[Maths-Education] Ability grouping in mathematics

[Dylan Wiliam]

While not disagreeing with Anne, I think that what it means to teach the
same or different curricula to the same or different students needs
unpacking.

At one extreme there is Germany, where at the age of 10 or 11, most students
are routed towards one of three different routes (Realschule, Hochschule,
Gymnasium) depending on some notion of academic ability or potential (a
small proportion of students go to comprehensive schools). The important
thing about the German system is that society sets different goals for
different students.

In England, all students (at least in the 5 to 14 age range) are nominally
working towards the same goals, but because the vast majority of secondary
schools use ability grouping in mathematics, then they learn at different
rates, and often different curricular materials are used. While this does
mean that the curriculum experienced by different students is, indeed,
different, the fact remains that the notional curriculum (and indeed the
national curriculum) is the same for all these students, and so the
situation is different in important ways from that in Germany.

The paradigm case for the other extreme, with the whole cohort working
towards the same goals in the same classrooms, is usually Japan, and it is
certainly the case that between class variation in attainment is lower in
Japan. Nevertheless there is strong between school differentiation, with the
prestige of a high school determined by the school's success in getting
students into the top universities, and the prestige of middle schools
determined by their success in getting students into the most prestigious
high schools.

I guess the important thing in all this is that there is a huge diversity
amongst learners of mathematics, which is exacerbated by some approaches to
mathematics, and ameliorated by others. National systems have 'official'
responses to this diversity, but these are often unhelpful or misguided, and
so schools and teachers make other adjustments at the local level. As anyone
who has tried to find out what a school's real, as opposed to stated, policy
on ability grouping can attest, the labels that people use are a poor guide
to what is happening

Dylan Wiliam
Director
Learning and Teaching Research Center
ETS
Rosedale Road (ms 04-R)
Princeton, NJ 08541

Tel (609) 734 1307
Fax (609) 734 1755

> From: Peter Gates <Peter.Gates at nottingham.ac.uk>
> Reply-To: Mathematics Education discussion forum
> <maths-education at nottingham.ac.uk>
> Date: Tue, 07 Jun 2005 10:22:46 +0100
> To: <anne.watson at educational-studies.oxford.ac.uk>,
> <maths-education at nottingham.ac.uk>
> Subject: Re: [Maths-Education] Ability grouping in mathematics
> 
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> 
> Thanks Anne for this. Anne's point here is close to one of the key reasons I
> asked the question - and thanks to those of you who have already responded to
> me. Naturally if anyone wishes to respond to the whole list - they can. I will
> collate responses and distribute them  -possibly via a web site. I just wanted
> to avoid lots of email - but this is clearly an important issue not just for
> those of us interested in equity in mathematics teaching and learning.
> 
> Peter
> 
> *****************************************************************8
> 
> There is a useful table in the most recent TIMSS or PISA reports (cannot lay
> my hands on which one right now - probably TIMSS) which purports to show how
> different nations group students for maths teaching.
> 
> I am replying to the whole list because the claim is that in England we teach
> the same curriculum to different students in different ways.  Well, folks, we
> don't.  We end up teaching a different curriculum to different students.
> 
> Do any others of you wish to comment on how your country's differentiation
> practices are officially reported?
> 
> Anne Watson.
> 
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