Mathematics Matters #MathsMatters Sally Fulton & Carolyn Copstick, Education Scotland Supporting schools, including through inspections: the Scottish model

UK Government Scottish Parliament 32 Local Councils

KEY NATIONAL BODIES INVOLVED IN SCOTTISH EDUCATION SCOTTISH GOVERNMENT First Minister Cabinet Secretary for Education & Lifelong Learning Education Scotland formed 1 July 2011 from former HM Inspectorate & curriculum development agency SCOTTISH PARLIAMENT GENERALTEACHINGCOUNCIL SCOTTISH QUALIFICATIONS AUTHORITY SCOTTISH FUNDING COUNCIL

EDUCATION AND OTHER SERVICES FOR CHILDREN IN SCOTLAND SCOTTISH GOVERNMENT 43 COLLEGES 60 PRIMARY SCHOOLS 53 SECONDARY SCHOOLS 42 SPECIAL SCHOOLS PRE-SCHOOL PROVISION 21 UNIVERSITIES/ HIGHER EDUCATION ESTABLISHMENTS INDEPENDENT SECTOR 2018 PRIMARY SCHOOLS 367 SECONDARY SCHOOLS 158 SPECIAL SCHOOLS PRE-SCHOOL PROVISION PSYCHOLOGICAL SERVICES COMMUNITY LEARNING and DEVELOPMENT OTHER SERVICES FOR CHILDREN 32 LOCAL AUTHORITIES

statistical information Number of pupils Primary – 366,429 Secondary – 297,109 Special schools – 6,973 Number of schools Primary – 2,081 Secondary – 367 Special 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 Maxwell Chief 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 INSPECTION BENEFITS 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) EarlyFirstSecondThirdFourth 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:  Measurement  Fractions, 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 Numeracy Professional 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 3 Pupil 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 P4 Counting 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. P7 Relationship between area and perimeter Calculating volumes Measuring and conversion of units, especially involving decimal fractions Fractions, decimal fractions and percentages as a secondary organiser S2 Relationships 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