The new national curriculum
arrived with us all in September where did you look first? I looked at year 5
and 6, the year groups where I teach maths. What had changed? What were the
raised expectations? Thinking of the least able pupils how would they cope with
the new demands? After that I looked at the beginning, at what I now think are
the three key points of the new curriculum, mathematical fluency, reasoning and
problem solving.
The national curriculum for mathematics aims to
ensure that all pupils:
become fluent in the fundamentals of mathematics, including
through varied and frequent practice with increasingly complex problems over
time, so that pupils develop conceptual understanding and the ability to recall
and apply knowledge rapidly and accurately…
What does fluency mean? The
Oxford Dictionary defines it as the ‘ability to express oneself easily and
articulately’. Google’s definition includes the synonyms, ‘fluidity,
effortlessness, ease, rhythm’. Wikipedia’s definition is ‘Fluency (also called volubility and loquaciousness) is the property of a person or of a system that
delivers information quickly and with expertise.’ The latter definition is the one I believe fits
best with fluency in a mathematical context. I want my pupils to be able to
deliver the answers to complex problems demonstrating their expertise and
understanding, to be able to do this quickly they need to have the facts at
their fingertips, rather than counting all the time. So often I feel that they
fail to see the connections between the different things that I teach, they see
them as isolated from each other rather than integrated as I see them.
I've done the investigation when
you add two odd numbers is the answer even or odd? Pupils have correctly
established that the answer is even and yet they will calculate 53 + 51 and give
the answer as 93 and fail to realise that cannot be correct for many reasons,
odd + odd is even, the units needs to be 4, slightly more than 50 plus slightly
more than 50 must make slightly more than 100.
Having identified the problem
what strategies could I employ to support pupils? I will be having a fact slot at the start of
every lesson, drilling children in the number facts not only to 10 but also to
9, 8, and so on so that they know that 3 + 4 is 7 rather than calculating it. It’s
not 1950’s education where drilling without understanding was the norm I want
children to investigate to find the solutions but then practice to get the
knowledge at their fingertips. I’ll be really emphasizing the even plus odd
must be odd much more. Once 3 + 4 = 7 is firmly established I’ll be expanding
it to 30 + 70 and 300 + 700 then to decimals 0.3 +0.4 and to fractions 3 ninths
add 4 ninths, then to algebra 3a + 4a =.
In this way I hope that their
‘mathematical fluency’ will develop and they can answer increasingly
complex problems with conceptual understanding and the ability to recall and
apply knowledge rapidly and accurately.
Julie Gallimore, Primary School Teacher
