Would you like to enthuse and challenge your more able mathematicians?

1
Would you like to enthuse and challenge your more
able mathematicians?

• Welcome!

2
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

3

• 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

4
Who are more able children?
5
Identifying more able mathematicians

•  

6
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?
7
What opportunities could you offer in maths
lessons to develop more able mathematicians?
What are we trying to encourage? What sort of
mathematics appeals to the More Able? What could
the problems look like? What thinking are we
encouraging? What kinds of questioning would help?

• Pupils with high mathematical ability will only
  show their special talent if stimulating
  opportunities are provided a child who is
  capable of detecting patterns and generalising
  will only do so if suitable activities are
  provided.
• Koshy (2001) Co-director of the Brunel Able
  Childrens Education Centre

8
Types of problems...

• ...

9
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 5p
How could the problem become more open?
10
(No Transcript)
11
(No Transcript)
12
How can we ensure that opportunities are provided
to challenge all learners and that higher levels
of thinking are developed?
13
Anderson and Krathwohl (2001) produced a revised
taxonomy
What do tasks that encourage higher order skills
look like?
14
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
factsI 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.

15
LETS GET PRACTICAL
To which level of Blooms Taxonomy does this
activity go?
Task Investigate the properties of a group of
numbers how many different sets of numbers
exist within your group?
16

• 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.

17
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 childrens 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.

18
LETS GET PRACTICAL
19
Prompts to guide childrens 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?
20
Language of reasoning...
it could be ..., because ... it cant be ...,
because ... it wont work, because ... if ...
then ... it would only work if ... so ... in that
case ... and phrases like since, therefore, it
follows that ..., it will/wont work when ...
21
Resources! NRich

• ABOUT NRICHThe 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.

22
More detailed menu
Plus poster problems
23
(No Transcript)
24
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 4-page 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.

25

• 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!!!