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Improving Numeracy through SSELorcán O CallaráinAnne MurphyPat Coffey
Picture
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Overview of SeminarSession 1
9.15 – 11.00
• Rationale for school improvement seminars• School reflection on SSE experiences• Exploring numeracy in a broad sense
11.00 – 11.15 Coffee
Session 2
11.15 – 12.45
• Exploring improvement in numeracy using the SSE process
12.45 – 1.30 LunchSession 3
1.30 – 3.30
• Exploring improvement in numeracy using the SSE process• Moving forward
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Overview of Days 1 and 2
• Day 1: Exploring improvements in numeracy, using the SSE process, with a particular emphasis on problem solving
• Day 2: Exploring improvements in numeracy, using the SSE process, with an emphasis on specific mathematical content
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Day 1 Objectives
• To facilitate reflection on individual school experiences of SSE
• To provide participants with an opportunity to explore numeracy in a broad sense
• To explore improvement process in numeracy using the SSE process
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School self-evaluation is a key tool in effective
school improvement
The six steps of the school self-evaluation
process are continuous but not strictly linear
School self-evaluation is an inclusive,
reflective, collaborative whole school process
Key Messages
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School Reflection
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Successes
ChallengesPossible Solutions
School Improvement Experience
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Learning to Date
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National Strategy
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Who are the numeracy teachers?
There may be a mistaken belief that the development of young people’s literacy and numeracy skills should be completed by the end of primary school: this is not the case……………
Teachers of all post-primary subjects have an important role to play in developing and consolidating students’ ability to use literacy and numeracy.
Literacy and Numeracy for Learning and Life, DES 2011
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So what do we really mean
when we talk about
numeracy?
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Numeracy?Awareness
Reasoning
Spatial Awareness
Real Data
ProcedureNumber
Computation
Critical Thinking
Organisation
Knowledge
Decision Making
Relationships
Symbol Sense
Understanding
Logic
Contextualising
Citizenship
Skills
Problem Solving
Mathematising
Language
Engagement
Reflection
Interpretation
Communication
Conversation
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Number (strand 3)
Geometry and Trigonometry (strand 2)
Statistics and Probability (strand 1)
Algebra /Functions (strands 4 and 5 )
Number
Measures
Shape and Space
Data
Algebra
SIXTH CLASS JUNIOR CYCLE
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Applying & Problem-Solving
Communicating & Expressing
Integrating & Connecting
Reasoning
Implementing
Understanding & Recalling
(PSMC:1999: 68)
Developing Mathematical Skills
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Definition of Numeracy
Numeracy is NOT LIMITED to the ability to use numbers, to add,
subtract, multiply and divide.
(Literacy and Numeracy for Learning and Life, DES 2011)
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Definition of Numeracy
Numeracy encompasses the ability to use mathematical understanding and skills to :• solve problems• meet the demands of day-to-day
living in complex social settings.
(Literacy and Numeracy for Learning and Life, DES 2011)
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Definition of Numeracy
Numeracy involves being able to:• Think and communicate quantitatively• Make sense of data• Have a spatial awareness• Understand patterns and sequences• Recognise situations where mathematical
reasoning can be applied to solve problems.
(Literacy and Numeracy for Learning and Life, DES 2011)
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In Summary...
Skills for Learning Skills for Work Skills for Life
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Numeracy Video
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What are the Issues concerning Numeracy?
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“Irish performance in mathematics in TIMSS (2011) is significantly above the international scale centre point of 500. However, results show that the percentage of Irish pupils reaching the Advanced Benchmark (9%) is lower than would be expected from overall Irish performance.” (Close 2013)
Of the mathematical content area subscales described, Ireland’s performance is best on the Uncertainty & Data subscale (508.7), followed by Quantity (505.2), Change & Relationships (501.1) and Space & Shape (477.8). (Perkins et al., 2013)
Male students have significantly higher mean print mathematics scores than females in Ireland (509.0 and 493.7, respectively) (Perkins et al. 2013)
About one quarter (26%) of adults in Ireland score at or below Level 1 on the numeracy scale compared to just 20% on average across participating countries. (CSO, 2013)
International Evidence
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Maths JC 2012 JC 2014 LC 2011 LC 2012 LC 2013 LC 2014
% % % % % %
Higher 48 54 16 22 26 27
Ordinary 45 40 72 67 63 62
Foundation 7 6 12 11 11 11
English JC JC LC 2011 LC 2012 LC 2013 LC 2014
Higher 72 75 64 65 65 67
Ordinary 26 23 36 35 35 33
Foundation 3 2
State Examinations 2014 Results
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Chief Inspector’s ReportIt is acknowledged that mathematics teaching must focus on skills and routine procedures if students’ understanding of, and their fluency in, Mathematics is to be developed. However, student disposition and commitment are equally important. This requires that the type of questions students encounter during school and homework be extended to include open-ended and multi-step questions. Students should be required to defend their reasoning as an integral part of the process. (Chief Inspector’s Report 2010-2012)
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SEC Chief Examiners’ Reports - Leaving CertificateChemistry OL 2013
‘Analysis demonstrated by candidates in text-based responses ranged from good to poor but the average performance in applications involving calculations or handling numerical data was weaker.’
Engineering (2011)‘Successful candidates gave structure to their answering
by, where appropriate, tabulating their answers, using bullet points to highlight and give emphasis, producing neat and accurate graphs, and using sketches and diagrams to illustrate their answers’
German (2010)‘A minority of candidates still have difficulty with number and letter
recognition in German, particularly numbers with a decimal point and the letters ‘e’ and ‘i’ ‘
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Geography 2012 OL ‘Poor and incorrect labelling of axes on the graph work was noted
both in the Geographical Investigation Report and in the written examination paper and identified as an area of weakness’
Construction Studies 2013 HL ‘The responses of such candidates tended to be brief and perfunctory
and did not provide sufficient analysis to achieve high marks. Again, the higher order skills of analysis, synthesis and evaluation proved challenging for the majority of candidates who attempted this question, resulting in a low average mark.’
Business 2013 Ordinary Level‘the graphical demands of some questions continue to pose challenges for some Ordinary level candidates’.
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Numeracy - Cross CurricularNumbers
Tim
eG
eom
etry
Percentages
Graphs
Distance
Patterns FractionsSpeed
Area
Co-ordinates
Measurement
SpaceEstimate
Circles
Simple Interest
Algebra
Charts
Logic
Volume
Addition
Proportion
Transformations
Dates
Angles
Weight
Translations
Scales Ratio
Statistics
Decim
als
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Place Mat Exercise
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Subject Planning
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Building Blocks of SSE
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Gather the evidence
Analyse the evidence
Draw conclusions
Write school self-evaluation report
Devise school improvement plan
Implement and monitor
improvement plan
The Six-Step Process
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The Teaching and Learning Quality Framework
33
Teaching & Learning
Learner outcomes
Learning experiences
Teachers’ practices
• Attainment of subject and programme objectives
• Learning environment
• Engagement in learning
• Learning to learn
• Preparation for teaching
• Teaching approaches
• Management of pupils
• Assessment
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Exploring the School Improvement Process
Workshop
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• What does the data tell us?
• What does the data not tell us?
• What else do we need to know?
Data AnalysisWorkshop
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Draw ConclusionsWorkshop
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Lunch
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Learner outcomes
Learning experiences
Teachers’ practices
Targets Actions
Teaching and Learning FrameworkWorkshop
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To increase the percentage of students who feel confident attempting problems that are difficult to solve from 30% to 60% over 3 years.
Sample Target
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Possible Actions
“Numeracy Moments”
Common Approaches
Mathematical Language
Estimate-Calculate-Check
Problem Solving Initiatives
Positive Attitude
Numeracy Rich Environment
Other
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Bloom’s Taxonomy of Critical Thinking
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Lateral Thinking Problemshttp://www.folj.com/lateral/
• You are driving down the road in your car on a wild, stormy night, when you pass by a bus stop and you see three people waiting for the bus:
1. An old friend who once saved your life.2. The perfect partner you have been dreaming of. 3. An old lady who looks like she is about to die.
Knowing that there can only be one passenger in the car, who would you choose?
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Where to next?
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• Establish/refine school structures to sustain improvement
• Explore ‘big picture’ numeracy• Consider possibilities for data gathering• Engage in data gathering• Engage in data analysis• Draw conclusions based on the evidence• Other?
Moving Forward…
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Resources
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School-Self EvaluationTeaching & Learning Framework; 6 Step SSE Process; gathering, collating & analysing relevant data; implementing the SIP for
literacy, numeracy and any other area of teaching & learning.
Assessment for Learning (AfL)Learning outcomes/context of learning/success criteria; effective feedback; questioning; Bloom’s Taxonomy and self & peer-assessment strategies e.g. rubrics.
Integrating ICTeAssessments & ePortfolios – Mahara, Google Apps for Education...ePlanning & Collaboration – Google Apps for Education.....Tablet Technology Integration – Effective use, pedagogy......Virtual Learning Environments (VLEs) – Google Classroom, EdmodoSSE – On-line tools for gathering, collating & analysing relevant dataVisual - Visualisers, Animoto, Wordle, Tagxedo, Photo-story....Auditory – Audacity, Vocaroo, Audioboo......Reading comprehension – Freerice, Studystack, Quizlet......Kinaesthetic – Tarzia, Cube Creator......
Subjects /Programmes & Generic SupportHealth & Wellbeing – PE, SPHE, mental health, anti-bullying and promoting the welfare & protection of studentsJunior & Leaving Certificate subject support & planningJCSP, TY, LCA & LCVP programme supportSchool planning (policies)Co-operative learningICT for teaching & learningDifferentiation/mixed ability teaching
PDST Websites
www.pdst.iepdsttechnologyineducation.iescoilnet.ie (portal for resources)teachercpd.ie (on-line courses)
PDST Leadership ProgrammesMisneach.....New PrincipalsTánaiste.......New Deputy PrincipalsTóraíocht.....Aspiring Leaders accredited by Maynooth UniversityForbairt .......Experienced Principals & ALNsSpreagadh...NAPD & PDST collaboration
Overview of PDST Post-Primary Supports for Leading Learning in the 21st Century
www.pdst.ie/schoolsupport
Models of support: whole staff days (circular 002/2014), Croke Park hours, subject departments/groups of teachers/co-ordinators (circular 0043/2014)It is essential to fill out the on-line application form @ www.pdst/schoolsupport in order for your application to be considered
NumeracySSE & strategies for implementing problem solving, estimation, a common approach to maths language and a numeracy rich environment across the curriculum.
Literacy SSE & strategies for improvingoral language, writing,reading comprehension, and the use of broadcast /digital media across the curriculum.
www.pdst.ie
The PDST is funded by the Teacher Education Section (TES) of the Department of Education and Skills (DES) and is managed
by Dublin West Education Centre
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