Numeracy English

New professional standards for teachers, tutorsand trainers in the lifelong learning sector in WalesApplication of the professional standards for teachers who develop learners’ skills in numeracy/number in the lifelong learning sector in Wales

LLUK Numeracy English - Website 15/5/08 18:34 Page 1

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Introduction 3

Section 1:Elements 7

Section 2: Elements and guidance on extent 14

Contents


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Lifelong Learning UK

The “New overarching professional standards for teachers,tutors and trainers in the lifelong learning sector in Wales”1

describe consistent performance for all teachers, interms of knowledge, understanding and professionalpractice. This document applies those generic standardsand describes consistent performance of teachers whodevelop learners’ skills in numeracy/number in particular,again in terms of knowledge, understanding andprofessional practice. In addition to this applicationdocument, LLUK has produced other applicationdocuments 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 mediumof Welsh.

The development of new professional standards forteachers, tutors and trainers in the lifelong learningsector in Wales

In March 2007, the Welsh Assembly Government taskedLifelong Learning UK (LLUK) to review the Standards forTeaching and Supporting Learning for Wales and England2.Whilst mindful of the need for cross bordertransferability, the review for Wales has presented theopportunity to develop standards for teachers to reflectthe uniqueness of the context in Wales. The standardsreflect the distinct needs of the sector in Wales andsupport the vision of “The Learning Country”3. Thestandards include ones relating specifically to bilingualism,cultural diversity and sustainable development and globalcitizenship. This enables the standards to meet theneeds of Wales but also allows for articulation with theprofessional standards for teachers in England.

The definitive professional standards for teachers, tutorsand trainers in the lifelong learning sector in Walesdescribe, in generic terms, the values, knowledge,understanding and professional practice required ofthose who perform the wide variety of teaching andtraining roles undertaken within the sector with learnersand employers. The standards:

• are context free and level free, in order to representall areas of work4 and new teachers, experiencedteachers and teacher educators

• represent the teaching and learning cycle, with whichall teachers engage: initial assessment, planning andpreparation, teaching, assessment, evaluation andquality improvement through responding to evaluation.

The development of application of the professionalstandards for teachers who develop learners’ skills in numeracy/number in the lifelong learning sector in Wales

In February 2008, the Welsh Assembly Governmenttasked Lifelong Learning UK (LLUK) to develop anapplication of the professional standards for teachers whodevelop learners’ skills in numeracy/number in Wales. Thisapplication document has been developed to describe theconsistent performance of these teachers, in terms ofknowledge, understanding and professional practice.

As with the generic standards for teachers, this applicationof the standards for teachers who develop learners’ skillsin numeracy/number is context free and level free. It is foruse in all constituencies and for new teachers, experiencedteachers and teacher educators. It can be used for thewhole 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 andmanagers, including those with responsibility for staffdevelopment and human resources. It will be ofparticular value for teacher educators in underpinningprofessional development opportunities. Theknowledge, understanding and professional practicedetailed in this document can inform the developmentof a wide range of accredited and unaccreditedprogrammes for teachers of literacy/communication.

Introduction

1Lifelong Learning UK (LLUK) 20082Further Education National Training Organisation 19993The Learning Country: Vision into Action (2001) Welsh Assembly Government (WAG)4Including community learning and development, further education, higher education, libraries, archives and information services, and work based learning across the UK


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Personal skills in Mathematics The application of the professional standards for teacherswho develop learners’ skills in numeracy/number detailsthe knowledge, understanding and professional practiceof these teachers. It does not detail required personalskills in Mathematics. Teachers who develop learners’skills in numeracy/number should have the appropriatelevel of personal skills in Mathematics to teach effectively.

Use of terminology – numeracy/numberThis document details the knowledge, understandingand professional practice of all teachers who developlearners’ skills in numeracy/number. This will include,importantly, teachers of Numeracy (Basic Skills) andNumber (Key Skills). The standards for Basic Skills andKey Skills are to be converged but the term to describethe converged standards is undecided at the time ofwriting (April 2008). In recognition of the importantaudience of this document, teachers of Basic and KeySkills, the term ‘numeracy/number’ has been usedthroughout the document. It is intended that whenconverged standards are named the title of thisdocument will be reviewed.

Organisation of the documentThe new overarching professional standards forteachers, tutors and trainers in the lifelong learningsector in Wales detail the values, knowledge,understanding and professional practice expected of allteachers in the lifelong learning sector in Wales. Thisinformation is detailed in domains. The domains reflectthe 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

The application of the standards

This document details the knowledge, understanding andprofessional practice required of teachers who developlearners’ skills in numeracy/number against the domainsof the professional standards.

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 allteachers. Domain C is concerned with a teacher’s area of specialism, whatever that may be. Developing anapplication of the professional standards for particularspecialist teaching and learning, in this instance teacherswho develop learners’ skills in numeracy/number,questioned the content of the two domains and how itwould differ. After looking at the detail of the standards indomains B and C, the following approach was adopted:

• professional practice, learning and teaching ofteachers who develop learners’ skills innumeracy/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 developmentprogrammes for teachers who develop learners’ skillsin numeracy/number would be expected to deal withthese aspects of knowledge, understanding andprofessional practice in a holistic fashion.

Introduction



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Within the domains, specific statements relating toknowledge or practice for teachers who develop learners’skills in numeracy/number have been detailed against thevalue and commitment statements (What teachers valueand what they are committed to). It was consideredunnecessary and unhelpful to try to detail the applicationof every value and commitment statement for teacherswho develop learners’ skills in numeracy/number. Somevalue and commitment statements are generic in everysense and little could usefully be added to make themsubject specific. The commitment statements are codedby the letter of the domain and S for scope, for example,FS 2. All the value and commitment statements from thestandards are included in this document. Where it wasconsidered there was nothing specialist to add, this ismade clear with the statement ‘Informed by professionalstandards only.’

Statements relating to knowledge or practice are detailedthroughout this document as elements. A comprehensivelist of these can be found in section one of this document.They are coded with the domain letter and then innumber sequence.

A suffix, Nu, denotes an element in the applicationdocument.

Elements have been written as areas of knowledge andpractice for teachers who develop learners’ skills innumeracy/number. They detail the specific applicationfor any value and commitment statement. The majorityof commitment statements have one associatedelement, a few have a significant number of elementsand some have none.

Extent is provided as guidance on the associatedcontent of each element. This extent is detailed insection two. The use of the terms element and extenthas been supported through consultation. Thosedeveloping and delivering teacher education programmeswill find it useful to consider this extent guidance whenmaking any decision to include more or less than thatdetailed for any particular cohort of trainee teachers.



Here is an example from Domain D

Element D1.1.NuApply knowledge of numeracy/number curriculum development to the planning process.

(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 embednumeracy/number

• how to plan effective programmes which incorporate opportunities to learn, practise, develop and accredit a range of appropriatetransferable skills.

(This is guidance on extent)

Standard DS1 Planning to promote equality, support diversity andto meet the aims and learning needs of learners

(This is a commitment statement from the professional standards)

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Section 1:Elements

Element A1.1 NuTake account of learners’ backgrounds, experience, goals and aspirations.

Element A2.1 NuMake links between numeracy/number development and other areas of development.

Element A3.1 NuAddress particular issues in relation to diversity, inclusion and learners of numeracy/number.

Element A4.1 NuEngage in professional development relating to international, national and local research relating to numeracy/number.

Element A5.1 NuCollaborate with others to develop learners’ numeracy/number knowledge in a wide range of settings and contexts.

Element A6.1 NuInformed by professional standards only.

Element A7.1 NuUse approaches which develop the quality of numeracy/number learning and teaching across an organisation.

Teachers who develop learners’ skills innumeracy/number in the lifelong learning sector in Wales value:

Standard AS1Learners, their progress and development, theirlearning goals and aspirations and the experiencethey bring to their learning

Standard AS2Learning, its potential to benefit peopleemotionally, intellectually, socially andeconomically, and its contribution to sustainabledevelopment in a community and global context

Standard AS3Equality, diversity, inclusion and bilingualism in relation to learners, the workforce, and the community

Standard AS4Reflection and evaluation of their own practice and their continuing professional development as teachers

Standard AS5Collaboration with other individuals, groups and/ororganisations with a legitimate interest in theprogress and development of learners

Teachers who develop learners’ skills innumeracy/number in the lifelong learning sector in Wales are committed to:

Standard AS6The application of the agreed codes of practiceand the maintenance of a safe environment

Standard AS7Improving the quality of their practice

Domain A:Professional values and practice


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Element B1.1 NuRecognise the effects of learner backgrounds on feelings aboutnumeracy/number and foster positive self-images as independent learners.

Element B2.1 NuCreate an environment where learners feel valued as members of a community.

Element B2.2 NuUse subject knowledge to adopt appropriate approaches tonumeracy/number teaching.

Element B2.3 NuUse specialist pedagogical knowledge to adopt appropriate learning and teaching strategies for numeracy/number.

Element B2.4 NuEmploy specialist pedagogical knowledge to support a wide range of learners’needs in numeracy/number.

Element B3.1 NuEnable learners to develop appropriate specialist numeracy/number language.

Element B3.2 NuUse a wide range of communication strategies to support conceptualunderstanding in numeracy/number.

Element B3.3 NuFacilitate appropriate learner-teacher and learner-learner interaction in orderto support learning.

Element B4.1 NuWork with teachers of other subjects where numeracy/number is embeddedto identify relevant numeracy/number and other transferable skills, and planhow to develop these in context.

Element B5.1 NuUse 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.

Section 1:Elements



Standard BS1Maintaining an inclusive, equitable, motivating and,where appropriate, bilingual learning environment

Standard BS2Applying and developing own professional skills to enable learners to achieve their goals

Standard BS3Communicating effectively and appropriately with learners to enhance learning

Standard BS4Collaborating with colleagues to support the needs of learners

Standard BS5Using a range of learning resources to support learners

Domain B:Learning and teaching


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Element C1.1 NuDevelop own knowledge and understanding of the development ofnumeracy/number across cultures and through time.

Element C1.2 NuDevelop own knowledge and understanding of the language and conceptsassociated with place value systems.

Element C1.3 NuDevelop own knowledge and understanding of the nature of argument and proof in number.

Element C1.4 NuDevelop own knowledge and understanding of how to critically gather, use, process, interpret and display data.

Element C1.5 NuDevelop own knowledge and understanding of a wide range of ways of defining or representing different concepts in numeracy/number.

Element C1.6 NuDevelop own knowledge and understanding of a range of commonnumeracy/number learner errors and misconceptions; possible reasons why they occur and approaches for addressing them.

Element C1.7 NuDevelop own knowledge and understanding of a wide range of mental, writtenand diagrammatic strategies that can inform their understanding and practice.

Element C1.8 NuDevelop own knowledge and understanding of the activities, processes andstages within mathematical problem solving /application.

Element C1.9 NuDevelop own knowledge and understanding of how context may determinethe approach used for mathematical problem solving or investigation.

Element C1.10 NuDevelop own knowledge and understanding of a range of connectionsbetween areas in numeracy/number.


Standard CS1Own specialist area including current development


Element C1.11 NuDevelop an understanding of the origins and status of mathematicalknowledge and the effect on curriculum development.

Element C2.1 NuUnderstand the roles of numeracy/number in the world at large.

Element C2.2 NuDevelop own knowledge and understanding of public/popular perceptions of numeracy/number and consider their impact on learner motivation.

Element C2.3 NuDemonstrate specialist knowledge of appropriate strategies that engage and enthuse learners in numeracy/number.

Element C3.1 NuDevelop knowledge and understanding of a range of learning and teachingtheories and strategies, relevant to numeracy/number, in order to apply them to practice.

Element C3.2 NuDevelop knowledge of the effects of learner backgrounds and needs onnumeracy/number learning.

Element C3.3 NuUse understanding of the different ways in which language and literacy skillsare integral to learners’ achievement, in numeracy/number, to address thedevelopment of these skills.

Element C3.4 NuUse of communication to promote and develop conceptual understanding of numeracy/number via collaborative tasks and sharing of strategies.

Element C4.1 NuUse specialist organisations and publications to develop own practice as anumeracy/number (numeracy) teacher.

Element C4.2 NuAccess subject specific training and development opportunities, using a reflectivecontinuing professional development cycle to critically select such opportunities.

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Section 1:Elements


Standard CS2Enthusing and motivating learners in own specialist area

Standard CS3Fulfilling the statutory responsibilities associatedwith own specialist area of teaching

Standard CS4Developing good practice in teaching ownspecialist area


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Element D1.1 NuApply knowledge of numeracy/number curriculum development to theplanning process.

Element D1.2 NuApply theoretical and practical numeracy/number knowledge to the planningof learning and teaching.

Element D2.1 Nu Apply knowledge of the learners to the planning process.

Element D3.1 NuEmploy strategies to evaluate numeracy/number learning and teaching.



Standard DS2Learner participation in the planning of learning

Standard DS3Evaluation of own effectiveness in planning learning



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Element E1.1 NuDevelop knowledge of the types of skills, knowledge and understanding thatcan be assessed in numeracy/number and use these to select or designappropriate assessment tools.

Element E2.1 NuRecognise that learners can have a wide variety of mathematical/numeracyskills, knowledge and understanding.

Element E2.2 NuDevelop awareness of the differences that learner backgrounds can makewith regard to approaches to numeracy/number assessment.

Element E3.1 NuDevelop strategies to involve learners in their own numeracy/numberassessment.

Element E4.1 NuApply specialist knowledge of assessment and feedback formathematical/numeracy learning to develop learner skills, knowledge and understanding in the subject.

Element E5.1 NuRecord relevant information about the mathematical/numeracy skills,knowledge and understanding of learners in order to progress learning.


Standard ES1Designing and using assessment as a tool for learning and progression

Standard ES2Assessing the work of learners in a fair and equitable manner

Standard ES3Learner involvement and shared responsibility in the assessment process

Standard ES4Using feedback as a tool for learning and progression

Standard ES5Working with the systems and qualityrequirements of the organisation in relation toassessment and monitoring of learner progress


Section 1:Elements


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Element F1.1 NuSignpost learners of numeracy/number to specialist support services, learning or progression opportunities.

Element F2.1 NuIdentify the boundaries between their own specialist areas and those of other specialists.

Element F3.1 NuMaintain professional knowledge in relation to progression opportunities for learners of numeracy/number.

Element F4.1 NuDevelop relationships with a range of specialist services, agencies andprofessionals for learners of numeracy/number.


Standard FS1Encouraging learners to seek initial and furtherlearning opportunities and to use services withinthe organisation

Standard FS2Providing support for learners within theboundaries of the teacher role

Standard FS3Maintaining own professional knowledge in orderto provide information on opportunities forprogression in own specialist area

Standard FS4 A multi-agency approach to supporting developmentand progression opportunities for learners


The document will be of valueto teachers and managers,including those with responsibilityfor staff development andhuman resources.


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Element A1.1 NuTake account of learners’ backgrounds, experience, goals and aspirations

Numeracy/number teachers know and understand:

• the nature of numeracy/number learning, and the need to supportlearners’ own ability to work independently

• the importance of identifying and drawing upon the range of skills,experiences, expertise, goals and other subject areas which interestand motivate learners.

Numeracy/number teachers:

• Apply their understanding of learners’ backgrounds, experiences, goals and aspirations to supporting their development and progression in numeracy/number.

Element A2.1 NuMake links between numeracy/number development and other areas of development


• the importance of supporting learners in making links between thedevelopment of their numeracy/number skills and other areas ofimportance to them, including vocational, economic and global contexts

• why learners benefit from reflecting on ways numeracy/numberdevelopment can empower them as individuals and positively influencetheir role within and outside the community.


• apply this knowledge and understanding in their practice.

Element A3.1 NuAddress particular issues in relation to diversity, inclusion and learners ofnumeracy/number


• the range and diversity of learners’ numeracy/number practices and howto help develop these

• the personal, emotional, social, economic and cultural factors which mayaffect the learning, development and progression of learners.

• the potential impact and implications of physical disabilities, sensoryimpairment and mental health issues for learners of numeracy/number

• current definitions of dyslexia, dyscalculia and related conditions, andstrategies for supporting learners with these particular needs.


• apply this knowledge and understanding in their practice.

Section 2: Elements and guidance on extent


Teachers who develop learners’ skills innumeracy/number in the lifelong learning sector in Wales value:

Standard AS1Learners, their progress and development, theirlearning goals and aspirations and the experiencethey bring to their learning

Standard AS2Learning, its potential to benefit peopleemotionally, intellectually, socially andeconomically, and its contribution to sustainabledevelopment in a community and global context

Standard AS3Equality, diversity, inclusion and bilingualism in relation to learners, the workforce, and the community

Domain A:Professional values and practice


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Element A4.1 NuEngage in professional development relating to international, national and local research relating to numeracy/number


• 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.


• reflect on research to inform classroom management and share good practice.

Element A5.1 NuCollaborate with others to develop learners’ numeracy/number knowledge in a wide range of settings and contexts


• how organisational policies can influence numeracy/number practices

• the importance of contributing to the development of the organisation’spolicies and practices relating to numeracy/number and language

• how collaboration with others can support cross disciplinary approachesto numeracy/number development.


• collaborate with colleagues to use numeracy/number and other subjectspecialist knowledge to develop learners’ numeracy/number.

Element A6.1 NuInformed by professional standards only

Element A7.1 NuUse approaches which develop the quality of numeracy/number learning andteaching across an organisation


• how numeracy/number practices are situated within organisational policy,planning and implementation processes and practice.


• evaluate their own contribution to the development of the organisation’spolicies and practices relating to numeracy/number.

Standard AS4Reflection and evaluation of their own practiceand their continuing professional development as teachers

Standard AS5Collaboration with other individuals, groups and/ororganisations with a legitimate interest in theprogress and development of learners


Standard AS6The application of the agreed codes of practiceand the maintenance of a safe environment

Standard AS7Improving the quality of their practice


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Element B1.1 NuRecognise the effects of learner backgrounds on feelings aboutnumeracy/number and foster positive self-images as independent learners


• use strategies to overcome the effects of numeracy/number anxiety in learners

• value learners’ existing strategies for using numeracy/number in their ownlives and provide opportunities to build on this

• use strategies to encourage learner motivation, independence andaspirations, for example, self-selection of tasks, opportunities to uncoverfacts for themselves, learner experimentation with and evaluation ofdifferent numeracy/number methods.

Element B2.1 NuCreate an environment where learners feel valued as members of a learning community


• recognise the possible effects of prior experiences (both positive andnegative) of mathematics learning and facilitate a culture where learnersare confident about asking questions and discussing methods and solutionswith other learners

• develop an ethos of mutual support and encouragement so that learners donot feel ‘judged’ by their peers in terms of their numeracy/number learning

• create an environment where learners are comfortable about makingmistakes, and see and use these as an opportunity for further learning

• manage group tasks so that participants recognise that interacting withothers can enhance numeracy/number learning and understanding.

Element B2.2 NuUse subject knowledge to adopt appropriate approaches tonumeracy/number teaching


• employ appropriate approaches to developing learners’ understanding ofconcepts in order to meet specified learning outcomes, for example todevelop learners’ ability judge which method of presenting information is appropriate to the context, such as whether to present 50% as aproportion (50 out of every 100) or a fraction (1/2)

• facilitate deeper understanding of the connections within and betweendifferent areas of the numeracy/number curriculum and other contextsand subjects.




Standard BS1Maintaining an inclusive, equitable, motivating and,where appropriate, bilingual learning environment

Standard BS2Applying and developing own professional skills to enable learners to achieve their goals

Domain B:Learning and teaching


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Element B2.3 NuUse specialist pedagogical knowledge to adopt appropriate learning andteaching strategies for numeracy/number


• use knowledge of theories of teaching and learning and own experienceto select and use teaching strategies that address learner needs, goalsand contexts

• use learning and teaching strategies designed to engage and motivatelearners of numeracy/number, taking account of their previousexperiences (positive and negative) of numeracy/number learning

• use learning and teaching strategies to promote learner independence in numeracy/number recognising that mathematics education is oftenperceived as teacher-centred.

Element B2.4 NuEmploy specialist pedagogical knowledge to support a wide range of learners’needs in numeracy/number


• use specialist knowledge to differentiate and support numeracy/numberlearning and teaching activities in order to make them more accessible for learners, for example, concrete experimentation, in order to developconceptual understanding, in addition to paper and pencil methods

• use specialist knowledge to extend numeracy/number activities forlearners where they would benefit from developing their skills andunderstanding 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 innumeracy/number and engaging all learners to take a full part in sessions,for example, language and literacy needs, global and specific learningdifficulties, physical disabilities or mental health issues.

Element B3.1 NuEnable learners to develop appropriate specialist numeracy/number language


• identify and use strategies for encouraging the active use of numeracy-related vocabulary by learners

• identify sources of linguistic confusion in numeracy/number and adoptstrategies to address these where appropriate.


Standard BS3Communicating effectively and appropriately with learners to enhance learning


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Element B3.2 NuUse a wide range of communication strategies to support conceptualunderstanding in numeracy/number


• use strategies such as discussion or question and answer to developunderstanding, modifying language according to audience, employingtechniques that address the needs of learners

• facilitate deeper understanding by appropriate use of open extendeddialogue and higher order questions

• use a wide range of non-verbal strategies to support conceptualunderstanding 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, withminimum compromise of meaning or accuracy, including using multimedia,non-verbal communication or visual aids to support learner understanding.

Element B3.3 NuFacilitate appropriate learner-teacher and learner-learner interaction in orderto support learning

Numeracy teachers:

• use skilfully framed open and closed, oral and written questions to elicitanswers from which learners’ numeracy/number understanding can bejudged, and use this information to take learning forward

• use a range of strategies to encourage collaborative learning ofnumeracy/number, where appropriate drawing on specialist researchand/or resources

• use tasks to promote discussion and develop the conceptualunderstanding and critical thinking skills of learners, for example, focusingon interpretation of data as well as extraction of numerical information.

Element B4.1 NuWork with teachers of other subjects where numeracy/number is embeddedto identify relevant numeracy/number and other transferable skills, and planhow to develop these in context


• design, adapt or select appropriate, authentic activities in collaborationwith colleagues in other areas to introduce and develop thenumeracy/number skills and knowledge needed in particular contexts

• collaborate with colleagues to identify opportunities where othertransferable skills can be learnt, practised, developed or accreditedthrough a numeracy/number context.


Standard BS4Collaborating with colleagues to support theneeds of learners


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Element B5.1 NuUse 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


• design, adapt, select and use resources from an appropriate range thatpromote factual knowledge, develop conceptual understanding and/orenable 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/numberlearning and teaching, for example, measuring instruments, physicalmodels, calculating aids, etc

• adapt the mathematical content of numeracy/number learning andteaching resources as appropriate for particular groups or individuals,either by simplification or extension

• use ICT and e-learning resources appropriately, to promote engagementwith tasks and activities.

Standard BS5Using a range of learning resources to support learners


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Element C1.1 NuDevelop own knowledge and understanding of the development of mathematics


• number system development

• measuring systems development

• recording and processing of data development.

Element C1.2 NuDevelop own knowledge and understanding of the language and conceptsassociated with place value systems


• other number bases

• simple calculations in other number bases

• standard form.

Element C1.3 NuDevelop own knowledge and understanding of the nature of argument and proof


• 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 NuDevelop own knowledge and understanding of how to critically gather, use, process, interpret and display data


• strategies for data collection

• the influence of sample size and data character (e.g. discrete, continuousor grouped)

• the choice and use of data processing techniques

• representation and misrepresentation of data and its analysis.


Standard CS1Own specialist area including current development



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Element C1.5 NuDevelop own knowledge and understanding of a wide range of ways ofdefining or representing different concepts in numeracy/number


• different ways of explaining common mathematical concepts

• higher level mathematics which can be used to support the developmentof mathematical understanding in learners at lower levels.

Element C1.6 NuDevelop own knowledge and understanding of a range of commonnumeracy/number learner errors and misconceptions, possible reasons why they occur and approaches for addressing them


• common errors and misconceptions in mathematical concepts andprocesses and ways of addressing these.

Element C1.7 NuDevelop own knowledge and understanding of a wide range of mental, writtenand diagrammatic strategies that can inform their understanding and practice


• 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 NuDevelop own knowledge and understanding of the activities, processes andstages within mathematical problem solving application


• 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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Element C1.9 NuDevelop own knowledge and understanding of how context may determinethe approach used for mathematical problem solving or investigation


• 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 NuDevelop own knowledge and understanding of a range of connectionsbetween areas in numeracy/number

Numeracy/number teachers know and understand

• that skills learned in one area of numeracy/number can be transferredand applied in another, eg the role of calculations in the analysis of data;place value in the measurement system; graphical representations ofalgebraic relationships

• that certain methods and mathematical procedures may suit particularapplications and why they may not suit others.

Element C1.11 NuDevelop an understanding of the origins and status of mathematicalknowledge and the effect on curriculum development


• the notions of ‘context’ and ‘embedding’ in relation tonumeracy/number learning

• different theories on how maths could be taught and learnt

• policy developments and initiatives relating to maths andnumeracy/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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Element C2.1 NuUnderstand the roles of numeracy/number in the world at large


• 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 inadvertising, 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 andimprove career development.

Element C2.2 NuDevelop own knowledge and understanding of public/popular perceptions of numeracy/number and consider their impact on learner motivation


• how the nature of maths related anxiety in individuals will impact on their learning

• that learners will have different motivations for improving theirnumeracy/number.

Element C2.3 NuDemonstrate 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 learningand experience, breaking down tasks into appropriate steps in order to create opportunities for success or by giving learners appropriatechallenges

• how to use a range of approaches to problem solving in numeracy/numberto 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.


Standard CS2Enthusing and motivating learners in own specialist area


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Element C3.1 NuDevelop knowledge and understanding of a range of learning and teachingtheories and strategies, relevant to numeracy/number, in order to apply them to practice


• a wide range of ways in which generic teaching and learning techniquesmay 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 areappropriate to the needs of the learner

• the rationale for encouraging learners to develop numeracy/numberknowledge in familiar contexts

• a range of teaching and learning techniques that will encourage learners to develop mathematical thinking

• that effective questioning facilitates the development ofnumeracy/number skills knowledge and understanding

• theories and research into assessment and its importance in learnerdevelopment

• the role of developing experiential problem solving in relevant practicalsituations to extend numeracy/number skills, knowledge andunderstanding 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 developmentof numeracy/number skills, knowledge and understanding and how somelearners may need support in this area.

Element C3.2 NuDevelop knowledge of the effects of learner backgrounds and needs on numeracy/number learning


• the possible effects of social and educational background, gender, culture,age and personal circumstances on numeracy/number learning and a rangeof strategies for responding to these

• the possible effects of physical disabilities, mental health issues, dyslexia,literacy needs and learning difficulties on numeracy/number developmentand a range of strategies for responding to these

• research into the relationship between dyslexia and numeracy/numberdevelopment

• the developing notions of dyscalculia, related research and strategies for responding to these.

Standard CS3Fulfilling the statutory responsibilities associatedwith own specialist area of teaching


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Element C3.3 NuUse understanding of the different ways in which language and literacy skillsare integral to learners’ achievement, in numeracy/number, to address thedevelopment of these skills


• that a learner’s lack of literacy or English/Welsh language skills will affecttheir acquisition of mathematical knowledge

• how to communicate with learners using the language of mathematics

• that some words can have a specific meaning within a mathematicalcontext which may be different from their everyday language meaning (eg product, mean etc).

Element C3.4 NuUse of communication to promote and develop conceptual understanding of numeracy/number via collaborative tasks and sharing of strategies


• that learners may develop their knowledge of mathematical conceptsthrough discussion in paired or group work and with peer support.

Element C4.1 NuUse specialist organisations and publications to develop own practice as a numeracy/number teacher


• 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 NuAccess subject specific training and development opportunities, using a reflective continuing professional development cycle to critically select such opportunities


• the need to take up further training opportunities to develop ownmathematical knowledge as well as knowledge and skills of teaching

• how to self-evaluate in order to continuously develop own practice.

Standard CS4Developing good practice in teaching own specialist area


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Element D1.1 NuApply knowledge of numeracy/number curriculum development to the planning process


• theories and models of curriculum development and how to apply them

• how to analyse the numeracy/number elements of a range of educationprogrammes

• how to plan, alone, or with colleagues, programmes which embednumeracy/number

• how to plan effective programmes which incorporate opportunities to learn,practise, develop and accredit a range of appropriate transferable skills.

Element D1.2 NuApply theoretical and practical numeracy/number knowledge to the planningof learning and teaching


• 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 andbalance a range of elements, including: development of numeracy/number,study and other transferable skills; relevant curricula and standards, awardsand assessment requirements

• how to use learner interests, contexts and experiences and otherprogrammes of learning to inform the planning of numeracy/numberlearning and teaching.







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Element D2.1 Nu Apply knowledge of the learners to the planning process


• the importance of dialogue with learners during the planning of learningand teaching, which involves:

– using accessible language to discuss and negotiate learning programmes

– understanding that previous educational experiences might affectlearners’ expectations of how much input and control they can havein 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.

Element D3.1 NuEmploy strategies to evaluate numeracy/number learning and teaching


• how to evaluate and analyse numeracy/number activities from theoreticaland practical perspectives, using a range of methods (eg in terms of whatwas learned, using the outcomes of assessment, using learner feedback,using feedback from colleagues)

• use appropriate general and numeracy-related learning theories to informthe planning of further teaching, learning and assessment activities.


Standard DS2Learner participation in the planning of learning

Standard DS3Evaluation of own effectiveness in planning learning


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Element E1.1 NuDevelop knowledge of the types of skills, knowledge and understanding that can be assessed in numeracy/number and use these to select or designappropriate assessment tools


• that assessment should cover the range of skills and applications requiredby the numeracy/number learner

• that the knowledge and understanding and ability to use numeracy/numberskills can vary over time for individual learners if they are not usedregularly, and that this can affect assessment results

• that assessment in numeracy/number should include information aboutthe whole learner, including previous learning experiences, personalcontexts 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/numberassessment activities.


• select, design, use and evaluate assessment tools that are appropriate tothe context of the learner and mathematical purpose of the assessment.

Element E2.1 NuRecognise that learners can have a wide variety of mathematical/numeracyskills, knowledge and understanding.


• individuals’ strengths in skills, knowledge and understanding innumeracy/number may not be uniform across the curriculum (i.e. they may have a spiky profile).


• assess learners across a range of types of skills, knowledge andunderstanding in numeracy/number (for example, problem-solving, mentalapproaches or measuring skills, as well as recall of multiplication facts) inorder to ascertain what learners can do as well as what they cannot do.




Standard ES1Designing and using assessment as a tool for learning and progression

Standard ES2Assessing the work of learners in a fair and equitable manner



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Element E2.2 NuDevelop awareness of the differences that learner backgrounds can makewith regard to approaches to numeracy/number assessment


• learners’ differing cultural and social backgrounds must be taken intoaccount in assessment

• the types of issues that learners with physical disabilities, mental healthissues, 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 carryingout assessment.


• conduct an assessment in a fair and inclusive manner, with due regard to validity and reliability.

Element E3.1 NuDevelop strategies to involve learners in their own numeracy/numberassessment


• that learners’ previous experience of assessment may affect their currentattitudes to it

• that learners will gain by being encouraged to make use of errors in theirown and the work of others as opportunities for further learning

• how and when to facilitate learner reflection on the process of learningnumeracy/number skills.


• 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 andencourage reflection and evaluation of alternative strategies.

Element E4.1 NuApply specialist knowledge of assessment and feedback formathematical/numeracy learning to develop learner skills, knowledge and understanding in the subject


• that assessment is more than testing but includes the consideration of methods and observation of learner practice.


• use effective questioning and constructive feedback to enable learners to self correct and help diagnose misconceptions.


Standard ES3Learner involvement and shared responsibility in the assessment process

Standard ES4Using feedback as a tool for learning and progression


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Element E5.1 NuRecord relevant information about the mathematical/numeracy skills,knowledge and understanding of learners in order to progress learning


• how to record appropriately, the progress in numeracy/number withregard to content and process skills, knowledge and understanding andpersonal 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 orderto progress.


• develop systems for recording learner progress in numeracy, such as anILP, which take into account the complex nature of numeracy/numberlearning and inform the learner, the teacher and the institution.




Standard ES5Working with the systems and qualityrequirements of the organisation in relation toassessment and monitoring of learner progress

Element F1.1 NuSignpost learners of numeracy/number to specialist support services, learning or progression opportunities


• how to identify, use and refer learners to sources of specialistinformation, support, advice and guidance relating to numeracy/number

• how to help learners develop the language and numeracy/number skillsneeded to research and use the organisation’s services, and also thoseoutside the organisation

• how to identify statutory entitlements to learning and personal supportfor learners along with the procedures in place to access them

• how to act appropriately as advocates for learners of numeracy/number.

Element F2.1 NuIdentify the boundaries between their own specialist areas and those of other specialists


• the boundaries between their own specialist area and those of otherspecialists (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.


Standard FS1Encouraging learners to seek initial and furtherlearning opportunities and to use services withinthe organisation

Standard FS2Providing support for learners within theboundaries of the teacher role


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Element F3.1 NuMaintain professional knowledge in relation to progression opportunities for learners of numeracy/number


• 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.

Element F4.1 NuDevelop relationships with a range of specialist services, agencies andprofessionals for learners of numeracy/number


• how to access the wide range of national, regional and local supportservices available to learners of numeracy/number to supportdevelopment 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.


Standard FS3Maintaining own professional knowledge in order to provide information on opportunities for progression in own specialist area

Standard FS4 A multi-agency approach to supportingdevelopment and progression opportunities for learners


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