In the
context of the challenge to raise standards in mathematics in schools in
England the word ‘mastery’ has recently become prominent in the vocabulary of
the English mathematics curriculum (NCTEM, 2014, www.ncetm.org.uk/public/files/19990433).
It is reassuring to note that the way in which the word ‘mastery’ is being used
is entirely consistent with the approach to children’s learning of mathematics
that I have promoted in my own writing.

Mastery
is seen as children developing fluency in mathematics alongside a deep
understanding of mathematical ideas and processes. So, for example, teaching
approaches for mastery should ‘foster deep conceptual and procedural knowledge’
and ‘exercises are structured with great care to build deep conceptual
knowledge alongside developing procedural fluency’ (op.cit.). This is a key
principle in teaching mathematics to young children: that mastery of the
subject is not achieved simply by repeated drill in various procedures.
Instead, the focus is on the development of understanding of mathematical
structures and on making connections.

Making
connections in mathematics – a recurring theme in all my books – ensures that
‘what is learnt is sustained over time, and cuts down the time required to
assimilate and master later concepts and techniques’ (op.cit.). Nearly all
mathematical concepts and principles occur and can be applied in a wide range
of contexts and situations. Because of this, the deeper understanding central
to mastery in mathematics is facilitated by a wide variation in the experiences
that embody mathematical ideas.

For
example, mastery of the 5-times multiplication table by Year 2 children is not
just a matter of memorizing a chant that begins ‘one five is five, two fives
are ten …’ – although that is part of it. It would also involve, for example:

· connecting each result in the table with a collection of 5p coins
and the total value;

· articulating the pattern of 5s and 0s in the units position in the
odd and even multiples of 5;

· explaining how to get from 4 fives to 8 fives by doubling;

· explaining how to get from 6 fives to 7 fives by adding 5;

· counting in steps of five along a counting stick;

· knowing that, say, ‘3 fives are fifteen’ is what you use for the
cost of 3 books at £5 each;

· constructing patterns with linked cubes that show 1 set of five, 2
sets of five, and so on;

· filling in the missing number in number sentences like ‘6 × □ = 30’.

To teach
for this kind of mastery teachers themselves need a deep structural
understanding of mathematics, an awareness of the range and variety of
situations in which a mathematical concept or principle can be experienced, and
confidence in exploring the connections that are always there to be made in
understanding mathematics. Any teachers looking for this? I can recommend one or
two books.

Hi,

ReplyDeleteWhich books would you recommend..?

Thank you!!

Thanks for asking ... but I assumed that it would be obvious that I had in mind my own books! Mathematics Explained for Primary Teachers and Understanding Mathematics for Young Children. Details available on my blog site.

ReplyDelete