Highly effective teachers were
characterised by beliefs about
What it means to be numerate:
§ having a
rich network of connections between different mathematical ideas
§ being able
to select and use strategies, which are both efficient and effective.
They used corresponding teaching approaches
that:
§ connected
different areas of mathematics and different ideas in the same area of
mathematics using a variety of words, symbols and diagrams
§ used pupils'
descriptions of their methods and their reasoning to help establish and
emphasise connections and address misconceptions
§ emphasised
the importance of using mental, written, part-written or electronic methods of
calculation that are the most efficient for the problem in hand
§ particularly
emphasised the development of mental skills.
How children learn:
§ almost all
pupils are able to become numerate
§ pupils
develop strategies and networks of ideas by being challenged to think, through
explaining, listening and problem solving.
They used teaching approaches that:
§ ensured that
all pupils were being challenged and stretched, not just those who were more
able
§ built upon
pupils' own mental strategies for calculating, and helped them to become more
efficient.
The role of the teacher:
§ discussion
of concepts and images is important in exemplifying the teacher's network of
knowledge and skills and in revealing pupils' thinking
§ it is the
teacher's responsibility to intervene to assist the pupil to become more
efficient in the use of calculating strategies.
These teachers used teaching approaches that
encouraged discussion, in whole classes, small groups, or with individual
pupils.
Less effective teachers believed
in the importance of either
§ pupils
acquiring a collection of facts and standard methods, and that pupils varied in
their ability to remember these. They used teaching approaches that:
o
dealt with areas of mathematics
discretely
o
emphasised teaching and practising standard methods and applying
these to abstract or word problems without considering whether there were
alternative more efficient ways of solving a particular problem.
or
§ developing
numeracy concepts using practical equipment and waiting until pupils were ready
to move onto more formal methods. They used teaching approaches that emphasised
pupils working things out for themselves, using any method with which they felt
comfortable.
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