Transcript PowerPoint Presentation - Numeracy Across the Curriculum

Implementing Numeracy
Across the Curriculum
Chris Olley
[email protected]
Implementing Numeracy
Across the Curriculum
 Successfully
moving from policy to
practice
 The numeracy strategy in a nutshell
 Developing cross-departmental
consistency in delivering numeracy
 Implementing a problem solving approach
 Mathematical modelling
 Data handling projects
© 2012 Chris Olley
Visit: www.themathszone.co.uk
FAQs from the DfES
 Be
honest, isn’t this idea really trivial?
 Why don’t you just give us a model
Numeracy Across the Curriculum policy
 Some departments say there is no
numeracy in their subject (e.g. English).
How do I address this?
 We have written a whole school
numeracy policy.
What do we do next?
© 2012 Chris Olley
Visit: www.themathszone.co.uk
What does it amount to?
A
consistent approach across the
school to support all students
develop their (mental) numeracy.
A consistent mathematics across the
school
Integrated problem solving
involving mathematical
methods
© 2012 Chris Olley
Visit: www.themathszone.co.uk
Activity
 Introduce
yourself to your neighbours!
 Share one instance of each of these:
A
teacher in a subject other than maths
helping a student solve an arithmetic problem
that cropped up in their lesson.
 Maths being used in a department other than
maths that really annoyed the maths
department
 The maths department working
together with another department
to engage students in a joint problem
solving task.
© 2012 Chris Olley
Visit: www.themathszone.co.uk
The Policy
Supporting
numeracy
A good maths guide
Opportunities for cross curricula
work
© 2012 Chris Olley
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Mechanisms
SMT
support
NAC working group
Inset time, departmental meeting
time, staff meeting time
Access to assemblies, tutor groups,
newsletters, poster campaigns
Timetabling input
© 2012 Chris Olley
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The NAC Development Plan
Staffing,
allocated time,
responsibility, success criteria,
monitoring, specified timescale,
costs.
At most one development per strand,
per term. Possibly per year!
© 2012 Chris Olley
Visit: www.themathszone.co.uk
Policy, what policy?
Work
in number groups:
Share
the key elements in your school’s
NAC policy.
Share the specific developments which
have been implemented from the policy.
Choose one example of a (specific!)
policy that has been put into
practice to share on the acetate
© 2012 Chris Olley
Visit: www.themathszone.co.uk
Albert Einstein
(1879-1955)
Do not worry about your difficulties
in mathematics, I assure you that
mine are greater.
© 2012 Chris Olley
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The Numeracy Strategy
Brainstorm:
Share with your neighbour for 2
minutes:
How
does the numeracy strategy
support student’s arithmetic?
Now
share with everyone…
© 2012 Chris Olley
Visit: www.themathszone.co.uk
The Message
If
students need to solve number
problems in your lessons, support
them to solve them mentally.
Don’t explain to them how you
would do it … encourage them to
reflect on their own knowledge
about numbers.
Don’t hand them a calculator!
© 2012 Chris Olley
Visit: www.themathszone.co.uk
Numeracy Support
 Students
are practiced in ways of
thinking that they have learned through
the National Numeracy Strategy.
 They can be quickly prompted into these
ways of thinking with open questions.
 Everyone can use mental methods if they
can find numbers they are
comfortable with.
© 2012 Chris Olley
Visit: www.themathszone.co.uk
Questions
 “Can
you see numbers close to these that
would be easier to deal with?”
 “Would it be easier the other way round?”
 “Could you break it up and work on the
bits separately?”
 “Could you use doubles or halves?”
 “Can you see an easier problem with the
same answer as this one?”
 “Would it help to jot down a
number half way?”
 “Would it help to use a number
© 2012 Chris Olley
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line?”
A Whole Staff Presentation 1
Mental
stress!
Staff
arithmetic causes people
and students alike …
A
calculator is the best tool to use
for problems beyond the scope of
mental arithmetic.
Mental arithmetic should always be
the first port of call.
© 2012 Chris Olley
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A Whole Staff Presentation 2
Everyone
has some knowledge of the
relationships between numbers …
the trick is to find out what … and
to use it!
© 2012 Chris Olley
Visit: www.themathszone.co.uk
A Whole Staff Presentation 3
 Solve
a collection of number problems
and discuss in detail how you did it (no
written methods allowed!)
 Recognise how many different methods
graduate teachers use!
 See how the problems are transformed
into the solvers comfort zone!
© 2012 Chris Olley
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A Whole Staff Presentation 4
Describe
how the methods that
teachers have used can be used to
support students.
Translate the methods used into:
Numeracy
buzz words!
Open questions
© 2012 Chris Olley
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Activity
If a student is stuck ask them …
Problem
148 + 148
224  4
79 + 52
162 – 28
87 x 6
© 2012 Chris Olley
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Question 1
Question 2
Question 3
A Whole Staff Presentation
The
presentation is available to
download at:
www.themathszone.co.uk
Discuss it with me at:
[email protected]
© 2012 Chris Olley
Visit: www.themathszone.co.uk
Samuel Taylor Coleridge
(1772-1834)
...from the time of Kepler to that of Newton,
and from Newton to Hartley, not only all
things in external nature, but the subtlest
mysteries of life and organization, and
even of the intellect and moral being, were
conjured within
the magic circle of
mathematical formulae.
The Theory of Life.
© 2012 Chris Olley
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Joseph Conrad
(1857 – 1924)
Don't talk to me of your Archimedes'
lever. He was an absentminded person
with a mathematical imagination.
Mathematics commands all my respect,
but I have no use for engines. Give me the
right word and the right accent and
I will move the world.
Preface to A Personal Record.
© 2012 Chris Olley
Visit: www.themathszone.co.uk
Where is maths used?
Work
in letter groups
Make a complete list of departments
where mathematics is used … in
descending order of frequency
Starting with the most frequent
user, note areas where you would
like to change practice
© 2012 Chris Olley
Visit: www.themathszone.co.uk
What maths is used?
 1.
Numeracy Methods
 Estimation
 Multiplication
 Addition
 Subtraction
 Division
 2.
Algebra
 Writing
 3.
Algebra
Charts and Graphs
 Graphs
 Statistical
© 2012 Chris Olley
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Charts
The Handbook
Based
on agreed principles
Within
the maths department
Within other departments (through the
NAC working group)
How
would you do yours differently?
© 2012 Chris Olley
Visit: www.themathszone.co.uk
Implementation
Simple
messages
Implementation:
Posters
Assemblies
Staff
meetings
© 2012 Chris Olley
Visit: www.themathszone.co.uk
Real Problem Solving in
Mathematics: Creating Models
 Flaubert,
Gustave (1821-1880)
Since you are now studying geometry
and trigonometry, I will give you a
problem. A ship sails the ocean. It left
Boston with a cargo of wool. It grosses
200 tons. It is bound for Le Havre. The
mainmast is broken, the cabin boy is
on deck, there are 12 passengers
aboard, the wind is blowing EastNorth-East, the clock points to a
quarter past three in the afternoon. It
is the month of May. How old is the
captain?
© 2012 Chris Olley
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Real Problems
Work in base groups
 Share examples of problems worked on by
students where the solution actually
mattered (i) within the school context
(ii) outside the school context:
 In
the maths department
 (That you know of) outside the maths
department
A
bonus star if you can share an
instance where maths was an
essential
part of the solution.
© 2012 Chris
Olley
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… Time for lunch
Consider
how opportunities for real
problem solving could be found in
school and how the difficulties in
finding the time and space to let
students solve them could be
overcome.
© 2012 Chris Olley
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George Polyá
(1887-1985)
One of the first and foremost duties of the
teacher is not to give his students the
impression that mathematical problems
have little connection with each other,
and no connection at all with anything
else. We have a natural opportunity to
investigate the connections of a
problem when looking back at its
solution.
How to Solve It. Princeton: Princeton
University Press. 1945.
© 2012 Chris Olley
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The Modelling Cycle
1: S p ec ify the
P ro b lem
2: S et up the M o d el
3: F o rm ulate the
M athem atic al
P ro b lem
6: C o m p are with
R eality
5: Interp ret the
S o lutio n
4: S o lve the
M athem atic al
P ro b lem
Discovering advanced mathematics, Collins Educational.
© 2012 Chris Olley
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Modelling Projects
Activities designed to engage students
in mathematical modelling:
A huddle of penguins
The cooling of pizzas
Second hand car prices
Running a school
Chinese New Year
© 2012 Chris Olley
Visit: www.themathszone.co.uk
Cross Curricula Work
 Ray
Spradbery: Pigeon Maths
 Steig Melin-Olsen: Bergen Airport
 Maths
and DT Textiles: Islamic Art
 English reading rates activity
 Numeracy through MFL
 Best fit functions for experimental
science
 Budget and ticketing for the drama
production
© 2012 Chris Olley
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Activity
 Work
in pairs/threes
 Choose one of the presented activities.
Sketch out a structure to model the
situation.
 Suggest the materials needed to support
students engage with it.
 Suggest the roles of the TWO
departments who could be involved.
© 2012 Chris Olley
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Sir Arthur Conan Doyle
(1559 – 1930)
It is a capital mistake to theorize before one
has data.
Scandal in Bohemia.
© 2012 Chris Olley
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The Data Handling Cycle
Specifying the
Problem and Planning
Interpreting and
Discussing Results
© 2012 Chris Olley
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Collecting
Data
Processing
and
Representing
Data
Data Handling Projects
Using
Census Data to support
analysis in Humanities (RSS,
Nottingham)
Maths and PHSE: The smoking
project
http://www.standards.dfes.
gov.uk/keystage3/respub/
num_xc_webresources
© 2012 Chris Olley
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Voltaire (1694-1778)
He who has heard the same thing
told by 12,000 eye-witnesses has
only 12,000 probabilities, which are
equal to one strong probability,
which is far from certain.
In J. R. Newman (ed.) The World of
Mathematics, New York: Simon and
Schuster, 1956
© 2012 Chris Olley
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Drawing Deductions
Hypothesis
(amenable to analysis)
Data (sampling, bias)
Interpretation (charts and statistics)
Analysis (making statements)
Critique (test the hypothesis)
© 2012 Chris Olley
Visit: www.themathszone.co.uk
Making it Happen
Cross
curricula mapping
Build it in to the scheme of work (of
both/all departments)
Supported with available materials
Maths be generous:
Key
stage 3 problem solving
Key stage 4 coursework
© 2012 Chris Olley
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Activity
Work
in number groups
Share successful cross curricula
activities:
What
were the benefits of succeeding
with this type of work?
How was it made to happen?
© 2012 Chris Olley
Visit: www.themathszone.co.uk