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New professional standards for teachers, tutors and trainers in the lifelong learning sector in Wales Application of the professional standards for teachers who develop learners’ skills in numeracy/number in the lifelong learning sector in Wales
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Contents Introduction
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Section 1: Elements
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Section 2: Elements and guidance on extent
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Lifelong Learning UK
Introduction The “New overarching professional standards for teachers, tutors and trainers in the lifelong learning sector in Wales”1 describe consistent performance for all teachers, in terms of knowledge, understanding and professional practice. This document applies those generic standards and describes consistent performance of teachers who develop learners’ skills in numeracy/number in particular, again in terms of knowledge, understanding and professional practice. In addition to this application document, LLUK has produced other application documents for: • teachers of English for Speakers of Other Languages
(ESOL) • teachers of Welsh for Adults • teachers who develop skills in literacy/communication
(English and/or Welsh) • teachers who teach bilingually or through the medium
of Welsh. The development of new professional standards for teachers, tutors and trainers in the lifelong learning sector in Wales In March 2007, the Welsh Assembly Government tasked Lifelong Learning UK (LLUK) to review the Standards for Teaching and Supporting Learning for Wales and England2. Whilst mindful of the need for cross border transferability, the review for Wales has presented the opportunity to develop standards for teachers to reflect the uniqueness of the context in Wales. The standards reflect the distinct needs of the sector in Wales and support the vision of “The Learning Country”3. The standards include ones relating specifically to bilingualism, cultural diversity and sustainable development and global citizenship. This enables the standards to meet the needs of Wales but also allows for articulation with the professional standards for teachers in England.
The definitive professional standards for teachers, tutors and trainers in the lifelong learning sector in Wales describe, in generic terms, the values, knowledge, understanding and professional practice required of those who perform the wide variety of teaching and training roles undertaken within the sector with learners and employers. The standards: • are context free and level free, in order to represent
all areas of work4 and new teachers, experienced teachers and teacher educators • represent the teaching and learning cycle, with which
all teachers engage: initial assessment, planning and preparation, teaching, assessment, evaluation and quality improvement through responding to evaluation. The development of application of the professional standards for teachers who develop learners’ skills in numeracy/number in the lifelong learning sector in Wales In February 2008, the Welsh Assembly Government tasked Lifelong Learning UK (LLUK) to develop an application of the professional standards for teachers who develop learners’ skills in numeracy/number in Wales. This application document has been developed to describe the consistent performance of these teachers, in terms of knowledge, understanding and professional practice. As with the generic standards for teachers, this application of the standards for teachers who develop learners’ skills in numeracy/number is context free and level free. It is for use in all constituencies and for new teachers, experienced teachers and teacher educators. It can be used for the whole range of purposes that standards are used for, including recruitment and selection, self assessment, and of course, all types of professional development. The document will be of value to teachers and managers, including those with responsibility for staff development and human resources. It will be of particular value for teacher educators in underpinning professional development opportunities. The knowledge, understanding and professional practice detailed in this document can inform the development of a wide range of accredited and unaccredited programmes for teachers of literacy/communication.
Lifelong Learning UK (LLUK) 2008 Further Education National Training Organisation 1999 The Learning Country: Vision into Action (2001) Welsh Assembly Government (WAG) 4 Including community learning and development, further education, higher education, libraries, archives and information services, and work based learning across the UK 1 2 3
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Introduction Personal skills in Mathematics
The application of the standards
The application of the professional standards for teachers who develop learners’ skills in numeracy/number details the knowledge, understanding and professional practice of these teachers. It does not detail required personal skills in Mathematics. Teachers who develop learners’ skills in numeracy/number should have the appropriate level of personal skills in Mathematics to teach effectively.
This document details the knowledge, understanding and professional practice required of teachers who develop learners’ skills in numeracy/number against the domains of the professional standards.
Use of terminology – numeracy/number This document details the knowledge, understanding and professional practice of all teachers who develop learners’ skills in numeracy/number. This will include, importantly, teachers of Numeracy (Basic Skills) and Number (Key Skills). The standards for Basic Skills and Key Skills are to be converged but the term to describe the converged standards is undecided at the time of writing (April 2008). In recognition of the important audience of this document, teachers of Basic and Key Skills, the term ‘numeracy/number’ has been used throughout the document. It is intended that when converged standards are named the title of this document will be reviewed.
Organisation of the document The new overarching professional standards for teachers, tutors and trainers in the lifelong learning sector in Wales detail the values, knowledge, understanding and professional practice expected of all teachers in the lifelong learning sector in Wales. This information is detailed in domains. The domains reflect the functions of the role. There are six domains:
Domain A: Professional values and practice Domain B: Learning and teaching Domain C: Specialist learning and teaching Domain D: Planning for learning Domain E: Assessment for learning Domain F: Access and progression
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An approach for developing the content of domains B and C had to be considered. In the generic standards, Domain B details teaching and learning in relation to all teachers. Domain C is concerned with a teacher’s area of specialism, whatever that may be. Developing an application of the professional standards for particular specialist teaching and learning, in this instance teachers who develop learners’ skills in numeracy/number, questioned the content of the two domains and how it would differ. After looking at the detail of the standards in domains B and C, the following approach was adopted: • professional practice, learning and teaching of
teachers who develop learners’ skills in numeracy/number to be detailed in Domain B • theory and knowledge related to developing learners’
skills in numeracy/number to be detailed in Domain C. These two domains should not be seen as sequential. Indeed, appropriate professional development programmes for teachers who develop learners’ skills in numeracy/number would be expected to deal with these aspects of knowledge, understanding and professional practice in a holistic fashion.
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Lifelong Learning UK
Within the domains, specific statements relating to knowledge or practice for teachers who develop learners’ skills in numeracy/number have been detailed against the value and commitment statements (What teachers value and what they are committed to). It was considered unnecessary and unhelpful to try to detail the application of every value and commitment statement for teachers who develop learners’ skills in numeracy/number. Some value and commitment statements are generic in every sense and little could usefully be added to make them subject specific. The commitment statements are coded by the letter of the domain and S for scope, for example, FS 2. All the value and commitment statements from the standards are included in this document. Where it was considered there was nothing specialist to add, this is made clear with the statement ‘Informed by professional standards only.’
Extent is provided as guidance on the associated content of each element. This extent is detailed in section two. The use of the terms element and extent has been supported through consultation. Those developing and delivering teacher education programmes will find it useful to consider this extent guidance when making any decision to include more or less than that detailed for any particular cohort of trainee teachers.
Statements relating to knowledge or practice are detailed throughout this document as elements. A comprehensive list of these can be found in section one of this document. They are coded with the domain letter and then in number sequence. A suffix, Nu, denotes an element in the application document. Elements have been written as areas of knowledge and practice for teachers who develop learners’ skills in numeracy/number. They detail the specific application for any value and commitment statement. The majority of commitment statements have one associated element, a few have a significant number of elements and some have none.
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Here is an example from Domain D Standard DS1
Element D1.1.Nu
Planning to promote equality, support diversity and to meet the aims and learning needs of learners
Apply knowledge of numeracy/number curriculum development to the planning process.
(This is a commitment statement from the professional standards)
(This is an element – this relates to knowledge or practice) Numeracy teachers know and understand: • theories and models of curriculum development and how to apply them • how to analyse the numeracy/number elements of a range of education programmes • how to plan, alone, or with colleagues, programmes which embed numeracy/number • how to plan effective programmes which incorporate opportunities to learn, practise, develop and accredit a range of appropriate transferable skills. (This is guidance on extent)
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Section 1: Elements
Teachers who develop learners’ skills in numeracy/number in the lifelong learning sector in Wales value:
Domain A: Professional values and practice
Standard AS1
Element A1.1 Nu
Learners, their progress and development, their learning goals and aspirations and the experience they bring to their learning
Take account of learners’ backgrounds, experience, goals and aspirations.
Standard AS2
Element A2.1 Nu
Learning, its potential to benefit people emotionally, intellectually, socially and economically, and its contribution to sustainable development in a community and global context
Make links between numeracy/number development and other areas of development.
Standard AS3
Element A3.1 Nu
Equality, diversity, inclusion and bilingualism in relation to learners, the workforce, and the community
Address particular issues in relation to diversity, inclusion and learners of numeracy/number.
Standard AS4
Element A4.1 Nu
Reflection and evaluation of their own practice and their continuing professional development as teachers
Engage in professional development relating to international, national and local research relating to numeracy/number.
Standard AS5
Element A5.1 Nu
Collaboration with other individuals, groups and/or organisations with a legitimate interest in the progress and development of learners
Collaborate with others to develop learners’ numeracy/number knowledge in a wide range of settings and contexts.
Teachers who develop learners’ skills in numeracy/number in the lifelong learning sector in Wales are committed to:
Standard AS6
Element A6.1 Nu
The application of the agreed codes of practice and the maintenance of a safe environment
Informed by professional standards only.
Standard AS7
Element A7.1 Nu
Improving the quality of their practice
Use approaches which develop the quality of numeracy/number learning and teaching across an organisation.
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Section 1: Elements
Teachers who develop learners’ skills in numeracy/number in the lifelong learning sector in Wales are committed to:
Domain B: Learning and teaching
Standard BS1
Element B1.1 Nu
Maintaining an inclusive, equitable, motivating and, where appropriate, bilingual learning environment
Recognise the effects of learner backgrounds on feelings about numeracy/number and foster positive self-images as independent learners.
Standard BS2
Element B2.1 Nu
Applying and developing own professional skills to enable learners to achieve their goals
Create an environment where learners feel valued as members of a community.
Element B2.2 Nu Use subject knowledge to adopt appropriate approaches to numeracy/number teaching.
Element B2.3 Nu Use specialist pedagogical knowledge to adopt appropriate learning and teaching strategies for numeracy/number.
Element B2.4 Nu Employ specialist pedagogical knowledge to support a wide range of learners’ needs in numeracy/number.
Standard BS3
Element B3.1 Nu
Communicating effectively and appropriately with learners to enhance learning
Enable learners to develop appropriate specialist numeracy/number language.
Element B3.2 Nu Use a wide range of communication strategies to support conceptual understanding in numeracy/number.
Element B3.3 Nu Facilitate appropriate learner-teacher and learner-learner interaction in order to support learning.
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Standard BS4
Element B4.1 Nu
Collaborating with colleagues to support the needs of learners
Work with teachers of other subjects where numeracy/number is embedded to identify relevant numeracy/number and other transferable skills, and plan how to develop these in context.
Standard BS5
Element B5.1 Nu
Using a range of learning resources to support learners
Use specialist knowledge and awareness of learner needs and goals to select, develop and use appropriate resources for numeracy/number learning, including new and emerging technologies where appropriate.
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Teachers who develop learners’ skills in numeracy/number in the lifelong learning sector in Wales are committed to:
Domain C: Specialist learning and teaching
Standard CS1
Element C1.1 Nu
Own specialist area including current development
Develop own knowledge and understanding of the development of numeracy/number across cultures and through time.
Element C1.2 Nu Develop own knowledge and understanding of the language and concepts associated with place value systems.
Element C1.3 Nu Develop own knowledge and understanding of the nature of argument and proof in number.
Element C1.4 Nu Develop own knowledge and understanding of how to critically gather, use, process, interpret and display data.
Element C1.5 Nu Develop own knowledge and understanding of a wide range of ways of defining or representing different concepts in numeracy/number.
Element C1.6 Nu Develop own knowledge and understanding of a range of common numeracy/number learner errors and misconceptions; possible reasons why they occur and approaches for addressing them.
Element C1.7 Nu Develop own knowledge and understanding of a wide range of mental, written and diagrammatic strategies that can inform their understanding and practice.
Element C1.8 Nu Develop own knowledge and understanding of the activities, processes and stages within mathematical problem solving /application.
Element C1.9 Nu Develop own knowledge and understanding of how context may determine the approach used for mathematical problem solving or investigation.
Element C1.10 Nu Develop own knowledge and understanding of a range of connections between areas in numeracy/number.
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Section 1: Elements
Element C1.11 Nu Develop an understanding of the origins and status of mathematical knowledge and the effect on curriculum development.
Standard CS2
Element C2.1 Nu
Enthusing and motivating learners in own specialist area
Understand the roles of numeracy/number in the world at large.
Element C2.2 Nu Develop own knowledge and understanding of public/popular perceptions of numeracy/number and consider their impact on learner motivation.
Element C2.3 Nu Demonstrate specialist knowledge of appropriate strategies that engage and enthuse learners in numeracy/number.
Standard CS3
Element C3.1 Nu
Fulfilling the statutory responsibilities associated with own specialist area of teaching
Develop knowledge and understanding of a range of learning and teaching theories and strategies, relevant to numeracy/number, in order to apply them to practice.
Element C3.2 Nu Develop knowledge of the effects of learner backgrounds and needs on numeracy/number learning.
Element C3.3 Nu Use understanding of the different ways in which language and literacy skills are integral to learners’ achievement, in numeracy/number, to address the development of these skills.
Element C3.4 Nu Use of communication to promote and develop conceptual understanding of numeracy/number via collaborative tasks and sharing of strategies.
Standard CS4
Element C4.1 Nu
Developing good practice in teaching own specialist area
Use specialist organisations and publications to develop own practice as a numeracy/number (numeracy) teacher.
Element C4.2 Nu Access subject specific training and development opportunities, using a reflective continuing professional development cycle to critically select such opportunities.
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Teachers who develop learners’ skills in numeracy/number in the lifelong learning sector in Wales are committed to:
Domain D: Planning for learning
Standard DS1
Element D1.1 Nu
Planning to promote equality, support diversity and to meet the aims and learning needs of learners
Apply knowledge of numeracy/number curriculum development to the planning process.
Element D1.2 Nu Apply theoretical and practical numeracy/number knowledge to the planning of learning and teaching.
Standard DS2
Element D2.1 Nu
Learner participation in the planning of learning
Apply knowledge of the learners to the planning process.
Standard DS3
Element D3.1 Nu
Evaluation of own effectiveness in planning learning
Employ strategies to evaluate numeracy/number learning and teaching.
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Section 1: Elements
Teachers who develop learners’ skills in numeracy/number in the lifelong learning sector in Wales are committed to:
Domain E: Assessment for learning
Standard ES1
Element E1.1 Nu
Designing and using assessment as a tool for learning and progression
Develop knowledge of the types of skills, knowledge and understanding that can be assessed in numeracy/number and use these to select or design appropriate assessment tools.
Standard ES2
Element E2.1 Nu
Assessing the work of learners in a fair and equitable manner
Recognise that learners can have a wide variety of mathematical/numeracy skills, knowledge and understanding.
Element E2.2 Nu Develop awareness of the differences that learner backgrounds can make with regard to approaches to numeracy/number assessment.
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Standard ES3
Element E3.1 Nu
Learner involvement and shared responsibility in the assessment process
Develop strategies to involve learners in their own numeracy/number assessment.
Standard ES4
Element E4.1 Nu
Using feedback as a tool for learning and progression
Apply specialist knowledge of assessment and feedback for mathematical/numeracy learning to develop learner skills, knowledge and understanding in the subject.
Standard ES5
Element E5.1 Nu
Working with the systems and quality requirements of the organisation in relation to assessment and monitoring of learner progress
Record relevant information about the mathematical/numeracy skills, knowledge and understanding of learners in order to progress learning.
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Teachers who develop learners’ skills in numeracy/number in the lifelong learning sector in Wales are committed to:
Domain F: Access and progression
Standard FS1
Element F1.1 Nu
Encouraging learners to seek initial and further learning opportunities and to use services within the organisation
Signpost learners of numeracy/number to specialist support services, learning or progression opportunities.
Standard FS2
Element F2.1 Nu
Providing support for learners within the boundaries of the teacher role
Identify the boundaries between their own specialist areas and those of other specialists.
Standard FS3
Element F3.1 Nu
Maintaining own professional knowledge in order to provide information on opportunities for progression in own specialist area
Maintain professional knowledge in relation to progression opportunities for learners of numeracy/number.
Standard FS4
Element F4.1 Nu
A multi-agency approach to supporting development and progression opportunities for learners
Develop relationships with a range of specialist services, agencies and professionals for learners of numeracy/number.
The document will be of value to teachers and managers, including those with responsibility for staff development and human resources.
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Section 2: Elements and guidance on extent
Teachers who develop learners’ skills in numeracy/number in the lifelong learning sector in Wales value:
Domain A: Professional values and practice
Standard AS1
Element A1.1 Nu
Learners, their progress and development, their learning goals and aspirations and the experience they bring to their learning
Take account of learners’ backgrounds, experience, goals and aspirations Numeracy/number teachers know and understand: • the nature of numeracy/number learning, and the need to support learners’ own ability to work independently • the importance of identifying and drawing upon the range of skills, experiences, expertise, goals and other subject areas which interest and motivate learners. Numeracy/number teachers: • Apply their understanding of learners’ backgrounds, experiences, goals and aspirations to supporting their development and progression in numeracy/number.
Standard AS2
Element A2.1 Nu
Learning, its potential to benefit people emotionally, intellectually, socially and economically, and its contribution to sustainable development in a community and global context
Make links between numeracy/number development and other areas of development Numeracy/number teachers know and understand: • the importance of supporting learners in making links between the development of their numeracy/number skills and other areas of importance to them, including vocational, economic and global contexts • why learners benefit from reflecting on ways numeracy/number development can empower them as individuals and positively influence their role within and outside the community. Numeracy/number teachers: • apply this knowledge and understanding in their practice.
Standard AS3
Element A3.1 Nu
Equality, diversity, inclusion and bilingualism in relation to learners, the workforce, and the community
Address particular issues in relation to diversity, inclusion and learners of numeracy/number Numeracy/number teachers know and understand: • the range and diversity of learners’ numeracy/number practices and how to help develop these • the personal, emotional, social, economic and cultural factors which may affect the learning, development and progression of learners. • the potential impact and implications of physical disabilities, sensory impairment and mental health issues for learners of numeracy/number • current definitions of dyslexia, dyscalculia and related conditions, and strategies for supporting learners with these particular needs. Numeracy/number teachers: • apply this knowledge and understanding in their practice.
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Standard AS4
Element A4.1 Nu
Reflection and evaluation of their own practice and their continuing professional development as teachers
Engage in professional development relating to international, national and local research relating to numeracy/number Numeracy/number teachers know and understand: • how research into numeracy/number, together with teachers’ and learners’ own insights, can inform learning and teaching and their own practice • the relationships between numeracy/number policies and initiatives, learning and teaching, and their own practice. Numeracy/number teachers: • reflect on research to inform classroom management and share good practice.
Standard AS5
Element A5.1 Nu
Collaboration with other individuals, groups and/or organisations with a legitimate interest in the progress and development of learners
Collaborate with others to develop learners’ numeracy/number knowledge in a wide range of settings and contexts Numeracy/number teachers know and understand: • how organisational policies can influence numeracy/number practices • the importance of contributing to the development of the organisation’s policies and practices relating to numeracy/number and language • how collaboration with others can support cross disciplinary approaches to numeracy/number development. Numeracy/number teachers:
Teachers who develop learners’ skills in numeracy/number in the lifelong learning sector in Wales are committed to:
• collaborate with colleagues to use numeracy/number and other subject specialist knowledge to develop learners’ numeracy/number.
Standard AS6
Element A6.1 Nu
The application of the agreed codes of practice and the maintenance of a safe environment
Informed by professional standards only
Standard AS7
Element A7.1 Nu
Improving the quality of their practice
Use approaches which develop the quality of numeracy/number learning and teaching across an organisation Numeracy/number teachers know and understand: • how numeracy/number practices are situated within organisational policy, planning and implementation processes and practice. Numeracy/number teachers: • evaluate their own contribution to the development of the organisation’s policies and practices relating to numeracy/number.
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Section 2: Elements and guidance on extent
Teachers who develop learners’ skills in numeracy/number in the lifelong learning sector in Wales are committed to:
Domain B: Learning and teaching
Standard BS1
Element B1.1 Nu
Maintaining an inclusive, equitable, motivating and, where appropriate, bilingual learning environment
Recognise the effects of learner backgrounds on feelings about numeracy/number and foster positive self-images as independent learners Numeracy/number teachers: • use strategies to overcome the effects of numeracy/number anxiety in learners • value learners’ existing strategies for using numeracy/number in their own lives and provide opportunities to build on this • use strategies to encourage learner motivation, independence and aspirations, for example, self-selection of tasks, opportunities to uncover facts for themselves, learner experimentation with and evaluation of different numeracy/number methods.
Standard BS2
Element B2.1 Nu
Applying and developing own professional skills to enable learners to achieve their goals
Create an environment where learners feel valued as members of a learning community Numeracy/number teachers: • recognise the possible effects of prior experiences (both positive and negative) of mathematics learning and facilitate a culture where learners are confident about asking questions and discussing methods and solutions with other learners • develop an ethos of mutual support and encouragement so that learners do not feel ‘judged’ by their peers in terms of their numeracy/number learning • create an environment where learners are comfortable about making mistakes, and see and use these as an opportunity for further learning • manage group tasks so that participants recognise that interacting with others can enhance numeracy/number learning and understanding.
Element B2.2 Nu Use subject knowledge to adopt appropriate approaches to numeracy/number teaching Numeracy/number teachers: • employ appropriate approaches to developing learners’ understanding of concepts in order to meet specified learning outcomes, for example to develop learners’ ability judge which method of presenting information is appropriate to the context, such as whether to present 50% as a proportion (50 out of every 100) or a fraction (1/2) • facilitate deeper understanding of the connections within and between different areas of the numeracy/number curriculum and other contexts and subjects.
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Element B2.3 Nu Use specialist pedagogical knowledge to adopt appropriate learning and teaching strategies for numeracy/number Numeracy/number teachers: • use knowledge of theories of teaching and learning and own experience to select and use teaching strategies that address learner needs, goals and contexts • use learning and teaching strategies designed to engage and motivate learners of numeracy/number, taking account of their previous experiences (positive and negative) of numeracy/number learning • use learning and teaching strategies to promote learner independence in numeracy/number recognising that mathematics education is often perceived as teacher-centred.
Element B2.4 Nu Employ specialist pedagogical knowledge to support a wide range of learners’ needs in numeracy/number Numeracy/number teachers: • use specialist knowledge to differentiate and support numeracy/number learning and teaching activities in order to make them more accessible for learners, for example, concrete experimentation, in order to develop conceptual understanding, in addition to paper and pencil methods • use specialist knowledge to extend numeracy/number activities for learners where they would benefit from developing their skills and understanding further, for example, using open ended tasks such as ‘How many different ways are there to do this?’ • incorporate opportunities for learners to justify their statements and conclusions • identify and use strategies for addressing individual needs in numeracy/number and engaging all learners to take a full part in sessions, for example, language and literacy needs, global and specific learning difficulties, physical disabilities or mental health issues.
Standard BS3
Element B3.1 Nu
Communicating effectively and appropriately with learners to enhance learning
Enable learners to develop appropriate specialist numeracy/number language Numeracy/number teachers: • identify and use strategies for encouraging the active use of numeracyrelated vocabulary by learners • identify sources of linguistic confusion in numeracy/number and adopt strategies to address these where appropriate.
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Section 2: Elements and guidance on extent
Element B3.2 Nu Use a wide range of communication strategies to support conceptual understanding in numeracy/number Numeracy/number teachers: • use strategies such as discussion or question and answer to develop understanding, modifying language according to audience, employing techniques that address the needs of learners • facilitate deeper understanding by appropriate use of open extended dialogue and higher order questions • use a wide range of non-verbal strategies to support conceptual understanding in numeracy/number, including the use of: diagrams, animation, colour, primary or secondary data collected by the learner, physical models, physical movement and multimedia approaches • use specialist knowledge to adapt written texts to appropriate levels, with minimum compromise of meaning or accuracy, including using multimedia, non-verbal communication or visual aids to support learner understanding.
Element B3.3 Nu Facilitate appropriate learner-teacher and learner-learner interaction in order to support learning Numeracy teachers: • use skilfully framed open and closed, oral and written questions to elicit answers from which learners’ numeracy/number understanding can be judged, and use this information to take learning forward • use a range of strategies to encourage collaborative learning of numeracy/number, where appropriate drawing on specialist research and/or resources • use tasks to promote discussion and develop the conceptual understanding and critical thinking skills of learners, for example, focusing on interpretation of data as well as extraction of numerical information.
Standard BS4
Element B4.1 Nu
Collaborating with colleagues to support the needs of learners
Work with teachers of other subjects where numeracy/number is embedded to identify relevant numeracy/number and other transferable skills, and plan how to develop these in context Numeracy/number teachers: • design, adapt or select appropriate, authentic activities in collaboration with colleagues in other areas to introduce and develop the numeracy/number skills and knowledge needed in particular contexts • collaborate with colleagues to identify opportunities where other transferable skills can be learnt, practised, developed or accredited through a numeracy/number context.
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Standard BS5
Element B5.1 Nu
Using a range of learning resources to support learners
Use specialist knowledge and awareness of learner needs and goals to select, develop and use appropriate resources for numeracy/number learning, including new and emerging technologies where appropriate Numeracy/number teachers: • design, adapt, select and use resources from an appropriate range that promote factual knowledge, develop conceptual understanding and/or enable practice of skills relating to numeracy/number • use new and emerging technologies appropriately to create resources for numeracy/number • select and use appropriate specialist equipment for numeracy/number learning and teaching, for example, measuring instruments, physical models, calculating aids, etc • adapt the mathematical content of numeracy/number learning and teaching resources as appropriate for particular groups or individuals, either by simplification or extension • use ICT and e-learning resources appropriately, to promote engagement with tasks and activities.
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Section 2: Elements and guidance on extent
Teachers who develop learners’ skills in numeracy/number in the lifelong learning sector in Wales are committed to:
Domain C: Specialist learning and teaching
Standard CS1
Element C1.1 Nu
Own specialist area including current development
Develop own knowledge and understanding of the development of mathematics Numeracy/number teachers know and understand: • number system development • measuring systems development • recording and processing of data development.
Element C1.2 Nu Develop own knowledge and understanding of the language and concepts associated with place value systems Numeracy/number teachers know and understand: • other number bases • simple calculations in other number bases • standard form.
Element C1.3 Nu Develop own knowledge and understanding of the nature of argument and proof Numeracy/number teachers know and understand: • the language of proof • how algebra can be used to create a generalised statement which can be manipulated to solve problems in everyday situations.
Element C1.4 Nu Develop own knowledge and understanding of how to critically gather, use, process, interpret and display data Numeracy/number teachers know and understand: • strategies for data collection • the influence of sample size and data character (e.g. discrete, continuous or grouped) • the choice and use of data processing techniques • representation and misrepresentation of data and its analysis.
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Element C1.5 Nu Develop own knowledge and understanding of a wide range of ways of defining or representing different concepts in numeracy/number Numeracy/number teachers know and understand: • different ways of explaining common mathematical concepts • higher level mathematics which can be used to support the development of mathematical understanding in learners at lower levels.
Element C1.6 Nu Develop own knowledge and understanding of a range of common numeracy/number learner errors and misconceptions, possible reasons why they occur and approaches for addressing them Numeracy/number teachers know and understand: • common errors and misconceptions in mathematical concepts and processes and ways of addressing these.
Element C1.7 Nu Develop own knowledge and understanding of a wide range of mental, written and diagrammatic strategies that can inform their understanding and practice Numeracy/number teachers know and understand: • a wide range of mental, written and diagrammatic strategies • the language used to describe and analyse these strategies, for example, decomposition and partitioning • the use of coping strategies might affect the efficiency of future learning.
Element C1.8 Nu Develop own knowledge and understanding of the activities, processes and stages within mathematical problem solving application Numeracy/number teachers know and understand: • the role and purpose of mathematical thinking skills including: –
exploring
–
planning
–
generalising
–
sorting
–
hypothesising
–
modelling
–
testing
–
adjusting/remodelling
–
reporting
–
representing
–
interpreting.
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Section 2: Elements and guidance on extent
Element C1.9 Nu Develop own knowledge and understanding of how context may determine the approach used for mathematical problem solving or investigation Numeracy/number teachers know and understand: • the role and implications of estimation and accuracy across the stages of calculation • how the choice of mathematical methods may be influenced by context • use of shortcuts, diagrams, practical experimentation • the interpretation and reporting of solutions.
Element C1.10 Nu Develop own knowledge and understanding of a range of connections between areas in numeracy/number Numeracy/number teachers know and understand • that skills learned in one area of numeracy/number can be transferred and applied in another, eg the role of calculations in the analysis of data; place value in the measurement system; graphical representations of algebraic relationships • that certain methods and mathematical procedures may suit particular applications and why they may not suit others.
Element C1.11 Nu Develop an understanding of the origins and status of mathematical knowledge and the effect on curriculum development Numeracy/number teachers know and understand: • the notions of ‘context’ and ‘embedding’ in relation to numeracy/number learning • different theories on how maths could be taught and learnt • policy developments and initiatives relating to maths and numeracy/number curriculum development and accreditation • the relationships between mathematics and culture • the impact of mathematics registers, for example, formal, scientific and street.
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Standard CS2
Element C2.1 Nu
Enthusing and motivating learners in own specialist area
Understand the roles of numeracy/number in the world at large Numeracy/number teachers know and understand: • the use of numeracy/number in everyday life • the use of numeracy/number in a range of vocational and work-related contexts • the use of numeracy/number in informing decision making such as the use of statistics in communicating ideas and messages for example in advertising, business or government initiatives • that numeracy/number skills may impact on employment, health, participation in the community and other aspects of life • that good numeracy/number skills can enhance other learning and improve career development.
Element C2.2 Nu Develop own knowledge and understanding of public/popular perceptions of numeracy/number and consider their impact on learner motivation Numeracy/number teachers know and understand: • how the nature of maths related anxiety in individuals will impact on their learning • that learners will have different motivations for improving their numeracy/number.
Element C2.3 Nu Demonstrate specialist knowledge of appropriate strategies that engage and enthuse learners in numeracy/number Numeracy/number teachers know and understand • how to build confidence in learners, for example, valuing prior learning and experience, breaking down tasks into appropriate steps in order to create opportunities for success or by giving learners appropriate challenges • how to use a range of approaches to problem solving in numeracy/number to address a variety of preferred ways of learning • the effects of teacher confidence and enthusiasm in motivating learners • the benefits of embedding mathematical learning into other subjects.
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Section 2: Elements and guidance on extent
Standard CS3
Element C3.1 Nu
Fulfilling the statutory responsibilities associated with own specialist area of teaching
Develop knowledge and understanding of a range of learning and teaching theories and strategies, relevant to numeracy/number, in order to apply them to practice Numeracy/number teachers know and understand: • a wide range of ways in which generic teaching and learning techniques may be applied to numeracy/number teaching • that numeracy/number learning, teaching strategies and activities may be analysed in terms of a range of theories of learning • the need to write and regularly use individual learning plans that are appropriate to the needs of the learner • the rationale for encouraging learners to develop numeracy/number knowledge in familiar contexts • a range of teaching and learning techniques that will encourage learners to develop mathematical thinking • that effective questioning facilitates the development of numeracy/number skills knowledge and understanding • theories and research into assessment and its importance in learner development • the role of developing experiential problem solving in relevant practical situations to extend numeracy/number skills, knowledge and understanding and promote ownership of relevant learning • the debates around what constitutes ‘good’ or ‘effective practice’ in numeracy/number • the debates around models of learning styles and their application to learning • the theories and research behind using group work for the development of numeracy/number skills, knowledge and understanding and how some learners may need support in this area.
Element C3.2 Nu Develop knowledge of the effects of learner backgrounds and needs on numeracy/number learning Numeracy/number teachers know and understand: • the possible effects of social and educational background, gender, culture, age and personal circumstances on numeracy/number learning and a range of strategies for responding to these • the possible effects of physical disabilities, mental health issues, dyslexia, literacy needs and learning difficulties on numeracy/number development and a range of strategies for responding to these • research into the relationship between dyslexia and numeracy/number development • the developing notions of dyscalculia, related research and strategies for responding to these.
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Element C3.3 Nu Use understanding of the different ways in which language and literacy skills are integral to learners’ achievement, in numeracy/number, to address the development of these skills Numeracy/number teachers know and understand: • that a learner’s lack of literacy or English/Welsh language skills will affect their acquisition of mathematical knowledge • how to communicate with learners using the language of mathematics • that some words can have a specific meaning within a mathematical context which may be different from their everyday language meaning (eg product, mean etc).
Element C3.4 Nu Use of communication to promote and develop conceptual understanding of numeracy/number via collaborative tasks and sharing of strategies Numeracy/number teachers know and understand: • that learners may develop their knowledge of mathematical concepts through discussion in paired or group work and with peer support.
Standard CS4
Element C4.1 Nu
Developing good practice in teaching own specialist area
Use specialist organisations and publications to develop own practice as a numeracy/number teacher Numeracy/number teachers know and understand: • the importance of reading and researching their subject in order to keep abreast of theoretical thinking and practical developments • the need to collaborate with specialist colleagues or other networks to facilitate professional development • the importance of accessing a range of professional organisations to support development.
Element C4.2 Nu Access subject specific training and development opportunities, using a reflective continuing professional development cycle to critically select such opportunities Numeracy/number teachers know and understand: • the need to take up further training opportunities to develop own mathematical knowledge as well as knowledge and skills of teaching • how to self-evaluate in order to continuously develop own practice.
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Section 2: Elements and guidance on extent
Teachers who develop learners’ skills in numeracy/number in the lifelong learning sector in Wales are committed to:
Domain D: Planning for learning
Standard DS1
Element D1.1 Nu
Planning to promote equality, support diversity and to meet the aims and learning needs of learners
Apply knowledge of numeracy/number curriculum development to the planning process Numeracy/number teachers know and understand: • theories and models of curriculum development and how to apply them • how to analyse the numeracy/number elements of a range of education programmes • how to plan, alone, or with colleagues, programmes which embed numeracy/number • how to plan effective programmes which incorporate opportunities to learn, practise, develop and accredit a range of appropriate transferable skills.
Element D1.2 Nu Apply theoretical and practical numeracy/number knowledge to the planning of learning and teaching Numeracy/number teachers know and understand: • the importance of having an overview of a range of relevant factors (eg age and experience of the learners, disabilities, cultural factors, specific learning needs, prior achievements, language or literacy needs) when planning a programme of learning • how to plan coherent programmes of learning which incorporate and balance a range of elements, including: development of numeracy/number, study and other transferable skills; relevant curricula and standards, awards and assessment requirements • how to use learner interests, contexts and experiences and other programmes of learning to inform the planning of numeracy/number learning and teaching.
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Standard DS2
Element D2.1 Nu
Learner participation in the planning of learning
Apply knowledge of the learners to the planning process Numeracy/number teachers know and understand: • the importance of dialogue with learners during the planning of learning and teaching, which involves: –
using accessible language to discuss and negotiate learning programmes
–
understanding that previous educational experiences might affect learners’ expectations of how much input and control they can have in a learning programme
–
agreeing relevant learning goals with learners based on personal aims, assessment results and curriculum requirements
• how to develop participatory and inclusive approaches to learning and select appropriate strategies for supporting a range of needs within a group.
Standard DS3
Element D3.1 Nu
Evaluation of own effectiveness in planning learning
Employ strategies to evaluate numeracy/number learning and teaching Numeracy/number teachers know and understand: • how to evaluate and analyse numeracy/number activities from theoretical and practical perspectives, using a range of methods (eg in terms of what was learned, using the outcomes of assessment, using learner feedback, using feedback from colleagues) • use appropriate general and numeracy-related learning theories to inform the planning of further teaching, learning and assessment activities.
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Section 2: Elements and guidance on extent
Teachers who develop learners’ skills in numeracy/number in the lifelong learning sector in Wales are committed to:
Domain E: Assessment for learning
Standard ES1
Element E1.1 Nu
Designing and using assessment as a tool for learning and progression
Develop knowledge of the types of skills, knowledge and understanding that can be assessed in numeracy/number and use these to select or design appropriate assessment tools Numeracy/number teachers know and understand: • that assessment should cover the range of skills and applications required by the numeracy/number learner • that the knowledge and understanding and ability to use numeracy/number skills can vary over time for individual learners if they are not used regularly, and that this can affect assessment results • that assessment in numeracy/number should include information about the whole learner, including previous learning experiences, personal contexts and goals • the ways in which information from assessment can feed into planning for numeracy/number learning and teaching • the advantages and disadvantages of the different types of methods of assessment that can be used in numeracy • that the character and purpose of assessment, including initial, diagnostic, formative or summative influences the nature of numeracy/number assessment activities. Numeracy/number teachers: • select, design, use and evaluate assessment tools that are appropriate to the context of the learner and mathematical purpose of the assessment.
Standard ES2
Element E2.1 Nu
Assessing the work of learners in a fair and equitable manner
Recognise that learners can have a wide variety of mathematical/numeracy skills, knowledge and understanding. Numeracy/number teachers know and understand: • individuals’ strengths in skills, knowledge and understanding in numeracy/number may not be uniform across the curriculum (i.e. they may have a spiky profile). Numeracy/number teachers: • assess learners across a range of types of skills, knowledge and understanding in numeracy/number (for example, problem-solving, mental approaches or measuring skills, as well as recall of multiplication facts) in order to ascertain what learners can do as well as what they cannot do.
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Element E2.2 Nu Develop awareness of the differences that learner backgrounds can make with regard to approaches to numeracy/number assessment Numeracy/number teachers know and understand: • learners’ differing cultural and social backgrounds must be taken into account in assessment • the types of issues that learners with physical disabilities, mental health issues, learning difficulties and literacy needs may have with assessment in numeracy/number, including the selection of appropriate tools • the need to be sensitive to previous learning experiences when carrying out assessment. Numeracy/number teachers: • conduct an assessment in a fair and inclusive manner, with due regard to validity and reliability.
Standard ES3
Element E3.1 Nu
Learner involvement and shared responsibility in the assessment process
Develop strategies to involve learners in their own numeracy/number assessment Numeracy/number teachers know and understand: • that learners’ previous experience of assessment may affect their current attitudes to it • that learners will gain by being encouraged to make use of errors in their own and the work of others as opportunities for further learning • how and when to facilitate learner reflection on the process of learning numeracy/number skills. Numeracy/number teachers: • encourage learners to participate in assessing their needs and progress, and check their own work using a range of strategies • value learner methods of problem solving in numeracy/number and encourage reflection and evaluation of alternative strategies.
Standard ES4
Element E4.1 Nu
Using feedback as a tool for learning and progression
Apply specialist knowledge of assessment and feedback for mathematical/numeracy learning to develop learner skills, knowledge and understanding in the subject Numeracy/number teachers know and understand: • that assessment is more than testing but includes the consideration of methods and observation of learner practice. Numeracy/number teachers: • use effective questioning and constructive feedback to enable learners to self correct and help diagnose misconceptions.
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Section 2: Elements and guidance on extent
Standard ES5
Element E5.1 Nu
Working with the systems and quality requirements of the organisation in relation to assessment and monitoring of learner progress
Record relevant information about the mathematical/numeracy skills, knowledge and understanding of learners in order to progress learning Numeracy/number teachers know and understand: • how to record appropriately, the progress in numeracy/number with regard to content and process skills, knowledge and understanding and personal attitudes • the need to record, e.g. in the form of an individual learning plan (ILP), the skills, knowledge and understanding required by the learner in order to progress. Numeracy/number teachers: • develop systems for recording learner progress in numeracy, such as an ILP, which take into account the complex nature of numeracy/number learning and inform the learner, the teacher and the institution.
Teachers who develop learners’ skills in numeracy/number in the lifelong learning sector in Wales are committed to:
Domain F: Access and progression
Standard FS1
Element F1.1 Nu
Encouraging learners to seek initial and further learning opportunities and to use services within the organisation
Signpost learners of numeracy/number to specialist support services, learning or progression opportunities Numeracy/number teachers know and understand: • how to identify, use and refer learners to sources of specialist information, support, advice and guidance relating to numeracy/number • how to help learners develop the language and numeracy/number skills needed to research and use the organisation’s services, and also those outside the organisation • how to identify statutory entitlements to learning and personal support for learners along with the procedures in place to access them • how to act appropriately as advocates for learners of numeracy/number.
Standard FS2
Element F2.1 Nu
Providing support for learners within the boundaries of the teacher role
Identify the boundaries between their own specialist areas and those of other specialists Numeracy/number teachers know and understand: • the boundaries between their own specialist area and those of other specialists (eg specialists in learning disabilities, Welsh for Adults, ESOL, literacy, educational psychologists or other specialists) • developments within the numeracy/number teaching profession, and related fields.
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Standard FS3
Element F3.1 Nu
Maintaining own professional knowledge in order to provide information on opportunities for progression in own specialist area
Maintain professional knowledge in relation to progression opportunities for learners of numeracy/number Numeracy/number teachers know and understand: • how to provide accurate and current information to learners on the place of numeracy/number in potential progression routes for education, training and/or career.
Standard FS4
Element F4.1 Nu
A multi-agency approach to supporting development and progression opportunities for learners
Develop relationships with a range of specialist services, agencies and professionals for learners of numeracy/number Numeracy/number teachers know and understand: • how to access the wide range of national, regional and local support services available to learners of numeracy/number to support development and progression • how to access support from other specialists to support their learners • how to work collaboratively with specialists from other areas, both within and outside the organisation, to support their learners • how to work with employers to promote the development of learners of numeracy/number.
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A glossary of terms used within this document and other Wales publications can be found on the LLUK website at www.lluk.org/2819.htm
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