[Maths-Education] Ability grouping in mathematics

Tue Jun 7 19:13:58 BST 2005

This starts getting more interesting by the minute. And I agree that a lot 
of this needs unpacking.

As someone who has lived three systems (either as pupil, teacher or 
parent), those of Germany, France and England, and researched them perhaps 
at another level, I would strongly emphasise the discrepancy between what 
is stated and what is 'lived' in schools and national curricula.

Germany was mentioned as the case for the tripartite system, three 
different routes, and indeed three different curricula. Well, supposedly 
different. If you have a closer look, and you can also see this in German 
textbooks at lower secondary level, the Realschul and Hauptschul curricula 
are in fact a kind of watered down Gymnasium version. There are 
differences, but the curriculum is not markedly different, except for its 
'depth' of treating the mathematical notions- supposedly.

Dylan makes the point that the federal state, in fact some argue each Land, 
sets different goals for different students. My concerns here are: what are 
these different goals, what is the purpose? And what are the different 
mathematical diets that students are provided with, what opportunities do 
they have to learn mathematics? Supposedly attending to the different needs 
of individual children. To what extent does the Hauptschul curriculum 
attend to the needs of a Russian immigrant child who can hardly speak 
German, but whose mathematics education diet might have been superior to 
what is offered in the German Hauptschule? What are the mathematical diets 
we offer to our English 'bottom' set students, as compared to the so-called 
high achievers? How can we justify this - on the background of a 'National 
Curriculum for all'?

Yes, these labels do not give us any clue about what is actually happening 
in our classrooms. Perhaps they give us an idea of what politicians and 
policy makers would like to show forth.

Birgit Pepin

At 08:36 07/06/2005 -0400, you wrote:
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>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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> > Dr Peter Gates
> > Director of Research Students
> > School of Education
> > The University of Nottingham
> > Wollaton Road
> > Nottingham
> > NG8 1BB
> > Great Britain
> >
> > email
> > 1) peter.gates at nottingham.ac.uk (work)
> > 2) peter.gates3 at btopenworld.com (personal)
> >
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> >
> > 
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> >
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> >
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> >
> > 
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> >
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Dr Birgit Pepin
Postgraduate Tutor
Westminster Institute of Education
Oxford Brookes University
Harcourt Hill Campus
Oxford OX2 9AT
UK

Tel.: ++44 (0)1865 488518
Fax: ++44 (0)1865 488484
e-mail: bpepin at brookes.ac.uk
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