ways.

The level of critical engagement needless to say is not always as great
as we would like, not least becuase it appears many mathematics teachers
in schools  are swallowing some very dubious practices.  They then pass
these on to our students.

Regularly I have to  challenge students to explain the meaning of 4a,
4b, and 4c when given as national curriculum levels without comment.  Or
worse 4.30, 4.60 etc (I think this is do to with the influence of the
Fischer Family Trust).  In particular questioning, if  a school is going
to have a decimal place for national curriculum levels, why this is
given as 4.30 rather than 4.3?

I point this out in the, I admit generally vain, hope that the students
might start to realise this has a lot more to do with ideology than any
meaningful quantitative measure.  Presumably 4.30 has greater weight as
it conforms more neatly to a metric measurement or perhaps it has a
greater finanical appeal - it looks more like a financial measure.  This
is after all, in pursuit of 'Value Added'.

But of course in the performance data competition between schools, it
would only be a matter of time before some schools will go one better,
and now I find data offered by a student from one particular school, via
its mathematics department, in the following way:

Y9 Level Feb 06 as being variously, 4.03, 3.54, 4.96, 5.03 etc.

So could anybody enlighten me as to exactly what 0.01 of a national
curriculum level is?  Is the difference between 4.96 and 4.97 the same
difference as between 5.03 and 5.04?  If we can have 0.01 then how about
0.001, surely we need to be able to distinguish between students who are
at 5.030 and 5.031?

What really concerns me about this is that I have not been able to find
any research papers actually debunking this sort of nonsense - any
suggestions?

Whilst I am at it, I also am deeply troubled by students reproducing
very dubious material and comment given by teachers in schools which
apparently originates with NFER with regard to CATS scores.  (For
overseas readers CATS scores are basically what used to be called
intelligence tests)

Apparently a pupil who scores low on verbal and non verbal reasoning
will be a 'kinaesthetic learner'
This apparently is because verbal reasoning indicates an 'auditory
learner' (!), and non verbal tests indicate a 'visual leaner' (!) 
Given that pupils must be either one of these or a kinaesthetic learner
then it follows logically that someone who scores low on both sorts of
tests must be a kinaesthetic learner  

Would anyone connected with NFER like to comment on this?  Again anyone
know of any critical comment on CATS etc?

Is this just going on in schools in South Yorkshire  (UK) or is it a
national phenomenon?

Is this happening in other countries?

regards
Mark

Dr Mark Boylan
Subject Leader, Mathematics Professional Year
Divsion of Education and Humanities
Faculty of Development and Society
25 Broomgrove Rd
Sheffield S10 2BP
+44 114 2252349
m.s.boylan at shu.ac.uk