Numeracy English

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

Contents
Introduction 3
Section 1:
Elements 7
Section 2:
Elements and guidance on extent 14

2

Lifelong Learning UK

Introduction
The “New overarching professional standards for teachers, The definitive professional standards for teachers, tutors
tutors and trainers in the lifelong learning sector in Wales”1 and trainers in the lifelong learning sector in Wales
describe consistent performance for all teachers, in describe, in generic terms, the values, knowledge,
terms of knowledge, understanding and professional understanding and professional practice required of
practice. This document applies those generic standards those who perform the wide variety of teaching and
and describes consistent performance of teachers who training roles undertaken within the sector with learners
develop learners’ skills in numeracy/number in particular, and employers. The standards:
again in terms of knowledge, understanding and • are context free and level free, in order to represent
professional practice. In addition to this application all areas of work4 and new teachers, experienced
document, LLUK has produced other application teachers and teacher educators
documents for: • represent the teaching and learning cycle, with which
• teachers of English for Speakers of Other Languages all teachers engage: initial assessment, planning and
(ESOL) preparation, teaching, assessment, evaluation and
• teachers of Welsh for Adults quality improvement through responding to evaluation.

• teachers who develop skills in literacy/communication The development of application of the professional
(English and/or Welsh) standards for teachers who develop learners’ skills
in numeracy/number in the lifelong learning sector
• teachers who teach bilingually or through the medium in Wales
of Welsh.
In February 2008, the Welsh Assembly Government
The development of new professional standards for tasked Lifelong Learning UK (LLUK) to develop an
teachers, tutors and trainers in the lifelong learning
application of the professional standards for teachers who
sector in Wales
develop learners’ skills in numeracy/number in Wales. This
In March 2007, the Welsh Assembly Government tasked application document has been developed to describe the
Lifelong Learning UK (LLUK) to review the Standards for consistent performance of these teachers, in terms of
Teaching and Supporting Learning for Wales and England2. knowledge, understanding and professional practice.
Whilst mindful of the need for cross border
As with the generic standards for teachers, this application
transferability, the review for Wales has presented the
of the standards for teachers who develop learners’ skills
opportunity to develop standards for teachers to reflect
in numeracy/number is context free and level free. It is for
the uniqueness of the context in Wales. The standards
use in all constituencies and for new teachers, experienced
reflect the distinct needs of the sector in Wales and
teachers and teacher educators. It can be used for the
support the vision of “The Learning Country”3. The
whole range of purposes that standards are used for,
standards include ones relating specifically to bilingualism,
including recruitment and selection, self assessment, and
cultural diversity and sustainable development and global
of course, all types of professional development.
citizenship. This enables the standards to meet the
needs of Wales but also allows for articulation with the The document will be of value to teachers and
professional standards for teachers in England. 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.

1
Lifelong Learning UK (LLUK) 2008
2
Further Education National Training Organisation 1999 3
3
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


Introduction
Personal skills in Mathematics The application of the standards
The application of the professional standards for teachers This document details the knowledge, understanding and
who develop learners’ skills in numeracy/number details professional practice required of teachers who develop
the knowledge, understanding and professional practice learners’ skills in numeracy/number against the domains
of these teachers. It does not detail required personal of the professional standards.
skills in Mathematics. Teachers who develop learners’ An approach for developing the content of domains B
skills in numeracy/number should have the appropriate and C had to be considered. In the generic standards,
level of personal skills in Mathematics to teach effectively. 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
Use of terminology – numeracy/number
application of the professional standards for particular
This document details the knowledge, understanding
specialist teaching and learning, in this instance teachers
and professional practice of all teachers who develop
who develop learners’ skills in numeracy/number,
learners’ skills in numeracy/number. This will include,
questioned the content of the two domains and how it
importantly, teachers of Numeracy (Basic Skills) and
would differ. After looking at the detail of the standards in
Number (Key Skills). The standards for Basic Skills and
domains B and C, the following approach was adopted:
Key Skills are to be converged but the term to describe
• professional practice, learning and teaching of
the converged standards is undecided at the time of
teachers who develop learners’ skills in
writing (April 2008). In recognition of the important
numeracy/number to be detailed in Domain B
audience of this document, teachers of Basic and Key
Skills, the term ‘numeracy/number’ has been used • theory and knowledge related to developing learners’
throughout the document. It is intended that when skills in numeracy/number to be detailed in Domain C.
converged standards are named the title of this These two domains should not be seen as sequential.
document will be reviewed. Indeed, appropriate professional development
programmes for teachers who develop learners’ skills
in numeracy/number would be expected to deal with
Organisation of the document these aspects of knowledge, understanding and
The new overarching professional standards for professional practice in a holistic fashion.
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

4


Within the domains, specific statements relating to Extent is provided as guidance on the associated
knowledge or practice for teachers who develop learners’ content of each element. This extent is detailed in
skills in numeracy/number have been detailed against the section two. The use of the terms element and extent
value and commitment statements (What teachers value has been supported through consultation. Those
and what they are committed to). It was considered developing and delivering teacher education programmes
unnecessary and unhelpful to try to detail the application will find it useful to consider this extent guidance when
of every value and commitment statement for teachers making any decision to include more or less than that
who develop learners’ skills in numeracy/number. Some detailed for any particular cohort of trainee teachers.
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.’
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.

5


Here is an example from Domain D
Standard DS1 Element D1.1.Nu
Planning to promote equality, support diversity and Apply knowledge of numeracy/number curriculum development
to meet the aims and learning needs of learners to the planning process.
(This is a commitment statement from the (This is an element – this relates to knowledge or practice)
professional standards) 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)

6


Section 1:
Elements

Teachers who develop learners’ skills in
numeracy/number in the lifelong learning
Domain A:
sector in Wales value: Professional values and practice

Standard AS1 Element A1.1 Nu
Learners, their progress and development, their Take account of learners’ backgrounds, experience, goals and aspirations.
learning goals and aspirations and the experience
they bring to their learning

Learning, its potential to beneﬁt people Make links between numeracy/number development and other areas
emotionally, intellectually, socially and of development.
economically, and its contribution to sustainable
development in a community and global context

Equality, diversity, inclusion and bilingualism Address particular issues in relation to diversity, inclusion and learners
in relation to learners, the workforce, of numeracy/number.
and the community

Reﬂection and evaluation of their own practice Engage in professional development relating to international, national
and their continuing professional development and local research relating to numeracy/number.
as teachers

Collaboration with other individuals, groups and/or Collaborate with others to develop learners’ numeracy/number knowledge
organisations with a legitimate interest in the in a wide range of settings and contexts.
progress and development of learners

sector in Wales are committed to:

The application of the agreed codes of practice Informed by professional standards only.
and the maintenance of a safe environment

Improving the quality of their practice Use approaches which develop the quality of numeracy/number learning
and teaching across an organisation.

7


Section 1:
Elements

Domain B:
sector in Wales are committed to: Learning and teaching

Standard BS1 Element B1.1 Nu
Maintaining an inclusive, equitable, motivating and, Recognise the effects of learner backgrounds on feelings about
where appropriate, bilingual learning environment numeracy/number and foster positive self-images as independent learners.

Applying and developing own professional skills Create an environment where learners feel valued as members of a community.
to enable learners to achieve their goals

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.

Communicating effectively and appropriately Enable learners to develop appropriate specialist numeracy/number language.
with learners to enhance learning

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.

Collaborating with colleagues to support Work with teachers of other subjects where numeracy/number is embedded
the needs of learners to identify relevant numeracy/number and other transferable skills, and plan
how to develop these in context.

Using a range of learning resources to Use specialist knowledge and awareness of learner needs and goals to select,
support learners develop and use appropriate resources for numeracy/number learning,
including new and emerging technologies where appropriate.
8


Domain C:
sector in Wales are committed to: 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.
9


Section 1:
Elements

Element C1.11 Nu
Develop an understanding of the origins and status of mathematical
knowledge and the effect on curriculum development.

Enthusing and motivating learners in own Understand the roles of numeracy/number in the world at large.
specialist area

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.

Fulfilling the statutory responsibilities associated Develop knowledge and understanding of a range of learning and teaching
with own specialist area of 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.

Developing good practice in teaching own Use specialist organisations and publications to develop own practice as a
specialist area 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.

10


Domain D:
sector in Wales are committed to: Planning for learning

Standard DS1 Element D1.1 Nu
Planning to promote equality, support diversity and Apply knowledge of numeracy/number curriculum development to the
to meet the aims and learning needs of learners planning process.

Element D1.2 Nu
Apply theoretical and practical numeracy/number knowledge to the planning
of learning and teaching.

Learner participation in the planning of learning Apply knowledge of the learners to the planning process.

Evaluation of own effectiveness in Employ strategies to evaluate numeracy/number learning and teaching.
planning learning

11


Section 1:
Elements

Domain E:
sector in Wales are committed to: Assessment for learning

Standard ES1 Element E1.1 Nu
Designing and using assessment as a tool Develop knowledge of the types of skills, knowledge and understanding that
for learning and progression can be assessed in numeracy/number and use these to select or design
appropriate assessment tools.

Assessing the work of learners in a fair Recognise that learners can have a wide variety of mathematical/numeracy
and equitable manner 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.

Learner involvement and shared responsibility Develop strategies to involve learners in their own numeracy/number
in the assessment process assessment.

Using feedback as a tool for learning Apply specialist knowledge of assessment and feedback for
and progression mathematical/numeracy learning to develop learner skills, knowledge
and understanding in the subject.

Working with the systems and quality Record relevant information about the mathematical/numeracy skills,
requirements of the organisation in relation to knowledge and understanding of learners in order to progress learning.
assessment and monitoring of learner progress

12


Domain F:
sector in Wales are committed to: Access and progression

Standard FS1 Element F1.1 Nu
Encouraging learners to seek initial and further Signpost learners of numeracy/number to specialist support services,
learning opportunities and to use services within learning or progression opportunities.
the organisation

Providing support for learners within the Identify the boundaries between their own specialist areas and those
boundaries of the teacher role of other specialists.

Maintaining own professional knowledge in order Maintain professional knowledge in relation to progression opportunities
to provide information on opportunities for for learners of numeracy/number.
progression in own specialist area

A multi-agency approach to supporting development Develop relationships with a range of specialist services, agencies and
and progression opportunities for learners 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.

13


Section 2:
Elements and guidance on extent

Domain A:
sector in Wales value: Professional values and practice

Learners, their progress and development, their Take account of learners’ backgrounds, experience, goals and aspirations
learning goals and aspirations and the experience Numeracy/number teachers know and understand:
they bring to their learning
• 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.

Learning, its potential to benefit people Make links between numeracy/number development and other areas
emotionally, intellectually, socially and of development
economically, and its contribution to sustainable Numeracy/number teachers know and understand:
development in a community and global context
• 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.
• apply this knowledge and understanding in their practice.

Equality, diversity, inclusion and bilingualism Address particular issues in relation to diversity, inclusion and learners of
in relation to learners, the workforce, and numeracy/number
the community 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.
• apply this knowledge and understanding in their practice.
14


Reflection and evaluation of their own practice Engage in professional development relating to international, national and
and their continuing professional development local research relating to numeracy/number
as teachers 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.
• reflect on research to inform classroom management and share
good practice.

Collaboration with other individuals, groups and/or Collaborate with others to develop learners’ numeracy/number knowledge
organisations with a legitimate interest in the in a wide range of settings and contexts
progress and development of learners 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.

Teachers who develop learners’ skills in Numeracy/number teachers:
numeracy/number in the lifelong learning • collaborate with colleagues to use numeracy/number and other subject
sector in Wales are committed to: specialist knowledge to develop learners’ numeracy/number.

The application of the agreed codes of practice Informed by professional standards only
and the maintenance of a safe environment

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

15


Section 2:

Domain B:
sector in Wales are committed to: Learning and teaching

Maintaining an inclusive, equitable, motivating and, Recognise the effects of learner backgrounds on feelings about
where appropriate, bilingual learning environment numeracy/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 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.

Applying and developing own professional skills Create an environment where learners feel valued as members of
to enable learners to achieve their goals a learning community
• 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
• 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.

16


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

Communicating effectively and appropriately Enable learners to develop appropriate specialist numeracy/number language
with learners to enhance learning Numeracy/number teachers:
• identify and use strategies for encouraging the active use of numeracy-
related vocabulary by learners
• identify sources of linguistic confusion in numeracy/number and adopt
strategies to address these where appropriate.

17


Section 2:

Element B3.2 Nu
Use a wide range of communication strategies to support conceptual
understanding in numeracy/number
• 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.

Collaborating with colleagues to support the Work with teachers of other subjects where numeracy/number is embedded
needs of learners to identify relevant numeracy/number and other transferable skills, and plan
how to develop these in context
• 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.

18


Using a range of learning resources to Use specialist knowledge and awareness of learner needs and goals to select,
support learners 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 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.

19


Section 2:

Domain C:
sector in Wales are committed to: Specialist learning and teaching

Own specialist area including current development Develop own knowledge and understanding of the development
of mathematics
• 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
• 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
• 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
• 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.

20


Element C1.5 Nu
Develop own knowledge and understanding of a wide range of ways of
deﬁning or representing different concepts in numeracy/number
• 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
• 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
• 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
• the role and purpose of mathematical thinking skills including:
– exploring
– planning
– generalising
– sorting
– hypothesising
– modelling
– testing
– adjusting/remodelling
– reporting
– representing
– interpreting.
21


Section 2:

Element C1.9 Nu
Develop own knowledge and understanding of how context may determine
the 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 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
• 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.

22


Enthusing and motivating learners in own Understand the roles of numeracy/number in the world at large
specialist area 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
• 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.

23


Section 2:

Fulﬁlling the statutory responsibilities associated Develop knowledge and understanding of a range of learning and teaching
with own specialist area of teaching theories and strategies, relevant to numeracy/number, in order to apply
them to practice
• 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
• 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.
24


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

Developing good practice in teaching Use specialist organisations and publications to develop own practice
own specialist area 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 Nu
Access 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 own
mathematical knowledge as well as knowledge and skills of teaching
• how to self-evaluate in order to continuously develop own practice.

25


Section 2:

Domain D:
sector in Wales are committed to: Planning for learning

Planning to promote equality, support diversity and Apply knowledge of numeracy/number curriculum development
to meet the aims and learning needs of learners 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 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
• 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.

26


Learner participation in the planning of learning Apply knowledge of the learners to the planning process
• 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.

Evaluation of own effectiveness in planning learning Employ strategies to evaluate numeracy/number learning and teaching
• 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.

27


Section 2:

Domain E:
sector in Wales are committed to: Assessment for learning

Designing and using assessment as a tool Develop knowledge of the types of skills, knowledge and understanding
for learning and progression that can be assessed in numeracy/number and use these to select or design
appropriate assessment tools
• 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.
• select, design, use and evaluate assessment tools that are appropriate to
the context of the learner and mathematical purpose of the assessment.

Assessing the work of learners in a fair Recognise that learners can have a wide variety of mathematical/numeracy
and equitable manner skills, knowledge and understanding.
• 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).
• 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.

28


Element E2.2 Nu
Develop awareness of the differences that learner backgrounds can make
with regard to approaches to numeracy/number assessment
• 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.
• conduct an assessment in a fair and inclusive manner, with due regard
to validity and reliability.

Learner involvement and shared responsibility Develop strategies to involve learners in their own numeracy/number
in the assessment process assessment
• 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.
• 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.

Using feedback as a tool for learning Apply specialist knowledge of assessment and feedback for
and progression mathematical/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.

29


Section 2:

Working with the systems and quality Record relevant information about the mathematical/numeracy skills,
requirements of the organisation in relation to knowledge and understanding of learners in order to progress learning
assessment and monitoring of learner progress 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.
• 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.

Domain F:
sector in Wales are committed to: Access and progression

Encouraging learners to seek initial and further Signpost learners of numeracy/number to specialist support services,
learning opportunities and to use services within learning or progression opportunities
the organisation 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.

Providing support for learners within the Identify the boundaries between their own specialist areas and those
boundaries of the teacher role of other specialists
• 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.

30


Maintaining own professional knowledge in Maintain professional knowledge in relation to progression opportunities
order to provide information on opportunities for learners of numeracy/number
for progression in own specialist area 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.

A multi-agency approach to supporting Develop relationships with a range of specialist services, agencies and
development and progression opportunities professionals for learners of numeracy/number
for learners 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.

31

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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