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Fiona Allan
Adults Do Count
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Adults Do Count
Aims
To think about the effective teaching and learning Maths
To enjoy doing Maths!
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Compare these two equations.
What is the same and what is different?
4)2()3(
4)5()2(
22
22
yx
yx
Let’s do some Maths!
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LSC leads on Themes 1 &
4
Meeting needs, improvingchoice
Developing leaders, teachers, trainers & support staff of the future
Developing a framework for quality and success
Putting teaching, training and learning at the heart of what we do
Accelerating Quality
Improvement
Success for All - launched 19 November 2002
DfES Standards Unit leads on
Theme 2, 3 & 6
Policy Coherence and
Communications
Background
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Putting teaching, training and learning at the heart of what we do
Priority areas phase 1 –
Business, Construction, E2E and
Science.
Priority areas for phase 2 –
Mathematics, ICT, Health & Social
Care, and Land-Based Studies. Building
on the work of phase 1 - delivery
undertaken by LSDA, supported by
regional and national Standards Unit
teams.
Priority areas for phase 3 –
Modern Foreign Languages,
Engineering, ACL, ITT.
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The resources were to be
• of world-class quality
• interactive
• developed with practitioners in trials and pilots
They had to contain
• activities for learners
• CPD resources for managers, teachers and trainers
• tutor guides
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The resources were to be• part of a national transformation programme.This programme would have • an unique focus on teaching, training and learning and would include •a national coaching programme • high quality resources and approaches.• subject specific regional networks.
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“All students can think hard about mathematics and thus do better at mathematics”
Deep Progress in Mathematics 2003
Research
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“There are two aspects to low attainment in mathematics: not knowing enough mathematics and not knowing how to learn mathematics.”
Deep Progress in Mathematics 2003
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“It is vital that society fully recognises the importance of mathematics
for its own sake, as an intellectual discipline;
for the knowledge economy;for science, technology and engineering;for the workplace;for the individual citizen.”
Post 14 Mathematics Inquiry, February 2004
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The following makes a significant contribution to high achievement in mathematics:
“Teaching that focuses on developing students’ understanding of mathematical concepts and enhances their critical thinking and reasoning, together with a spirit of collaborative enquiry that promotes mathematical discussion and debate”.
Evaluating mathematics provision for 14-19-year-olds, (Ofsted 2006)
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All students (Source: Allan 2005)
I enjoy Maths
0
10
20
30
40
50
60
70
Maths AoN Sociology
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Frequently or sometimes (Source: Allan 2005)
0
20
40
60
80
100
120
Computer
s
Graph
ics ca
lcs.
Teach
er(s
) lectu
red
Notes f
rom
boa
rd
Group
work
Pairs.
Puzzle
s
Videos
Mad
e up e
xerc
ises
Textb
ook e
xerc
ises
Past p
apers
Maths
AoN
Sociology
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Teacher(s) stood at the front of the classroom and lectured (Source: Allan 2005)
0
10
20
30
40
50
60
Never Occasionally Sometimes Frequently
With IAW
No IAW
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We copied notes from the board (Source: Allan 2005)
0
10
20
30
40
50
60
70
Never Occasionally Sometimes Frequently
With IAW
No IAW
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Lessons were sometimes or frequently boring (Source: Allan 2005)
0
5
10
15
20
25
30
35
40
45
Never Occasionally Sometimes Frequently
With IAW
No IAW
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Students’ learning styles (Source: Allan 2005)
0
2
4
6Activist
Reflector
Theorist
Pragmatist
Maths
AoN
Sociology
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http://tlp.excellencegateway.org.uk/teachingandlearning/downloads/?#math
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Improving learning
"When you explain something to someone else then you really understand it."
"When you really understand
something, you don't need to revise - you've got it for life!"
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https://www.ncetm.org.uk/resources/5845
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Learning Mathematics in Contexthttp://tlp.excellencegateway.org.uk/tlp/xcurricula/lmic/
Teaching and learning functional mathematics
http://www.excellencegateway.org.uk/pdf/TandLMathematicsHT281107.pdf
Mathematics Mattershttps://www.ncetm.org.uk/resources/12491
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Principles for effective teaching
• Build on the knowledge learners already have. • Expose and discuss misconceptions.• Develop effective questioning.• Make appropriate use of whole class interactive teaching,
individual work and cooperative small group work. • Encourage reasoning. • Use rich collaborative tasks.• Create connections between mathematical topics and the real world. • Use technology in appropriate ways.• Confront difficulties rather than seek to avoid or pre-empt them• Develop mathematical language• Recognise both what has been learned and how it has been learned
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Adults Don’t Count
https://www.ncetm.org.uk/community/8207
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Build on the knowledge learners already have
Write down everything you know about
Triangles
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Develop effective questioning
Spread out the fraction cards on the table in front of you.
How many questions have you answered in the last few minutes?
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Encourage reasoning.
Mathematical Moments
Topic: Percentages (Encouraging reasoning rather than ‘answer getting’)
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Create connections between mathematical topics
Write the following numbers at the top of your flipchart paper: 5, 12, 15
Write down beneath the numbers anything which links any two of the numbers.
Use mathematical language appropriately and also be imaginative!
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…… and the real world
Golf Course Measurements
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“The only way to avoid the formation of entrenched misconceptions is through discussion and interaction. A trouble shared, in mathematical discourse, may become a problem solved.”
Wood 1988
Thinking Through Mathematics
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Expose and discuss misconceptions
1. Cut out the cards
2. Stick the Always True, Sometimes True and Never True cards on to a sheet of flip-chart paper.
3. Stick each of other cards under an appropriate title card and explain why you have put it there.
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Use rich collaborative tasks Multiple representations
Evaluating statements
Creating problems
Analysing Solutions
Classifying
Tarsia jigsaws and dominoes
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Use a Range of Activity Types
Multiple representations Evaluating statements Creating problems Analysing Solutions Classifying Questioning Use of IT Card activities Ideas for open questions Encouragement to develop and extend ideas
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Use technology in appropriate ways
ICT and Digital Technology used in mathematics teaching
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Develop mathematical language
Mathematical Moment 2D and 3D shapes (Developing mathematical language)
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Make appropriate use of whole class interactive teaching, individual work and cooperative small group work.
When?
What?
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Recognise both what has been learned and how it has been learned
What I Learned from Reading the Entire Encyclopaedia A.J.Jacobs
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And now ….
Look again at the list of principles for effective teaching.
Which of these are you going to concentrate on for the rest of this term?
Start by focusing on one.
When you have embedded it into your practice, choose another one.
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Principles for effective teaching
• Build on the knowledge learners already have. • Expose and discuss misconceptions.• Develop effective questioning.• Make appropriate use of whole class interactive teaching,
individual work and cooperative small group work. • Encourage reasoning. • Use rich collaborative tasks.• Create connections between mathematical topics and the real world. • Use technology in appropriate ways.• Confront difficulties rather than seek to avoid or pre-empt them• Develop mathematical language• Recognise both what has been learned and how it has been learned
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And now ….
What will you do next week?
What will you do for the rest of the term?
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Fiona Allan
Thinking Through Mathematics