[Maths-Education] The resource for the course

[Tanner H.F.]

This rather depressing arguement seems to hinge on what we think "in =
the
long run" means when we say that instrumental learning fails and =
relational
understanding wins "in the long run".  Bob seems to think it takes =
years for
the advantages/disadvantages to reveal themselves.  I think they show =
within
weeks!

In intervention studies which we have been involved in here in Swansea, =
the
advantages of teaching mathematical thinking skills showed themselves =
with
reasonable effect sizes after as little as 12 weeks.=20

See Tanner H & Jones S, Scaffolding for success: reflective discourse =
and
the effective teaching of mathematical thinking skills in Rowland and =
Morgan
(eds) research in mathematics education vol2: papers of british society =
for
research into learning mathematics (pp19-32) London, BSRLM.

See also the inpact within 12 months reported by Cobb et al in ed studs =
in
maths 25 (3) 483-504 and CASE.

Instrumental teaching remains a strategy for failure.  If a teacher =
wishes
to score highly in value added analyses they should teach relationally. =
 The
Raising Standards in Numeracy project showed that schools which scored
exceptionally highly in VA analyses used such approaches

See Tanner, H., Jones, S., & Treadaway, M. (1999). Schools that add =
value:
raising standards in mathematics. Proceedings of the British =
Educational
Research Association (BERA-99), Brighton,
http://www.leeds.ac.uk/educol/bera99.htm, 1-18.


Dr Howard Tanner
University of Wales Swansea
Department of Education
Hendrefoelan
Swansea
SA2 7NB

e-mail:=A0 h.f.tanner@swan.ac.uk
Fax: 01792 298499
Tel:=A0 01792 518642

"A professor is someone who talks in someone else's sleep"=20
  W.H.Auden

Why not visit my web page on=20
http://www.swan.ac.uk/education/staff/hftanner/index.html

Or look at my recent books at:
http://www.amazon.co.uk/exec/obidos/ASIN/0415230691/qid=3D982957393/sr=3D=
1-2/202
-7449646-0205428
or=20
http://www.amazon.co.uk/exec/obidos/ASIN/041523512X/qid=3D983294824/sr=3D=
1-4/202
-7449646-0205428


-----Original Message-----
From: Bob Ansell [mailto:bob.ansell@northampton.ac.uk]
Sent: 19 September 2001 10:11
To: maths-education@nottingham.ac.uk
Subject: RE: [Maths-Education] The resource for the course


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On Tue 18 Sep, Stuart Rowlands wrote:

> Anne's original point that developing understandings=20
> about mathematics make passing tests a lot easier is similar to=20
> Skemp's argument that developing a relational understanding of a=20
> topic may take a longer time than memorising appropriate techniques,=20
> but, paradoxically, is also shorter in the long run. Developing a=20
> relational understanding develops the cognitive structures necessary=20
> to handle unfamiliar situations.
>=20

And time of course is part of the problem. Developing appropriate
cognitive structures is more effective 'in the long run'. Today, it is
a brave (or far sighted) teacher who can afford to take a long-run =
view.
Teachers are increasingly under pressure to produce results in the =
short
run. In some cases their salary depends upon it.

In secondary schools teachers may be measured against the 'value added'
for their teaching groups. Performance related pay and threshold
allowances will increasingly become available to those who 'add more
than the average value' to their students. This 'value' is not measured
by long-term understanding and application of concepts but by =
short-term
tests. We may find a brave teacher with vision is sacrificing their own
pay rise to the teacher who inherits their group.

In many primary schools mathematics is tested annually now that other
'optional' tests have punctuated the gaps between KS1 and KS2 SATs.
Hence the same pressure for short termism applies here. In many primary
schools you have your class for one year only.

To its credit the National Numeracy Strategy offers some encouragement
for a relational, connectionist view of mathematics (...better numeracy
standards occur when teachers... demonstrate, explain and illustrate
mathematical ideas, making links between different topics in =
mathematics
and other subjects (FfTM Section 1 page 5)). On the same page is
encouragement for maintaining interest and the use 'non-routine'
problems. We need to sieze upon these gems and use them.

What all this means is that we are tackling a political problem as well
as an educational one - and that may be a more intractable issue.

Bob


--=20
Bob.Ansell@northampton.ac.uk
Tel 01604 735500 Ext 2074



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