awarding organisation guidance

AWARDING ORGANISATION GUIDANCE

June 2007 (amended February 2010)

Criteria for entry to mathematics (numeracy)and English (literacy and ESOL) teachertraining in the lifelong learning sector

Contents

Introduction 3

Entry criteria for mathematics (numeracy) 4

Process skills in mathematics 5

Content knowledge and skills in mathematics 8

Entry criteria for English (literacy and ESOL) 10

Content knowledge and skills in English 11

Guidance on entry assessment 13

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Criteria for entry to mathematics (numeracy) and English (literacy and ESOL) teacher training in the lifelong learning sector

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Introduction

From September 2007, new qualifications wereintroduced for the initial training of teachers inthe lifelong learning sector in England. It willcontinue to be a requirement for teachers ofmathematics (numeracy) and English (literacy andEnglish for speakers of other languages - ESOL)to gain subject specific teaching qualifications.

This guidance concerns those intending toundertake a Standards Verification UK (SVUK)endorsed subject specific diploma qualification,for teachers of mathematics (numeracy) andEnglish (literacy and ESOL) in the lifelong learningsector in England. They will be required todemonstrate the underpinning skills required tofunction effectively as users of mathematics orEnglish. These must be demonstrated beforeundertaking any of the qualifications.

The skills are detailed in this document as entrycriteria and have been developed using a processskills based model, which has drawn upondevelopments within functional skills and researchwithin learning and teaching. The skills must bedemonstrated at level 3 of the Qualifications andCredit Framework (QCF).

The nine (SVUK endorsed) subject specificdiploma qualifications listed on the right havebeen available since September 2007.

120 credit diploma qualifications:Fully integratedLevel 5 Diploma in teaching Mathematics(Numeracy) in the Lifelong Learning Sector

Level 5 Diploma in teaching English(Literacy) in the Lifelong Learning Sector

Level 5 Diploma in teaching English (ESOL)in the Lifelong Learning Sector

Partly integratedLevel 5 Diploma in teaching in the LifelongLearning Sector (Mathematics Numeracy)

Level 5 Diploma in teaching in the LifelongLearning Sector (English Literacy)

Level 5 Diploma in teaching in the LifelongLearning Sector (English ESOL)

45 credit diploma qualifications:Level 5 Additional Diploma in teachingMathematics (Numeracy) in the LifelongLearning Sector

Level 5 Additional Diploma in teachingEnglish (Literacy) in the Lifelong LearningSector

Level 5 Additional Diploma in teachingEnglish (ESOL) in the Lifelong LearningSector

Awarding institutions providing qualifications for teachers of mathematics (numeracy) andEnglish (literacy and ESOL) in the lifelonglearning sector must ensure a potential teachertrainee can evidence the appropriate LifelongLearning UK entry criteria before admittingthem to the qualification programme. Furtherinformation concerning entry processes,assessment and the role of awarding institutionscan be found on page 11.

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Entry criteria for mathematics(numeracy)Level 3 (QCF)Potential trainees must be able to:

• demonstrate the ability to use the functionalprocesses of mathematics whilst engaging withcontexts that require extended mathematicalproblem solving to be resolved.

• think in extended logic chains involving multiplesteps. This should occur both within processingand analysis elements and holistically across allelements of the functional process.

• demonstrate good understanding whenworking in familiar situations; this willenable demonstration of secure processingskills (the ability to use and apply mathematicsin a context) and is often governed, amongstother things, by the degree of familiarity.

• demonstrate development of understandingby investigation in unfamiliar situations; thiswill support demonstration of mathematicaltransferability and development ofmathematical conceptualisation.

Potential teacher trainees must demonstrateboth process skills and content knowledgeand skills in mathematics. These are detailedseparately below. They must evidence each ofthe elements using the extent detailed asappropriate.

Process skills in mathematics are thoserequired to be able to function effectively asusers of mathematics. It is essential that potentialtrainees evidence functionality in mathematics,that is, the ability to use process skills in differentcontexts. Contexts include other specialisms orsituated examples.

Use of content knowledge and skills inmathematics will be demonstrated whenevidencing the elements and extent of thespecified process skills in mathematics. Theseshould go beyond the requirement of study inall existing level 2 mathematics qualifications.

Having appropriate process skills and contentknowledge and skills in mathematics will enabletrainees not only to benefit from their teachertraining programme, but also to build on anddevelop their skills in mathematics throughouttheir programme of study.

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Process skills in mathematics

1. Making sense of situations and representing them

2. Processing and analysis

3. Interpreting and evaluating results

4. Communicating and reflecting on findings

1. Making sense of situations and representing them

Element Extent

1.1 Situations that can be • Recognise situations can be explored beneficially by using analysed and explored mathematicsthrough numeracy • Use interrogation/interpretation by asking questions and

considering responses. This is in order to negotiate and hence recognise the mathematics within situations

1.2 The role of models in • Demonstrate understanding of the purpose and benefits of representing situations mathematical modelling

• Demonstrate understanding of the stages and iterative nature of mathematical modelling including development, trialling, evaluating, amending, applying and representing/displaying

• Demonstrate understanding of the benefits of identifying and applying the most appropriate and efficient mathematical conceptual knowledge and procedures

• Demonstrate that making conceptual links between different areas of mathematics, and differing mathematical procedures, can support mathematical modeling

1.3 Methods, operations and • Make reasoned selections of appropriate mathematical tools that can be used in procedures a situation • Make reasoned selection of tools such as ICT, measuring,

calculating and recording equipment

1.4 The importance of • Select and extract information appropriately from text, numerical, selecting the appropriate diagrammatic and graphical sources in contextual based informationnumerical information and • Research and analyse context to support the selection of and skills to use application of appropriate skills

• Demonstrate understanding of and act on the implications of estimation


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2. Processing and analysis

Element Extent

2.1 The importance of using • Use efficient procedures in familiar situations and coping appropriate procedures strategies in unfamiliar settings, accepting that change to efficient

procedures is necessary for future development• Recognise, visualise and represent mathematical equivalences as

a mechanism for finding/using an appropriate procedure

2.2 The role of identifying and • Identify and justify patterns for summarising mathematical situationsexamining patterns in making • Identify and justify patterns for prediction of trends/changes/ sense of relationships (linear probabilitiesand non-linear situations) • Compare patterns to find potential simultaneous meeting

of conditions

2.3 The role of changing • Identify variables and their characteristicsvalues and assumptions in • Adapt mathematical models to modify/improve the investigating a situation mathematical representation

• Use the analysis of pattern to evaluate particular predicted examples of pattern summaries

2.4 Use of logic and structure • Organise methods and approaches during investigative processes when working towards that allow structured development and testing of models, and finding results and solutions acceptance/rejection of particular methods/operations/tools

• Collaborate and engage in critical debate as a mechanism for development and testing of logic and structure during processing/analysis

• Use extended logic and structures when working in multi-step situations

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4. Communicating and reflecting on findings

Element Extent

4.1 The importance of • Make reasoned selection and use of mathematical language,choosing appropriate appropriate to target audience, including interpretation for language and forms of inclusiveness and accessibility for non mathematicianspresentation to • Make reasoned selection and use of communication communicate results methodologies including numerical, symbolic, diagrammatic and

graphical display• Use communication techniques that display accurately the

development of mathematical processing and analysis, including multi-step processing

• Use oral debate and tactile/kinaesthetic representation appropriately in communicating results

4.2 The need to reflect on • Evaluate efficient/rigorous and coping strategies, comparing any process to consider advantages and disadvantageswhether other approaches • Evaluate the clarity of mathematical arguments to self and audiencewould have been more • Use self and group reflection as a mechanism to address effective mathematical efficiency

• Evaluate impact of conclusions on future investigations

3. Interpreting and evaluating results

Element Extent

3.3 The role of interpretation • Apply numerical/mathematical solutions to original contextof results in drawing • Use solutions to inform future mathematical practiceconclusions • Use derived knowledge to inform practice in context. For

example, work, everyday life and study

3.4 The effect of accuracy on • Demonstrate understanding of the role/application of the reliability of findings approximation across processing/analysis and summary

• Demonstrate understanding of the characteristics of error including the effect of compounding in predictive situations

• Evaluate the impact of inaccuracies in the application of mathematical procedures

3.5 The appropriateness and • Test solutions for appropriateness/accuracy via experimentation,accuracy of results and inverse operations, alternative methods and comparisonconclusions • Recognise errors/misconceptions

• Demonstrate logic in choice of appropriate stage of mathematical interrogation and processing to revisit/revise if results obtained are considered to be inappropriate

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Content knowledge and skills in mathematicsContent knowledge and skills in mathematics gained in differing contexts are equally valid fordemonstrating mathematical process skills. The examples given below are given to demonstrate howindividuals can draw predominantly on skill areas relevant to their own backgrounds to evidenceprocess skills in mathematics.

The following examples are for illustrative purposes only; they are neither complete lists ofrequirements nor the only acceptable contexts. They are limited to those regularly found in relevantmathematical areas of study at level 3.

Example contexts1. Sample mathematics content knowledge and skills for engineeringAreas of study Sections Examples

Trigonometry Ratios, measures • Sine, cosine, tangent, radian measureand techniques • Cartesian and polar coordinates

• Solution of triangles, including sine, cosine rules and area of triangle

• Vector force systems

Functions and • Nature and graphs of oscillatory functionsgraphs • Periodic times, frequency and amplitude

• Phase difference, angle, harmonics

Applications • Metrology/precision measurement, alternating currents, voltages and electrical power, structural design

NB. Sample applications are listed for engineering given the wide ranging nature of this study area.

2. Sample mathematics content knowledge and skills for businessAreas of study Sections Examples

Financial Interest • Compound and annual equivalent ratesmathematics • Depreciation

• Net present values – tables and calculation comparison• Internal rate of return

Annuities • Annuities and perpetuities – tables and calculation comparison

• Loans and mortgages• Regular payments – with use of geometric progressions

Time • Price indices, for example, aggregative and retail price• Time series - additive and multiplicative models,

seasonality• Trends and forecasting

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3. Sample mathematics content knowledge and skills for social sciencesAreas of study Sections Examples

Collection and Survey design • Data sources including use of primary and secondary datadisplay of data • Populations, samples and sampling methodology

• Questionnaire design• Discrete and continuous data characteristics• Large and raw data sets

Graphical display • Standard methods of display and their appropriate selection, comparison and use, for example, histograms, ogives, box and whisker diagrams, probability distributions

• Inappropriate display as a mechanism of distortion

Summarising data Measures of • Mean, median, modelocation and • Graphical and numeric calculationdispersion • Range, semi-interquartile range, deciles

• Mean absolute deviation and standard deviation• Coefficient of variation• Continuous and discrete data types• Comparison of use

4. Sample mathematics content knowledge and skills computingAreas of study Sections Examples

Algebra and its Vectors and • Addition, subtraction and multiplicationapplication matrices • Transformations, translations, inverses

• Determinants• Simultaneous equations

Logic circuits • Boolean algebra –zero/unit rules• Logic design and gates• Commutative, distributive associative laws• Boolean expressions for logic circuits

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Entry Criteria for English (literacy and ESOL)Level 3 (QCF)Potential trainees must be able to:

• apply English language content knowledgeand skills to complex and non-routinecontexts

• transfer their English language contentknowledge and skills from familiar contextsto new situations that may require theadaptation and extension of these skills inorder to attempt the task

• demonstrate that they are able to approachlanguage situations that are well defined, but complex

• make appropriate choices, independently,concerning the most effective communicationmethods and language skills to be used in anygiven situation

• exercise autonomy and judgement incompleting tasks and procedures

• reflect on and evaluate language use in a rangeof situations.

Potential teacher trainees must demonstratecontent knowledge and skills in English. This isdetailed below. They must evidence each of theelements and all the associated extent.

Use of content knowledge and skills in English(speaking, listening, reading and writing) shouldbe evidenced through tasks which require theapplication of that content knowledge andskills rather than through discrete item testing.These tasks should provide evidence of contentknowledge and skills beyond the requirement ofstudy in all existing Level 2 English qualifications.

Element 1.4 (explicit knowledge about language)should be evidenced through discussion of pre-course task material or within other interviewtasks. Providers should look for interest in andability to analyse language while avoiding thedanger of a narrow focus on linguisticterminology. Candidates should be made awareof the need for this prior to interview and giventhe opportunity to prepare.

Having appropriate content knowledge andskills in English will enable trainees not only tobenefit from their teacher training programme,but also to build on and develop their skills inEnglish throughout their programme of study.

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Content knowledge and skills in English1. Speaking and listening

2. Writing

3. Reading

4. Knowledge about language

1. Speaking and listening

Element Extent

1.1 Present, listen and Candidates are able to:respond to information • Express themselves clearly and effectively

• Select appropriate linguistic techniques/ strategies to ensuredesired cohesion

• Recognise, use and respond to non verbal communication• Listen critically and evidence understanding• Recognise speaker’s intention• Listen and respond appropriately

2. Writing

Element Extent

1.2 Compose written texts Candidates are able to:• Plan appropriately according to audience, purpose and situation• Draft, using techniques at text, sentence and word level• Write fluently, coherently and cohesively• Write accurately and legibly using conventions of lexis and syntax, to

include grammar, spelling and punctuation appropriate to purpose• Edit and proof read at text, sentence and word level

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4. Knowledge about language

Element Extent

1.4 Explicit awareness Candidates are able to discuss (with or without accurate use about language of terminology):

• Aspects of the meaning of words• Key features of word formation • Different word classes• Verb forms• The relationship between grammatical form and meaning• Simple aspects of phonology, including identification of phonemes

and stress patterns

3. Reading

Element Extent

1.3 Read and respond to Candidates are able to:written text • Locate, research and select text relevant for purpose

• Use a range of reading skills appropriate to purpose e.g. identifyand compare lines of reasoning and main points

• Recognise and evaluate linguistic devices in texts• Use results of reading effectively• Record own interpretation of texts coherently

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Guidance on entry assessment

Awarding institutions providing qualifications forspecialist teachers of mathematics (numeracy)and English (literacy and ESOL) in the lifelonglearning sector are required to implement aprocess for the evidencing of Lifelong LearningUK entry criteria. This process should enable allpotential trainees to have the opportunity todemonstrate appropriate skills in their chosensubject prior to joining a qualification programme.It should be conducted in a fair and consistentmanner with relevant safeguards in place,including meeting the equality and diversityrequirements of the awarding institution.Assessment should be carried out by trainerswith appropriate knowledge and experience.

A distinction should be made between assessmentfor entry to a qualification programme, andassessment once accepted on to the programme.The latter would include initial assessment toidentify support needs, undertaken once acandidate has been accepted on to a programmeof study.

Awarding institutions should be confident that theassessment criteria stipulated in this document isbeing met and that their centres have anassessment strategy in place that describes theprocesses and procedures they carry out toassess the suitability of all candidates.

Awarding institutions should be aware, and maketheir centres aware, of examples of appropriateassessment materials.

The entry criteria detailed in this document mustbe evidenced by all those wishing to join aqualification programme, unless they meet theexemption conditions described below.

Entry assessment to evidence criteria inmathematics and EnglishAwarding institutions must provide theopportunity for potential trainee teachers toevidence process skills and content knowledgeand skills in mathematics, or, content knowledgeand skills in English through an entry assessment.

Initial assessment activities should include, but notbe limited to, opportunities for the use of:

• extended and suitably complex situations

• collaborative and individual assessment based tasks

• materials situated in varying vocational orother specialisms

• pre-prepared materials (these should besubject to scrutiny regarding validity andauthenticity and must enable demonstrationof currency of skills).

Specifically excluded are:

• self assessment

• short question/multi-choice type assessmentactivities which focus on breadth of personalskills rather than complex extended processskills

• fixed tools with no potential/flexibility foradaptation/selection across cohorts.

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Mathematics entry assessment characteristicsMathematics entry assessment should cover allthe specified elements in the process skills. It is not necessary for all of the extent of theseelements to be covered within any oneassessment. However, minimal coverage ofextent against any one element would bedeemed insufficient. There is no requirementfor the process elements to be evidenced usingall the main mathematical skill areas.

It is expected that the entry assessment formathematics will include a significant proportion ofrecognised level 3 personal skills in mathematics,although others more regularly acquired at level 2and below may also be used in activities. Potentialtrainees are required to demonstrate that theyhold mathematical skills which go beyond therequirement of study in all existing level 2mathematics qualifications.

Entry assessment should be based in familiarcontexts or situations, but should also includeaspects of the unfamiliar.

English entry assessment characteristicsEnglish entry assessment should cover eachelement of the content knowledge and skills andall of the associated extent.

ExemptionsThose intending to undertake an SVUK endorsedsubject specific diploma qualification for teachersof mathematics (numeracy) who hold thequalifications detailed below may be exemptedfrom any entry assessment in mathematics.

• BA or B.Sc or B.Ed. or higher degree inmathematics

• A’ Level mathematics grade A-E gained sinceSeptember 2004.

There are no exemptions for those intending toundertake an SVUK endorsed subject specificdiploma qualification for teachers of English(literacy and ESOL).

Accreditation of prior learningNo other qualifications exempt an individual fromthe requirement to undertake an entry assessmentfor English or mathematics. However, it isacknowledged that a broad range of qualificationswill have developed the skills detailed in the entrycriteria. Therefore individuals may wish to provideevidence of appropriate skills through providers’accreditation of prior learning processes.

Those unable to evidence the entry criteriaPotential trainees who, following initialassessment procedures, are unable to evidencethat they can fully meet the entry criteriaelements, should be advised of appropriateroutes to enable them to develop the relevantskills in mathematics or English.

Lifelong Learning UK

BELFAST2nd Floor, Alfred House, 19-21 Alfred Street, Belfast, BT2 8EDTel: 0870 050 2570 Fax: 02890 247 675

CARDIFFSophia House, 28 Cathedral Road, Cardiff, CF11 9LJTel: 029 2066 0238 Fax: 029 2066 0239

EDINBURGH CBC House, 24 Canning Street, Edinburgh, EH3 8EGTel: 0870 756 4970 Fax: 0131 229 8051

LEEDS 4th Floor, 36 Park Row, Leeds, LS1 5JLTel: 0870 300 8110 Fax: 0113 242 5897

LONDON Centurion House, 24 Monument StreetLondon, EC3R 8AQTel: 0870 757 7890 Fax: 0870 757 7889

Email: [email protected] and Advice Service: 0300 303 1877

www.lluk.org

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Ref: 2000910.053

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