[Maths-Education] The resource for the course

[Bob Ansell]

On Tue 18 Sep, Stuart Rowlands wrote:

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

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


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