Mathematics Matters #MathsMatters

Sally Fulton & Carolyn Copstick,

Education Scotland Supporting schools, including through inspections: the

Scottish model

UK Government

Scottish Parliament

32Local Councils

KEY NATIONAL BODIES INVOLVED IN SCOTTISH EDUCATION

SCOTTISH GOVERNMENTFirst Minister

Cabinet Secretary for Education & Lifelong Learning

Education Scotlandformed 1 July 2011

from former HM Inspectorate & curriculum development agency

SCOTTISH PARLIAMENT

GENERAL GENERAL TEACHINGTEACHINGCOUNCILCOUNCIL

SCOTTISH QUALIFICATIONS

AUTHORITY

SCOTTISH FUNDING COUNCIL

EDUCATION AND OTHER SERVICES FOR CHILDREN IN SCOTLAND

SCOTTISH GOVERNMENT

43 COLLEGES

60 PRIMARY SCHOOLS53 SECONDARY SCHOOLS

42 SPECIAL SCHOOLSPRE-SCHOOL PROVISION

21 UNIVERSITIES/HIGHER

EDUCATION ESTABLISHMENTS

INDEPENDENT SECTOR2018 PRIMARY SCHOOLS

367 SECONDARY SCHOOLS158 SPECIAL SCHOOLS

PRE-SCHOOL PROVISIONPSYCHOLOGICAL SERVICES

COMMUNITY LEARNING and DEVELOPMENTOTHER SERVICES FOR CHILDREN

32 LOCAL AUTHORITIES

statistical information

Number of pupils 2010-11Primary – 366,429Secondary – 297,109Special schools – 6,973

Number of schoolsPrimary – 2,081Secondary – 367Special schools – 158

Education Scotland:a new agency

• Scottish Government’s national development and improvement agency for education charged with providing support and challenge to the education system, from the early years to adult learning came into existence on 1 July 2011

Bill MaxwellChief Executive

Our vision

• Scottish learners will progress in one of the most

effective education systems in the world,

renowned for the ability of national and local

partners to work flexibly together to achieve

high quality and equitable outcomes for

all.

Our mission

• We will provide the best blend of national support

and challenge to inspire and secure continuous

improvement in the opportunities all Scottish learners can access.

who are we?348 staff: •HM Inspectors •Senior Education Officers•Educational Development Officers •seconded teachers•corporate services colleagues

and also:•450 Associate Assessors •75 Lay Members• 6 Student Team Members

• The Scottish approach to educational improvement

CHARACTERISTICS OF QUALITY APPROACHES

external pressure

supportchallenge

quality control quality improvement

internal pressure

THE QUALITY INITIATIVE IN SCOTTISH SCHOOLS FUNDAMENTAL PRINCIPLE

• The most effective way of

improving the quality of education

is to expect schools to take responsibility for their own

quality improvement.

Standards in Scottish Schools 2000

• legal requirement for local authorities to provide education and ensure continuous improvement in their schools

• schools produce annual reports on the standards and quality of their work

A three-way partnership

• Schools evaluate the quality of their • own provision...

• supported and challenged by the • education authority…

• backed up by rigorous external • evaluation by HM Inspectors.

KEY BUILDING BLOCKS OF THE NATIONAL QUALITY IMPROVEMENT FRAMEWORK

• performance data – national data and support for its use in self-evaluation

• quality indicators – national framework with support for their use in self-evaluation

• a professional workforce of reflective practitioners

• independent, external inspection

SOURCES OF EVIDENCE

• performance/outcome data• surveys of pupils, parents and staff• interviews, focus groups, discussions• documentation: policies, plans, reports, course materials• direct observation of learning and teaching • pupils’ work

THREE BASIC QUESTIONS AT THE HEART OF SELF-EVALUATION

1. How are we doing?

2. How do we know?

3. What are we going to do now?

The key principle is one of continuous improvement based on a process of self-evaluation.

Ensuring continuous improvement in education and other services for children: the Scottish approach

A Framework for Evaluating the Quality of Services and Organisations

• The Child at the Centre (second edition) • How good is our school? (third edition) • How good is our community learning and development? (second edition) • How well are children and young people protected and their needs met?• Quality Management in Education (second edition)• Quality Management in Local Authority Educational Psychology Services 1. • HMIE quality framework for reference during the external review of Scotland’s colleges

ACCOUNTABILITY AT SCHOOL LEVEL

On an annual basis, each school:

• produces its own handbook and self-evaluation report

• produces a plan for improvement, including targets

BUT A WORD OF WARNING!

SELF-EVALUATION OR

SELF DELUSION?

Self-evaluation needs strong, independent external support and moderation to work well

INDEPENDENT EXTERNAL INSPECTIONBENEFITS

• authoritative accountability to parents, pupils, Ministers and the public

• strong evidence base for policy development

• building capacity for improvement

What happens at the end of the inspection?

 •Option 1 – no continuing engagement•Option 2 – additional support for improvement •Option 3 – further inspection•Option 4 – innovative practice

We INSPECT, REVIEW and REPORT on:

pre-school centres, primary, secondary and

special schools

community learning and development (CLD)

colleges (including language colleges from

August 2011)

aspects of teacher education

care and welfare of pupils [including

residential pupils]

the education functions of local councils

(validated self-evaluation VSE)

voluntary organisations

education in prisons

educational psychology services

• Education Scotland – Corporate Plan: launched September 2013

• Third strategic objective:

• Build the capacity of education providers to improve continuously their performance

• The cultural cycle of improvement

Scottish Curriculum- Numeracy

Numeracy•Estimation and rounding •Number and number processes•Fractions, decimal fractions and percentages•Money •Time •Measurement •Data and analysis•Ideas of chance and uncertainty

•Mathematics

Scottish Curriculum-Mathematics

Number Money Measure •Estimation and rounding •Number and number processes•Multiples, factors and primes•Powers and roots•Fraction, decimal fractions and percentages•Money•Time •Measurement •Mathematics – its impact on the world, past present and future •Patterns and relationships •Expressions and equations

Shape Position and movement•Properties of 2D shape and 3 D objects •Angle symmetry and transformation

Information Handling•Data and Analysis•Ideas of chance and uncertainty

Number, money and measure (continued)   Early First Second Third Fourth

 Fractions, decimal fractions and percentages including ratio and proportion  

 I can share out a group of items by making smaller groups and can split a whole object into smaller parts.

MNU 0-07a 

 Having explored fractions by taking part in practical activities, I can show my understanding of: how a single item can be shared equally ,the notation and vocabulary associated with fractions where simple fractions lie on the number line.

MNU 1-07a 

Through exploring how groups of items can be shared equally, I can find a fraction of an amount by applying my knowledge of division.

MNU 1-07b 

Through taking part in practical activities including use of pictorial representations, I can demonstrate my understanding of simple fractions which are equivalent.

MTH 1-07c 

 I have investigated the everyday contexts in which simple fractions, percentages or decimal fractions are used and can carry out the necessary calculations to solve related problems.

MNU 2-07a

I can show the equivalent forms of simple fractions, decimal fractions and percentages and can choose my preferred form when solving a problem, explaining my choice of method.

MNU 2-07b

 

 I can solve problems by carrying out calculations with a wide range of fractions, decimal fractions and percentages, using my answers to make comparisons and informed choices for real-life situations.

MNU 3-07a 

By applying my knowledge of equivalent fractions and common multiples, I can add and subtract commonly used fractions.

MTH 3-07b

Having used practical, pictorial and written methods to develop my understanding, I can convert between whole or mixed numbers and fractions.

MTH 3-07c 

 I can choose the most appropriate form of fractions, decimal fractions and percentages to use when making calculations mentally, in written form or using technology, then use my solutions to make comparisons, decisions and choices.

MNU 4-07a 

I can solve problems involving fractions and mixed numbers in context, using addition, subtraction or multiplication.

MTH 4-07b  

 

Specific support for mathematics and numeracy –

•Education Authority support •Additional support for schools•National Numeracy Network •Professional Learning Resource •Regional Events January to March 2013

What is the Scottish Survey of Literacy and Numeracy?

• National survey of numeracy

• Delivered in partnership, (EAs, SQA, ES, ADES)

• P4, P7, S2

• Alternate years literacy and numeracy› Numeracy 2011› Literacy 2012› Numeracy 2013

Scottish Survey of Literacy and Numeracy 2011 (Numeracy)

Highlights from the report:

•“ the vast majority of pupils said they enjoyed learning, though the strength of agreement reduced among older pupils. Over 90 per cent of pupils agreed that what they were learning would be useful to them outside school”

•“ The percentage of pupils not yet working within their respective levels in numeracy was less than 1% in P4, about 2% in P7 and about 32% in S2”

•“ Pupils were less likely to receive feedback on performance and improvement in S2 than in P4 and P7.”

Scottish Survey of Literacy and Numeracy 2011 (Numeracy)

• “ pupils were generally more successful with tasks assessing data and analysis and time. Tasks assessing measurement and fractions, decimal fractions and percentages were found to be more challenging for learners”

• “ Teachers reported high levels of confidence in delivering the Curriculum for Excellence (CfE) numeracy experiences, with generally over 95% of primary and secondary maths teachers confident or fairly confident. The one exception was the area of ideas of chance and uncertainty…”

Scottish Survey of Literacy and Numeracy ( Numeracy ) 2011

•The SSLN Numeracy 2011 survey reported that there are many strengths in children and young people’s performance within numeracy.

•The results from the SSLN numeracy survey highlighted the need to improve aspects of learning in the following numeracy organisers:

MeasurementFractions, decimal fractions and percentages (including ratio and proportion)

•Primary teachers and non-maths secondary teachers expressed a lack of confidence in delivering ‘ideas of chance and uncertainty’

Scottish Survey of Literacy and NumeracyProfessional Learning Resource ( Numeracy)

Professional learning materials provide:• guidance and advice to help inform

learning and teaching practices in line with the survey’s main objectives

• practitioners with more detail on children’s and young people’s strengths and areas for improvement identified within the in-depth analysis of the survey data

• opportunities for members of the learning community to engage in professional reflection, dialogue and debate about numeracy.

Authority level

Cluster level

School level

National level

SSLN Numeracy survey findings

National picture

Professional Learning Resource

Section 1 Introduction

•Setting the scene

•CPD presentation

Section 3Pupil Performance

•Pupil performance in measurement

•Pupil performance in fractions, decimal fractions and percentages (including

ratio and proportion)

•Ideas of chance and uncertainty

Section 2

Numeracy

• The place of numeracy within the curriculum

• Discrete and contextualised learning

• Word problems, real life problems and problem solving

• Links between attitudes and attainment

Big ideas we need to think about now?

A. Programmes of learning in mathematics and numeracy

B. Balance of discrete learning versus learning across the curriculum

C. Improving children and young people’s numeracy skills further

D. Progression pathways

Progression in Learning

Scottish Survey of Literacy and Numeracy 2011 (Numeracy) findings

60% of tasks, based on the measurement organiser, were answered correctly by P4 pupils.

52% of tasks, based on the measurement organiser, were answered correctly by P7 pupils.

36% of tasks based on the measurement organiser, answered correctly by S2 pupils.

Second First Third Fourth Early

P4Counting squares to measure area of irregular shapes

Using length, area and volume of one item to estimate the length area and volume of another

Reading a scale to measure length, volume and weight.

Measuring lengths and weights involving every-day objects, particularly when involving halves or quarters.

P7Relationship between area and perimeterCalculating volumes

Measuring and conversion of units, especially involving decimal fractions

Fractions, decimal fractions and percentages as a secondary organiser

S2Relationships between length, area and volume (including inverse operations)

Problem solving in context of length, perimeter, area and volume

Conversion of units for length, weight and volume

Fractions, decimal fractions and percentages as a secondary organiser

Progression in Measurement