Transcript Numeracy Link Teacher Seminar 2012

Numeracy Link Teacher
Day 1 Seminar 2012
Session 1
Drumcondra Education Centre
04.12.12
David Mc Mahon
Overview of Seminar
9.20 – 10:50
• Rationale
• SSE and Literacy and Numeracy Strategy
• Instructional Framework for Mathematics
10.50 – 11.10
Coffee
Session 2
• Fractions: Learning Trajectory
• Fractions Manual: Practical Tasks
Session 1
11.10 – 12.45
12.45 – 1.30
Lunch
Session 3
• Fractions Manual: Practical Tasks
• Successful Whole School Implementation
• ‘Between Session Tasks’
1.30 – 3.00
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Session 1 Objectives
• To outline a rationale and set the context for
the link teacher model
• To provide participants with a brief overview
of SSE and aspects of the Literacy and
Numeracy strategy
• To familiarise participants with an
instructional framework for mathematics
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Why the link
teacher model?`
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Timeline of CPD model
Nov./Dec. 2012: Link Teacher Day 1
Dec. 2012 – Spring 2013: Back in school + follow
on support
March 2013: Link Teacher Day 2
Follow on support
(school/clusters/workshops)
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Targets in the L & N Strategy
• Increase the percentage of primary children
performing at Level 3 and Level 4 (the highest levels) in
the National Assessment of Mathematics and English
Reading by at least 5 percentage points at both second
class and sixth class by 2020
• Reduce the percentage of children performing at or
below Level 1 (minimum) in the National Assessment
of Mathematics and English Reading by at least 5
percentage points at both second class and sixth class
by 2020
*Summary available on ERC Website
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Targets in the L & N Strategy
• Create greater awareness of, and more
positive attitudes towards, Mathematics
among the public
• Promote better attitudes to Mathematics
among children and young people
*Outlined in ERC Summary Report / Literacy & Numeracy Strategy
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Under the strategy all schools must engage in :
© PDST, 2010
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
8
SSE: Broad Requirements
Schools are asked to:
• Build on existing school development planning
processes by engaging in school self-evaluation of
teaching and learning from 2012/13
• Evaluate the quality of teaching and learning in
literacy, numeracy and at least one other
curriculum area in the four years from 2012/13 to
2015/16
• Write a short SSE report for the area examined
• Devise a School Improvement Plan for aspects of
practice identified for improvement
* See Circular 0039/2012
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
The Teaching and Learning Quality Framework
Teaching & Learning Framework
Sub-themes
Theme
SSE Guidelines p.24 / p.25
Learner
outcomes
• Attainment of
curriculum
objectives
Learning
experiences
•Learning
environment
•Pupils’ engagement
in learning
•Learning to learn
Teachers’
practices
•
•
•
•
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Preparation for
teaching
Teaching approaches
Management of
pupils
Assessment
10
Key steps in the SSE process
Gather the
evidence
Implement and
monitor
improvement plan
Analyse the
evidence
Devise a 3-year
school
improvement plan
Make judgements
about strengths
and areas for
development
Write school
self-evaluation
report
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Key Messages for Day 1
The link teacher for
numeracy is a facilitator of
change for improvement
A variety of learning
experiences enhances the
understanding of
mathematical concepts/skills
and allows for differing
abilities and learning styles
Mathematical thinking is
developed by eliciting,
supporting and extending
children’s mathematical
ideas
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Challenges
• What are the challenges to teaching
mathematics in Irish primary schools?
• What are the obstacles to developing
reasoning and conceptual / higher order
mathematical skills in our students learning?
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Sources
NAMER
Inspectorate
DES / NCCA
Whole-Class
Teaching v
Differentiation
High focus on
procedure and
drill
Over-reliance
on textbooks
Low focus on
reasoning and
problem solving
Under-use of
concrete
materials
Insufficient
pair and group
work
Teacher as sole
validator of
mathematical
ideas
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Fractions
See Fraction Manual p.12 & p.13
Classroom Culture
Most important
Least important
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
See Manual p.9
See Manual p.89
Revoicing Technique
‘…the reporting, repeating,
expanding or reformulating a
student's contribution…'
Forman & Larreamandy-Jones, 1998, p. 106
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Instructional Framework: Strategies for Supporting
and Developing Mathematical Thinking
• Read and discuss your section
• Summarise and record the main points
• Report back to your home group
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Activity based on
Manual p.8
• Eliciting
• Supporting
• Extending
Book Walk Activity
•
•
•
•
•
•
•
•
•
•
•
•
•
Resources p.4
Differentiation p.5
Instructional Framework p.8
Background Knowledge p.11
Fractions Trajectory p.19
Fractions Level A p.29
Fractions Level B p.39
Fractions Level C p.51
Fractions Level D p.63
Fractions Level E p.81
Appendix B p.88 / p.89
Appendix D p.94
Appendix E p.98
Same
Different
Instructional Framework
Current Teaching
Teacher Reflection Exercise
*See Reflection Framework
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Session 1: Recap before break
• To outline a rationale and set the context for
the link teacher model
• To provide participants with a brief overview
of SSE and aspects of the Literacy and
Numeracy strategy
• To familiarise participants with an
instructional framework for mathematics
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Numeracy Link Teacher
Day 1 Seminar 2012
Session 2
Key Messages for Day 1
The link teacher for
numeracy is a facilitator of
change for improvement
A variety of learning
experiences enhances the
understanding of
mathematical concepts/skills
and allows for differing
abilities and learning styles
Mathematical thinking is
developed by eliciting,
supporting and extending
children’s mathematical
ideas
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Session 2 Objectives
• To provide participants with a clear
understanding of the Learning Trajectory for
Fractions
• To promote a child-centred approach to the
teaching and learning of fractions
• To highlight the use of a variety of approaches
to cater for individual differences, abilities and
learning styles
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Developmental
5 levels
Based on PSC
Fractions
Trajectory
Concrete
Pictorial
Abstract
See Manual p.20
See Fractions Trajectory A
Linear
Area
Set
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Level B.1 and B.6
• Compare, order, count and identify fractions
and equivalent fractions
 Denominators 2, 4, 8, 10
 Denominators 3, 5, 6, 9, 12
*Prior Level 1 Brownie Activity p.29 / p.30
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Counting (Appendix D on p .94)
•
•
•
•
•
•
Sound of a Number p.95
Feely Bag p.95
Rope Activity p.97
Stand & Sit Game p .95
Counting Stick p.94
Target Boards p.96
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Compare, order and identify fractions and
equivalent fractions
• Linear
 Paper Strips p.39
 String and Paper Clips p.40
 Cuisenaire Rods p.40
• Area




Geoboards p. 41
Dotted Paper p.42
Rectangular Pieces p.42
Pie Pieces p.42
• Set
 Vehicles p.43
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
See Manual p.87
*Learning Log
Benchmarking & Estimation
• Benchmarks are helpful for pupils to develop
their number sense in relation to fractions.
• Estimation is central to applying benchmarks.
Pupils need lots of opportunities to compare
fractions to benchmarks.
• The most important reference points or
benchmarks for fractions are 0, ½ or 1.
See Manual p.45
Fractions Pairs Activity
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Consolidation Activities
• Fish for Fractions Game p.90
• Fraction Dice Game p.34
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Book Walk Activity p.47 – p. 54
•Level B.2 - Level B.5 Activities
•Level C - Teaching & Learning
•Unifix Cubes p.52
•Benchmarks Number line p.52
•Fraction Pieces p.53
•Fraction Wall p.54
Level C.3: Construct Algorithms for Equivalent
and Simplified Fractions p.58 & p.59
Slicing Squares Activity
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Session 2: Recap before lunch
• To provide participants with a clear
understanding of the Learning Trajectory for
Fractions
• To promote a child-centred approach to the
teaching and learning of fractions
• To highlight the use of a variety of approaches
to cater for individual differences, abilities and
learning styles
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Numeracy Link Teacher
Day 1 Seminar 2012
Session 3
Key Messages for Day 1
The link teacher for
numeracy is a facilitator of
change for improvement
A variety of learning
experiences enhances the
understanding of
mathematical concepts/skills
and allows for differing
abilities and learning styles
Mathematical thinking is
developed by eliciting,
supporting and extending
children’s mathematical
ideas
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Session 3 Objectives
• To promote a child-centred approach to the
teaching and learning of fractions
• To examine appropriate modes of assessment
for fractions
• To clarify the role of the link teacher
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Common Errors
• What are the common errors that children
make with fractions?




Adding
Subtracting
Multiplying
Dividing
 See Manual p.12 & p.13
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Level D.1
Add and subtract fractions (first with like
denominators, then repeat with unlike denominators)
1
3
1 +
8
4
5
3
4
9
10 +
7
8
11
–
12
3
4
• Estimate using Benchmarks of 0, ½, 1 or 2
• See Manual p.63
Concrete – PICTORIAL – Abstract
1
Two brothers ate some pizza. John ate 4 of the
3
pizza and Mark ate . How much of the pizza
8
did they eat altogether?
See Manual p.64
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Empty number lines
3¼-1½
3
1
4
0
1
1
2
4
2
1
3
4
3
4
5
See Manual p.69
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Level D.3 Multiply a fraction by a
whole number
6
3
×
4
Represent this equation pictorially
*See Manual p.72
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Assessment (Appendices)
• Whole- Class Checklist p. 100
• Individual Pupil Checklist p. 106
• Teacher Reflection p. 111
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Classroom & School
Where to next?
Exploring The Role of the Link
Teacher
Responsibilities of Link Teacher
Maintenance
• Keeping school informed of
current policy reforms and
initiatives
• Promoting Numeracy in
accordance with the needs of
school
• Supporting the SSE process
• Accessing and organising
resources
• Remaining up to date with
current research
Dynamic
• Promoting positive change
• Facilitating staff reflection and
the sharing of good classroom
practice
• Engaging teachers/parents and
community
• Facilitating a range of
continuing professional
development opportunities for
staff
Facilitating In-School Models of CPD
Opportunity to report on a course attended
Facilitated sharing of successful classroom practice
Working together to produce and share resources
Lesson Study
Action Learning
Coaching & Mentoring
Update Resources, Approaches & Planning
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Different strokes for different folks!
Ready to Go
20%
Wait and see
60%
Put on the brakes
20%
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Between session tasks
•
•
•
•
Discussion with principal
Identify and source resources for fractions
Use the manual as a teaching tool
Present some of the content to staff or groups
of teachers
• Avail of CPD opportunities
*Planning Diary Activity
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
ICT / Future Support
•
•
•
•
•
•
Numeracy Link cluster meetings
In-school support
Clustering of schools
Fraction workshops for other staff members
Online support
PDST Technology in Education
PDST Maths & ICT Curriculum Links
Scoilnet Fractions
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Focus for Day 2
Percentages
Decimals
Place Value
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013
Recap: Session 3
• To promote a child-centred approach to the
teaching and learning of fractions
• To examine appropriate modes of assessment
for fractions
• To clarify the role of the link teacher
The PDST is funded by the Department of Education and Skills
under the National Development Plan, 2007-2013