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This Scottish Extension was linked to the
Phase II project, 'The Role of Awareness
in the Teaching and Learning of Literacy and Numeracy in Key Stage
2'.
In mathematics and science
education, there is an important distinction to be made between
two types of quantity, extensive (e.g., height, weight, volume)
and intensive (e.g., speed, density, temperature). This distinction
is recognised elsewhere in the world, but it has been neglected
throughout the UK, where teaching concentrates on extensive quantities.
This seems likely to have serious implications for pupil attainment,
as there is evidence that in the absence of teaching, intensive
quantities are treated as if they were extensive.
Until recently, there has been little psychological analysis of
the contrasts between intensive and extensive quantities, of what
pupils should learn in order to avoid confusion, and of how they
should be taught. However, previous TLRP work in England by two
of the investigators demonstrates difficulties that vary with the
logical moves required by the problem, the language used in problem
description, and the specific type of intensive quantity. These
difficulties cannot be remedied by the teaching of extensive quantities
alone. An equivalent situation can be anticipated in Scotland,
although differences stemming from the Scottish 5-14 Programme
indicate that their form may vary.
In view of the above, this two-year Scottish extension aimed:
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to document the ways in which primary school pupils in Scotland
learn about intensive quantities, and the difficulties that
they have with this learning;
- to identify modes of teaching that
are both effective and sensitive to the Scottish context;
- to ensure that the results have maximal impact upon
policy and
practice.
The specific objectives were:
- To provide researchers, policy makers, teachers and trainers of
teachers with reliable information about the extent to which
intensive quantities are currently grasped by primary school pupils in Scotland,
and about areas of particular difficulty;
- To develop a whole-class plus small-group approach to the teaching
of intensive quantities, and to make controlled comparisons
with alternative methods;
- To contrast the efficacy of ratio and fractional approaches to
the teaching of intensive quantities;
- To explore how base-line knowledge of intensive quantities, and
responses to the teaching intervention, vary with pupil age,
sex and mathematical ability;
- To develop an impact strategy, and to implement this with policy
makers, trainee teachers and relevant academic staff.
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