Would you like to enthuse
and challenge your more
able mathematicians?
Welcome!
Course objectives..
• To Identify more able mathematicians
• To know the characteristics of more able
mathematicians and reasons why some do not
make good progress
• To plan for more able mathematicians
• To have practical KS1 and KS2 maths activities
which develop higher order thinking
Mathematics is not only taught because it
is useful. It should also be a source of
delight and wonder, offering pupils
intellectual excitement, for example in the
discovery of relationships, the pursuit of
rigour and the achievement of elegant
solutions. Pupils should also appreciate
the creativity of mathematics.
DFEE 1988
Who are more able children?
Identifying more able mathematicians
Mathematically More Able Pupils
What are the key
characteristics
displayed by
mathematically
able pupils?
How do they
differ in their
approach to
mathematics
when compared
to other
children?
What opportunities could you offer in maths
lessons to develop more able mathematicians?
“Pupils
high
mathematical
will only
Whatwith
are
we
trying toability
encourage?
show their special talent if stimulating
What
sort
of
mathematics
appeals
to
opportunities are provided … a child who is capable
of detecting patterns
and generalising
the More
Able? will only do
so if suitable activities are provided.”
What could the problems look like?
Koshy (2001) Co-director of the Brunel Able
What
thinking
are we encouraging?
Children’s
Education Centre
What kinds of questioning would help?
Types of problems...
...
How many 5p coins are needed to
make 45p?
Kind of
Knowledge
Details
Known
The final amount of
money
45p
Unknown
The number of coins ?
Restrictions
All coins have the
same value
How could the
problem become
more open?
5p
How can we ensure that
opportunities are provided
to challenge all learners
and that higher levels of
thinking are developed?
Anderson and Krathwohl (2001) produced
a revised taxonomy:
t
hi
Derive and recall multiplication facts for the
2, 3, 4, 5, 6 and 10 times-tables and the
corresponding division facts; recognise
multiples of 2, 5 or 10 up to 1000
I know the 2, 3, 4, 5, 6 and 10 times-tables
and use them for division facts
I recognise multiples of 2, 5 and 10
Look for evidence of the range of number
properties children choose to use, for
example, when they sort numbers for a
partner to work out their ‘rules’ or criteria.
Look for children choosing criteria such as
multiples of 10, even or greater than 20,
and applying them consistently and
accurately.
LET’S GET PRACTICAL…
Task: Investigate the properties of a
group of numbers – how many different
sets of numbers exist within your group?
Paragraph 235 of the Williams Review (2008)
stated that
“in-class provision is sometimes not stretching
enough for the gifted and talented pupils. Part of
the reason why in-class provision might not be
stretching can be attributed to teachers’ lack of
knowledge of what might be possible and of the
types of activities that would allow the most able to
flourish, for instance open-ended investigative
tasks. In discussion with Ofsted, it has become clear
that many primary teachers lack confidence at this
level of mathematics and are often unaware of the
bigger picture and network of interrelationships.”
How can Teachers use the Primary Framework Learning
Overviews to design an investigation that meets the needs of
all – including the most able?
Primary Framework Y4 Block B Unit 1 Learning Overview
Assessment focus: Ma1, Reasoning
Look for evidence of children’s reasoning about shapes and
look out for children who can visualise 3-D shapes and
changes made to them. For example, identify children who
can visualise a solid cube, imagine using a saw to cut the
shape in half and then describe the two new shapes that have
been created. Look for children who can explain what they
see in order to justify their response and for children who can
pose similar problems for others to respond to.
LET’S GET PRACTICAL…
Prompts to guide children’s reasoning…
What can you work out (from the
information)?
If you know that, what else do you
know?
Can you tell me what your thinking is?
Shall we test that?
Does it work?
Do you still think it is ... ?
Do you agree that ... ?
Why is that bit important?
So, what must it be?
Language of reasoning...
it could be ..., because ...
it can’t be ..., because ...
it won’t work, because ...
if ... then ...
it would only work if ...
so ...
in that case ... and phrases like: since,
therefore, it follows that ...,
it will/won’t work when ...
Resources! NRich
ABOUT NRICH
The NRICH Project aims to enrich the mathematical
experiences of all learners. To support this aim, members of
the NRich team work in a wide range of capacities, including
providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom
practice.
On our website you will find thousands of free mathematics
enrichment materials (problems, articles and games) for
teachers and learners from ages 5 to 19 years. All the
resources are designed to develop subject knowledge,
problem-solving and mathematical thinking skills. The
website is updated with new material on the first day of every
month.
More detailed
menu
Plus poster
problems
Resources! Circa
ABOUT CIRCA MATHS
Circa Maths publishes two mathematical magazines for
children; Buzz, a new magazine for Key Stages 1 and 2 and
the much acclaimed CIRCA for Key Stages 2 and 3. Both are
informative, challenging and jam-packed cover-to-cover with
mathematics.
BUZZ is an A5 (148x210mm) 16 page magazine printed full
colour through out.
CIRCA is 16 pages printed in full colour and are supplied with
teacher's notes. Each issue of CIRCA comes with a FREE 4page booklet of Teacher's Notes. These show the content,
levels, answers and, where appropriate, additional
information on a topic with suggestions for further work.
There is also a reproducible worksheet which is often a
starting point for a wider investigation.
“There is very clear
evidence that focusing
sharply on what the
most able children can
achieve raises the
expectations generally,
because essentially it
involves careful
consideration of the
organisation and
management of teaching
and learning.” OFSTED
I love
maths!!!