Sharing Good Practice
MASTERY IN MATHEMATICS FEWER THINGS
IN GREATER DEPTH
BY CLIVE DAVIES OBE
Clive Davies OBE – a former
headteacher, and founder of a
consultancy providing curriculum and
inspection advice to schools – shares
his thoughts on reaching the ‘mastery’
level in mathematics.
“If people knew how hard I worked to
get my mastery, it wouldn’t seem so
wonderful at all.”
Michelangelo
We are in the midst of a great change
to classroom practice, particularly in
mathematics. The method of racing
learning, through the sub levels, is
being abandoned to ensure a deeper
understanding against each objective.
‘Mastery’ is now at the heart of
mathematics, and teachers must get
to grips with what tha t means and how
to identify and achieve it with pupils.
In an international environment, the
in-depth study of a concept is vital
to learning in order to create links
between inner subject topics and
other curriculum contexts.
Perhaps the above quotation from
Michelangelo illustrates it best - the
‘mastery’ level can only be achieved
with work and time. With limited time
to achieve this in each school year,
we’re forced to cut the objectives
down in order to teach fewer things in
greater depth.
‘Mastery’ has no single definition, but
it may be linked with the concepts of
shallow and deep learning. If shallow
learning is superficial and temporary,
then deep learning can be recalled
and used appropriately. Mastery takes
this one level further, where learning
can be transferred and applied to
different contexts.
The Four Stages of Competence is a
useful model for illustrating mastery:
For a child to have reached that
‘effortless’ level, they should:
• Be fluent in the fundamentals of
mathematics. This includes varied,
frequent practice with increasingly
complex problems.
• Reason mathematically by following
a line of enquiry, conjecturing
relationships and generalisations,
and developing an argument,
justification
or
proof
using
mathematical language.
• Solve problems by applying
mathematics to a variety of routine
and non-routine problems with
increasing sophistication.
Mastery boils down to independent,
consistent working and an ability to
explain one’s own understanding.
Some practical indicators of when a
child has reached the mastery level
could be: being able to describe
the concept to somebody else,
recognising real-life instances of
problems (i.e noticing that triangles
are used in the environment for their
strength, such as in pylons) or making
up their own examples of the problem.
But how can we ensure a child is able
to complete the above? We must be
wary of defaulting to accelerating able
pupils through new material once a
concept appears to be grasped; we
should also recognise that a child’s
ability to answer questions with more
difficult numbers does not necessarily
equate to mastery. The increase in
challenge should come from thinking
harder about the concept or topic
being taught.
An indicative question to judge a Year
6 pupil’s mastery of times tables might
be: “My age this year is a multiple of 8.
Next year it will be a multiple of 7. How
old am I?”
Essentially, I believe we need to build
into our maths subject the important
stage of checking if pupils have ‘got
it’ through the form of formative
assessment, rather than testing. This
can be accomplished by using well
thought out activities related to the
actual objective being taught. If we
do this regularly then it may be more
reliable than testing, and we may see
an end to the worrying feature of
pupils struggling with greater depth
questions due to insecurity or lack of
fluency with basic mathematical skills.
To find out more about Focus Education
visit: www.focus-education.co.uk
Clive Davies, OBE, is the founder of Focus Education, a family-run organisation
providing advice and educational support to both UK and International schools.
Clive has vast experience in primary education spanning 40 years, having
inspected over 200 schools and serving as a head teacher, Ofsted inspector,
Local Authority adviser, trainer and consultant
Class Time
|
|
Mar - Apr 2018
| 15