Transcript Slide 1

NQT KS1 and KS2 Mathematics Course
Event Code: LIS
13/253
Tutors: Kathryn
Roper and Simon
Nortcliffe
Venue: Kesgrave
High School, Ipswich
Aims of the course
• To develop a clearer understanding of children’s
progression in mathematics
• To know some of the key hard to teach, difficult
to learn aspects of the mathematics curriculum
• Understand how to transfer knowledge gained
from assessment and tracking data into practical
teaching to impact on learning
Session 1
Key principles to help with the teaching of
mathematics
 Every day is a mental mathematics day
 Hands-on learning is still important
 Seeing mathematics through models and
images supports learning
 Talking mathematics clarifies and refines
thinking
 Make mathematics interesting
 Learning from mistakes should build up
children’s confidence
Progression Activity
•
Working with a partner can you put the
objectives in order starting with Reception
and ending with Progression to Year 7.
• Consider whether your children are
working at age related expectations; where
they are doing well and areas where more
support is required.
• What is the progression from the previous
year group to your year group?
Teaching children to calculate mentally
• How do you support children in your school to
progress with their mental calculations?
• Turn to ‘Progression in mental calculations’
beginning on page 4 of the document. Work with
someone on your table to devise an activity,
using practical resources, to support the skills
required for your year group focusing on addition
and subtraction or multiplication and division.
• Share your activity with another pair.
Tea/Coffee
Reflection
Reflecting on your mathematics teaching to
date consider the following questions:
What is working well?
What would you like to have more support
in moving your mathematics teaching
forward?
Please write your comments on sticky
notes and put them on the flip chart sheets.
Session 2
Strategies to promote speaking and
listening in mental mathematics
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Visualisation / mathematical imaginings
Always, sometimes, never true
True or false
Negotiation of meaning
Using one of the above strategies plan an activity
to address the objectives in Block B, Unit 3.
Lunch
U2 Bridge Crossing Problem
All four band members need to cross a bridge.
They start on the same side of the bridge.
A maximum of two people can cross at any time.
It is night and they have just one lamp.
People that cross the bridge must carry the lamp to see the way.
A pair must walk together at the rate of the slower person:
Bono: - takes 1 minute to cross
Edge: - takes 2 minutes to cross
Adam: - takes 7 minutes to cross
Larry: - takes 10 minutes to cross
The second fastest solution gets the friends across in 21 minutes.
The fastest takes 17 minutes. Can you work out how it is done?
Solutions
1 and 2 cross over first.
7 and 10
2 minutes
Then 1 goes back.
1 minute
1
Then 7 and 10 cross over.
10 minutes
1
Then 2 crosses back.
2 minutes
1 and 2
Then 2 and 1 cross together.
2 minutes
Total Time: 17 minutes!
1 and 2
2
2,7 and 10
7 and 10
1,2,7
and
10
Interim task
• Carry out your planned activity and reflect on the
children’s responses and the impact on pupil
learning.
• Be ready to discuss the outcomes of the planned
activity and anything else you have undertaken
as a result of attending day 1.
Day Two – Monday 10th June 2013
Why teach problem solving?
Children need to be able to analyse everyday situations
and apply their maths to real life problems
Children enjoy problem solving activities - Maths is
enjoyable!
Children with a wide range of attainment can participate
Children learn not to expect immediate answers
Develops children’s skills of co-operation and
collaboration
Encourages children to check their answers and use
mathematical language
Develops thinking and reasoning skills
Numeracy framework has been revised to include
renewed emphasis on Speaking and Listening and Using
and Applying Mathematics
Two aspects to teaching problem
solving
• Teaching specific strategies to solve
particular types of problem, for example in
units on reasoning about number or shape;
• Posing questions in ‘everyday’ teaching for
children to practise and develop their general
mathematical thinking and reasoning skills
across the full mathematics curriculum, not
just in the units on problem solving.
Problem Solving
Two methods of approach
Approach A
Approach B
Approach A
Start with a problem or investigative task
during an initial whole-class discussion.
Children then continue the same task or
activity, often in pairs or small groups,
developing it to a level appropriate to their
attainment.
Collect together children’s responses and
set similar problems.
Open-ended problems are useful for this.
Approach B
Complete an activity during an initial
whole-class discussion and highlight the
strategies used.
Follow this by providing different, but
related, tasks.
Most children will work on a task; however
some could work on a simplified task and
some on a harder task.
Problem solving materials
Research shows that…
Mayher (1985) identified the following factors as
contributing towards problem solving
performance:
• Practice in recognising problem types.
• Practice in representing problems – whether
concretely, in pictures, in symbols, or in words.
• Practice in selecting relevant and irrelevant
information in a problem.
Extract taken from ‘Primary Mathematics – Teaching
for understanding’ Barmby et al, 2009.
Classification of problems
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Finding all possibilities;
Logic problems;
Finding rules and describing patterns;
Diagram problems and visual puzzles;
Word problems.
Finding all possibilities
Finding all possibilities
Children’s strategies
• Have a system for finding the possibilities
• Organise a way of recording
ideas/strategies
• Use a method of tracking what has been
included and what has not
• Have a way of deciding when all
possibilities have been found
Logic problems
Logic problems
Children’s strategies
• Identify the given facts and prioritise them
• Look for any relationships and patterns in the
information given
• Use one piece of information at a time and see
what effect it has, then keep one fixed and test
the other
• Choose and use a recording system to
organise the given information
• Check that the answer meets all the criteria
Finding rules and describing
patterns
Finding rules and describing
patterns
Children’s strategies
• Decide on the information you need to describe
and continue the pattern
• Give examples to match a given statement and
ones which do not
• Describe a rule of a pattern or relationship in
words or pictures
• Predict the next few terms in a sequence to test
the rule
• Use a rule to decide whether a given number will
be in the sequence or not
Diagram problems and visual puzzles
Diagram problems and visual
puzzles
Children’s strategies
• Identify the given information and represent it
in another way
• Use a systematic approach to solve the
problem and a way of recording if necessary
• Use drawings or annotations to help visualise
the problem using familiar shapes or patterns
• Try other possibilities to check the solution
Word problems
Nadia is working with whole numbers. She says: ‘If
you add a two-digit number to a two-digit
number you cannot get a four-digit number.’ Is
she correct? Explain why.
Word problems
Children’s strategies
• Read and make sense of the problem
• Recognise key words, relevant information and
redundant information
• Decide which number operations to use and in
which order
• Choose an efficient way to calculate
• Check their work to see whether it makes sense
Other resources to support the
teaching and learning of problem
solving
Problem solving pack - DCSF
Mathematical challenges for able children in Key Stages 1 and
2 - DCSF
Developing the Mathematical Challenges for able children Suffolk
We can work it out! – ATM
It makes you think! – ATM
NRICH website – www.nrich.maths.org
Talk Maths – Camden Maths Learning Network
Targeting Level 4 through Problem solving
Questioning
‘Good questioning techniques have long
being regarded as a fundamental tool of
effective teachers.’
Jenni Way, October 2001.
Changing the
mind-set
When we ask a question,
we’re not only interested
in the correct answer
but in what children think.
What makes questioning effective?
Prepare key questions to ask.
Ask fewer but better questions.
Use appropriate language and content.
Give pupils “thinking time” to respond to
questions, and pause between them.
Prompt pupils, give cues.
Listen, and acknowledge pupils’ responses
positively.
From 'How do they walk on
hot sand', Suffolk Publication,
2001.
Bloom’s taxonomy
Odd one out
Which is the odd one out? Why?
Odd one out
Which is the odd one out? Why?
The only
shape with
curved
sides?
Odd one out
Which is the odd one out? Why?
The only
shape with
curved
sides?
The only
shape with
three
sides?
Odd one out
Which is the odd one out? Why?
The only shape
with four equal
sides?
The only
shape with
curved
sides?
The only
shape with
three
sides?
Odd one out
The only
shape with
three
sides?
Which is the odd one out? Why?
The only shape
with four equal
sides?
?
The only
shape with
curved
sides?
Odd one out
Which is the odd one out? Why?
6, 15, 28, 36, 66
Odd one out
Which is the odd one out? Why?
Hide the hand……..
I have 5 coins totalling 22p in my hand. What are the coins?
Hide the hand……..
I have 5 coins totalling 22p in my hand. What are the coins?
Hide the hand……..
I have 5 coins totalling 22p in my hand. What are the coins?
Hide the hand……..
I have 5 coins totalling 22p in my hand. What are the coins?
Hide the hand……..
I have 5 coins totalling 22p in my hand. What are the coins?
Hide the hand……..
I have 5 coins totalling 22p in my hand. What are the coins?
Give me…… and
another…..and….
A multiple of 2
The dimensions of a polygon with a perimeter of
36 centimetres
3 numbers with a mean of 12
A net of a cube
A fraction bigger than 1/2
Convince Me
That this isn’t a square?
Convince Me
The hidden shape is a yellow triangle
Convince Me
The hidden shape isn’t a yellow triangle
What is wrong with the
statement …?
How can you correct it?
When I count in 2s,
the numbers will
always be even.
If I count on in 10s
from 15, the units
digit will change
each time.
What is the same and
what is
different about...?
27
227
37
237
272
22
Sometimes, always, never
true?
Helen says that when you add two consecutive numbers the
answer is always odd.
Is she right? Explain your answer.
eg 26 and 27
POGs
Providing pupils with a structure of answering
questions; a peculiar, obvious and general
example.
Can you think of an example for numbers with a
product of 60.
Peculiar – 240 x 0.25
Obvious – 10 x 6
General rule – two numbers that make 60 when
multiplied together
The Suffolk Hub –
www.suffolklearning.co.uk
Contact Information
By phone:
Office - (01473) 263962 Liz Rivett
E-mail:
[email protected]
[email protected]
Website:
www.suffolklearning.co.uk