Transcript Engaging Mathematics For All Learners

Developing teachers’ mathematics
subject knowledge in primary schools
to improve the attainment of all pupils
Liz Woodham, NRICH Project
&
Michael Hall, Open University
2014 - 2015
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In between face-to-face days …
Don’t forget
https://nrich.maths.org/haringey
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Day 8 – 17 March 2015
9.15-9.30 Welcome
9.30-10.45 Working on mathematical tasks together
Tackling tasks and reflecting on them in terms of subject knowledge and pedagogy
10.45-11.00
Break
11.00-11.15 Data collection
11.15-12.00
Working on more mathematical tasks together
Tackling one or more tasks and reflecting on them in terms of subject knowledge and
pedagogy
12.00-12.15
Curriculum priorities
12.15-1.00 Lunch
1.00-1.20 Update on various project strands
1.20-2.20 Curriculum development work
In pairs, planning for at least one task back at school
2.20-3.10 Working on more mathematical tasks together – algebra follow-up
3.10-3.15 Reflection
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Common themes from
mathematical needs identified
on day 1
The following were flagged up by at least two schools:
• Fractions/decimals/percentages
• Problem solving
• Place value
• Time
• Algebra
• Word problems
• Application of calculation strategies
• Subtraction
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Common mathematical needs
identified on day 7
In order of preference:
• mental maths
• assessment (planning and progression)
• problem solving
• challenging SEN children
• challenging the gifted
• division (not chunking)
• word problems (especially money)
• ratio
• subtraction
• multiplication
• place value
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Second aim of the
Mathematics National
Curriculum
All pupils will:
reason mathematically by following a line of
enquiry, conjecturing relationships and
generalisations, and developing an argument,
justification or proof using mathematical
language.
(DfE, 2013)
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In order to explore this aim, three questions
need to be answered:
• When is reasoning necessary?
• What do we do when we reason?
• How do we support children to develop
their reasoning skills?
http://nrich.maths.org/10990
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Maze 100
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When did you do some reasoning?
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Mystery Matrix
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Numbers 212.
Only one
number
used exactly
twice
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When did you do some reasoning?
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What do we do when
we reason?
•
•
•
•
•
•
Evaluate situations
Select problem-solving strategies
Draw logical conclusions
Develop solutions
Describe solutions
Reflect on solutions
etc …
http://nrich.maths.org/10990
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Helping learners get
better at reasoning
Progression in reasoning:
•
•
•
•
•
Describing
Explaining
Convincing
Justifying
Proving
http://nrich.maths.org/11336
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Make 37
Four bags contain a large number of 1s, 3s,
5s and 7s.
Pick any ten numbers from the bags above
so that their total is 37.
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Thinking about Make 37 …
What might each of the five stages of
reasoning ‘look like’ in the context of this
task?
Reminder of the five stages:
Describing, Explaining, Convincing, Justifying, Proving
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Reasoning is fundamental to
knowing and doing
mathematics
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Reasoning feature
http://nrich.maths.org/11018
Is in two parts:
• Reasoning: Identifying Opportunities
• Reasoning: The Journey from Novice to Expert
Each part comprises an article and a selection of
tasks
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YEAR FOUR MATHS DATA – SCHOOL NAME
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YEAR n MATHS APS – SCHOOL NAME
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Year 3 class data sample
1b
2b
2b
2a
2b
2b
2b
3b
2a
2c
1b
1a
2a
2b
2a
2a
2a
2a
3b
3c
2b
1a
+1 Subs
+1 Subs
O
O
+1 Subs
+1 Subs
+1 Subs
O
+1 Subs
+1 Subs
+1 Subs
Below
Above
Met
Above
Above
Above
Above
Above
Above
Met
Below
2c
2c
2b
2b
+1 Subs
+1 Subs
Met
Met
2c
2a
2a
3c
3c
3c
2a
3b
3b
2a
1a
2b
2a
2b
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+2 Subs
+1 Subs
+1 Subs
+1 Subs
+2 Subs
+2 Subs
+1 Subs
O
+2 Subs
+2 Subs
+1 Subs
+2 Subs
+1 Subs
Below
Met
Met
Above
Above
Above
Met
Above
Above
Met
Below
Below
Met
Below
2c
2a
2a
3c
3c
3c
2a
3b
3b
2a
1a
2b
2a
2a
+2 Subs
+1 Subs
+1 Subs
+1 Subs
+2 Subs
+2 Subs
+1 Subs
O
+2 Subs
+2 Subs
+1 Subs
+2 Subs
+2 Subs
Maths Age
Expect Sum
.Year 3 Summer
Maths Yr
Progress Sum
.Year 3 Summer
Maths TA Sum
.Year 3 Summer
Maths Age
Expect Spr
.Year 3 Spring
Maths Yr
Progress Spr
.Year 3 Spring
Maths TA Spr
.Year 3 Spring
Maths Age
Expect Aut
.Year 3 Autumn
Maths Yr
Progress Aut
.Year 3 Autumn
Maths TA Aut
.Year 3 Autumn
NAME
Maths Target
.Year 3 Autumn
Maths TA KS1
.Year 2 Summer
Export
Date :
YR 3 Maths 20/10/2014
Below
Met
Met
Above
Above
Above
Met
Above
Above
Met
Below
Below
Met
Met
Before we meet again …
• Continue to try out rich tasks with your learners
and colleagues
• Lead a staff meeting/follow-up staff meeting
• Take a look at the NRICH Reasoning Feature
• Collect data about the attainment of children in
your class
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Liz Woodham [email protected]
Michael Hall [email protected]
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