inTuition Maths supplement

inTUITION MATHS An inTuition supplement exploring developments in mathematics education and training

Summer 2018 set.et-foundation.co.uk

Making maths bear fruit for learners Teachers need more opportunities to ensure this vital subject thrives p3

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Boosting your Helping students knowledge to teach with the most inspiring maths severe needs

How to seize the digital opportunities

SKILLSETS P6

TECHNOLOGY P14

SEND P10

WELCOME

CONTENTS

THE PLUS SIDE OF TEACHING MATHS

An inTuition supplement exploring developments in mathematics education and training

MORE WELL-QUALIFIED TEACHERS WILL ENCOURAGE MORE YOUNG MATHS LEARNERS

Summer 2018 set.et-foundation.co.uk

Making maths bear fruit for learners Teachers need more opportunities to ensure this vital subject thrives p3

ER R POST COVE -OUT CK PULLSIDE BA IN

Helping students improve their maths is a challenge, and the thought-provoking articles in this supplement aim to give you extra inspiration. By David Russell

inTUITION MATHS

OVERVIEW

Boosting your Helping students knowledge to teach with the most inspiring maths severe needs

How to seize the digital opportunities

SKILLSETS P6

TECHNOLOGY P14

SEND P10

Cover illustration: Cameron Law

Overview 3 Making sure maths advances

Ensuring maths advances as a vital subject in further education cannot be done in a silo – teachers need opportunities to develop their knowledge, skills and confidence, argues The Royal Society’s Professor Frank Kelly

Practice 4 Testing ‘Teaching for Mastery’ Cutting through the jargon

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he challenge of helping learners with their maths skills is not new. Whatever an individual’s circumstances or aspirations, the need to understand and work with numbers is a core part of their life in our society.

The rights and wrongs of curriculum in schools, exam design, teaching approaches and so many other factors have been much debated in recent years, and there is a growing alarm that our young people are lagging a long way behind those in other developed education systems around the world.

Whatever the reason, education professionals in our sector are charged with supporting students to succeed, whether in basic skills for adults, Functional Skills or GCSE resits. We need to understand how best to help them, whether by overcoming previous misconceptions, boosting their confidence or by wholesale ‘re-teaching’.

It is no small task and, while exam results for GCSE resits aren’t where any of us might like, teachers across the country are engaged in a professional and pedagogic drive to help their students succeed. The Education and Training Foundation (ETF) has, since its inception, worked to help support the workforce in this challenge. We have delivered over 5,000 maths training courses across the country with a range of expert organisations. Our online support modules in maths and English have been accessed over 75,000 times.

The Professional Standards for Teachers and Trainers, on which the work of the ETF and the Society for Education and Training (SET) are built, make specific reference to supporting learners with their maths and English needs. We do a great deal to support our profession in meeting this long-standing challenge, but there’s always more to be done. While I would recommend you take the time to look at the range of CPD and support we have to offer you, teachers are busy people, and sometimes it takes a spark to get things going.

It’s a great pleasure to introduce this supplement to inTuition. It’s a first for the ETF and SET, bringing together ideas and thoughts from our work across the sector that we hope will be interesting, informative, challenging and, above all, thought-provoking. We could never hope to fully address a complex and multi-layered challenge like this in a short publication, but I hope we can spark debate, inspire further reading and research, and, at the very least, erect a few signposts about what other professionals are doing that might support our learners on this often challenging part of their educational journey.

Skillsets 6 Expanding know-how to teach Post-16 Maths inspiringly The benefits of mentoring Embedding Practical steps for teachers

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SEND 10 A partnership to help students Motivation Making resits rewarding

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Learning tech 14 Exploring the opportunities of digital technology Resources

David Russell is chief executive of the Education and Training Foundation

inTUITION EDITORIAL

membership.communications@etfoundation.co.uk The Society for Education and Training, 157-197 Buckingham Palace Road, London SW1W 9SP. Editor: Alan Thomson alan@createpublishing.uk.com Editorial readers: Norma Honey, Cathy Smith, Sue Southwood, Maggie Gregson.

2 SUMMER 2018 • InTUITIONMATHS

PUBLISHING

The inTuition Maths Supplement is produced and published on behalf of The Society for Education and Training by: Create Publishing Ltd, Anchor House, Bath Road, Lymington SO41 9GH Advertising: 020 3092 5001 Printed by: PCP Ltd, Telford The views expressed in this publication are not necessarily those of the Education and Training Foundation or the Society for Education and Training.

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athematics and quantitative skills are a necessary component of many disciplines, ranging from the sciences to humanities.

The availability of large data sets is changing the way many disciplines approach questions and solve problems, all requiring greater levels of mathematical skill and confidence.

Mathematics is also a rich discipline in its own right – with individuals working on both pure and applied mathematics.

The Royal Society has long appreciated the role of mathematics in education, instilling financial capability, problemsolving and tools for addressing real, practical issues. That’s why in 2014 the Society published its Vision for science and mathematics education, with the ambitious aim that all young people study mathematics up to the age of 18.

A levels will not suit all learners and the Society is pleased to be involved in developing the mathematical framework for the new T levels.

We have heard industry call for greater mathematics and quantitative skills among its current and future employees.

It is essential that the right messages

REFERENCES If reading your digital version of the Maths supplement, then simply click on the Google links below. Otherwise all papers can be found on The Royal Society website.

• Vision for science and mathematics education goo.gl/vPVM77 • Beginning teaching: best in class? goo.gl/5BGGoW • Professional learning for all teachers of mathematics goo.gl/7DxX9i • Read the Maths Snapshot papers at goo.gl/45k3G2

are sent about the importance of mathematics during, and out of, school as well as the wide range of opportunities available to young people who are confident in maths.

As chair of The Royal Society’s Advisory Committee on Mathematics Education (ACME), I am privy to both industry and tertiary education concerns about mathematics and quantitative skills.

However, encouraging more young people to study maths must not be done in a silo. It will require a greater number of well-qualified and supported teachers.

In 2015 we published Beginning Teaching: best in class? It recognised that initial teacher education programmes varied greatly, so it detailed initial first steps towards a strategic plan for the ITE of teachers of mathematics: • Investment in data collection, analysis and monitoring • Development of clear lines of accountability • Mapping initiatives and identifying gaps to develop an action plan.

In 2016 the Society convened an expert panel to develop the report, Professional learning for all teachers of mathematics.

The continued professional development and training of teachers is integral to the success of their pupils.

We divide the knowledge needs of teachers of mathematics into two categories: knowledge about the subject and knowledge about teaching it.

Teachers need opportunities to continue to develop in each area to ensure they have the knowledge, skills and confidence needed to excel. Everyone involved in mathematics education has a role to play in ensuring they support the development of teachers.

FURTHER READING The Royal Society’s remit covers all aspects of mathematics education policy, including supporting inspirational maths teaching, and professional development for maths teachers.

The Society’s Advisory Committee on Mathematics Education (ACME), chaired

by Professor Kelly, advises the Society on mathematics education policy.

ACME’s current priority areas include technical education and providing advice on the mathematical and computational skills components of new technical education pathways in England. A Maths Snapshot paper, Teachers of maths: supply, training and development, produced by ACME in 2014, noted several points about the training and development available to maths teachers, including: • There are no guidelines about progression from novice to expert teacher of maths.

• Teachers’ access to maths-specific professional development is variable and geographically inequitable.

• There is no system-wide quality assurance of professional development.

• There is an urgent need to recruit and retain more maths teachers in secondary and further education.

• A strategy for recruiting teachers of maths to further education is needed.

• Salaries and other incentives, like job satisfaction, should reflect the growing market for mathematical skills.

Professor Frank Kelly is professor of the mathematics of systems at the University of Cambridge. He is a Fellow of The Royal Society and chair of the Society’s Advisory Committee on Mathematics Education (ACME). He was awarded a CBE for services to mathematical science in 2013.

InTUITIONMATHS • SUMMER 2018 3

PRACTICE

CALCULATING THE BENEFITS OF ‘TEACHING FOR MASTERY’ IN FURTHER EDUCATION AND TRAINING Teaching for Mastery (TfM) is making an impact in primary and secondary schools. Built on the premise that all students can achieve, could it work for under-achieving post-16 learners, asks Norma Honey

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here is much interest in the Teaching for Mastery (TfM) approaches in mathematics, and in primary and secondary schools that use a mastery approach, significant progress is being observed.

The question for us is whether there is merit in TfM approaches for GCSE resit and other programmes post-16.

It is well known that many students resitting their maths GCSE have a negative attitude towards the subject.

Many feel like failures, and have poor attendance records and little commitment to ongoing study.

How might TfM support both teachers and students to effect some change in this situation?

At the heart of TfM is the belief that there is no such thing as a ‘maths gene’. The premise is that all students can achieve and that teachers, through careful planning of lessons and selection of resources, can support students in their learning.

Carefully drafting and planning lessons are key. Effective use of resources and questioning which support deeper understanding of topics, combined with using visual representations and manipulatives (physical aids to mathematical understanding), can help build confidence and understanding, as well as enrich formative assessment.

For instance, the Singapore bar model has proved to be very useful to illustrate basic maths (see diagram).

The bar model helps build confidence in learners – doing things differently, 4 SUMMER 2018 • InTUITIONMATHS

6 4 and showing success, is important for students who feel like failures.

A small project for the Education and Training Foundation (ETF) is supporting a trial of mastery approaches, such as the bar model, in an FE college.

While it is a small trial, early findings are promising. Feedback from students trialling an algebra resource appear positive in both sense of achievement and attitude. Students became more resilient when attempting different questions, where previously they would not have attempted them.

TfM, as implemented in schools, supported by the National Centre for Excellence in the Teaching of Mathematics (NCETM), may not be perfectly adapted for resit students in further education and training. FE and training staff have just eight months to turn students around and make progress.

However, there are certainly aspects

of the TfM approaches which can help teachers to engage students with mathematical concepts they have been over many times. It does require a change in the way the resit is taught, and probably an end to schemes of work which attempt to reteach the whole specification.

The following five big ideas are the basis of the NCETM approach. They are developed over time in a school setting. While time is limited in post-16, an understanding of how these can be accommodated into the resit curriculum is helpful when considering how to structure the teaching and learning.

• Coherence Connecting new ideas to concepts that have already been understood, and ensuring that new ideas are used again in next steps of learning – all steps being small steps.

• Representation and structure Representations used in lessons expose the mathematical structure being taught, the aim being that students can do the maths without necessarily referring to the representation.

• Mathematical thinking If taught ideas are to be understood deeply, they must not merely be passively received but be worked on by the student: thought about, reasoned with and discussed with others.

• Fluency Quick and efficient recall of facts and procedures, and the flexibility to move between different contexts and representations of mathematics.

MATHS JARGON-BUSTER If taught ideas are to be understood deeply, they must be thought about, reasoned with and discussed

• Variation Varying the way a concept is initially presented to students, by giving examples that display a concept as well as those that don’t. Also, carefully varying practice questions so that mechanical repetition is avoided, and thinking is encouraged.

Some of these stand out as being relatively easy to incorporate into FE and training settings, and would provide a different ‘look’ at well-known topics which have caused difficulties for students.

Representation and structure, for example, is an area which can be applied to most areas of mathematics, and students should be encouraged to draw pictures and diagrams when looking at problems. And careful selection of examples can determine the learning required and reduces the need for ploughing through worksheets.

In conclusion, I believe that there is a place for TfM approaches to be incorporated in GCSE resits. More investigation is needed and further trialling to develop an appropriate model for further education and training. There is, of course, a need for CPD for teachers to gain the most benefit for their students.

Norma Honey is an educational consultant and is an ETF regional specialist lead (maths) for the East Midlands. She is a Member of SET.

Teaching, like all professions, is full of jargon and specific terms, especially in relation to pedagogy and subject-specific pedagogy.

We’ve compiled a short glossary of just a few of the terms you may come across generally in teaching, and specifically in maths.

GENERAL PRACTICE TERMS

• Action research = a form of continuing professional development (CPD) based around enquiry questions which, when answered, benefit the performance of the practitioner and build community knowledge.

• Coaching = a one-to-one relationship between an expert coach and a learning coachee, improving the professional performance of the coachee, while also benefiting the coach.

• Community of learning = a group of practitioners with shared learning aims who support each others’ learning goals.

• Contextualisation = using real life/authentic examples to teach specific concepts.

• Embedding = finding examples of maths in a vocational area e.g. using ratio and proportion in hairdressing.

• Evidence-informed = based on, or coming from, research.

• Mentoring = a one-to-one relationship between a more experienced mentor and a less experienced mentee. A mentor aims to support and empower the mentee with advice on their professional development and other aspects of professional life.

• Modelling = demonstrating or illustrating a particular method/approach.

In mathematics it also means choosing the maths concepts and techniques to represent a word problem.

• Scaffold practice = to give more steps to solution.

MATHS SPECIFIC TERMS

• Algorithm = a step-by-step procedure to answer a calculation.

• Bar modelling = an approach to maths which allows learners to draw and visualise mathematical concepts to solve problems. Commonly used in Singapore and other parts of SE Asia.

• Bridging = a mental method of calculation, which may use a number line. Involves jumping up to and across tens or hundreds, e.g. 36 + 47 might be calculated as: 36 + 40 = 76 + 4 = 80 + 3 = 83 • Chunking = a method used for dividing larger numbers which involves repeated subtraction of the divisor and multiples of the divisor.

• Connected teaching = an approach which emphasises the interconnectedness of maths, and values discussion of different methods of calculation and common misconceptions.

• Fermi question = a question which requires making assumptions and estimates to arrive at an answer that may seem difficult or impossible to answer precisely, but encourages mathematical thinking, e.g. how many hours will you spend asleep during your lifetime?

• Mathematical reasoning = systematic thinking that enables a learner to make use of their other mathematical skills.

• Misconception = a mistake in maths that indicates faulty reasoning or a lack of conceptual understanding.

• Number talk = a discussion in which learners verbally share their methods of performing a calculation. Helps promote mental maths and the importance of being flexible with computational methods.

• Partitioning = a number is split up into component parts. It can help develop understanding of place value and move learners toward the ability to work in columns when adding, subtracting etc.

Thanks to Norma Honey, Cathy Smith, Steve Pardoe and Sue Southwood. for their contributions.

InTUITIONMATHS • SUMMER 2018 5

SKILLSETS

Experienced teachers can benefit just as much as beginners from mathematical knowledge for teaching (MKT), with big plusses for their expertise and professional development, says Dr Cathy Smith

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hen you have been teaching for a number of years, you will have got to grips with the initial knowledge you need as a teacher. This is when you might turn your attention to developing your mathematical knowledge for teaching (MKT).

In the research literature, MKT has mainly been studied to educate beginner teachers. But a more interesting question is how teachers can use this research to think about their own expertise and professional development.

One framework I have found useful is Deborah Ball’s ‘knowledge egg’ (named after an egg-shaped diagram, right, showing six categories of teacher knowledge (Ball, Thames, & Phelps, 2008)).

The framework was derived from studying hours of video of classroom teaching in the US. It starts from the commonly accepted distinction that teachers do not just need subject content knowledge, they also need pedagogic REFERENCES

•B all, D. L., Thames, M. H., & Phelps, G. (2008).

Cont Journal of Teacher Education, 59(5), 389–407.

•S hulman, L. S. (1986). Those Who Understand: Knowledge Growth in Teaching.

Educational Researcher, 15(2), 4–14. https://doi.org/10.2307/1175860 •S mith, C., Golding, J., & Bretscher, N. (2018). Special Issue: Learning to Teach on Advanced School Mathematics Pathways.

Teaching Mathematics and Its Applications, 37(2).

6 SUMMER 2018 • InTUITIONMATHS

UNDOING PROBLEMS 80 x 30 ÷ 100 = 24

70%

30%

100%

80 x 0.70 = £56

80 - 24 = £56 7 x 8 = 56

content knowledge (Shulman, 1986).

Ball’s team broke down pedagogic content knowledge even further, and applied it to mathematics. Can we apply them to a post-16 context?

Pedagogic content knowledge has three sub-categories: knowledge of content and students (KCS); knowledge of content and teaching

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8

8

£80

(KCT), and knowledge of content and curriculum (KCC).

Experienced teachers rapidly build KCS, but this can also come from wider reading. KCT comes from knowing the words and representations that are effective in the classroom, and how to sequence and organise them.

In the percentages example above,

MATHEMATICAL KNOWLEDGE FOR TEACHING (MKT) Subject Matter Knowledge

Common content knowledge (CCK) Horizon content knowledge (HCK)

Pedagogical Content Knowledge Knowledge of content and students (KCS)

Specialised content knowledge (SCK)

Knowledge of content and teaching (KCT)

Knowledge of content and curriculum (KCC)

2010 Mathematics Teaching and Learning to Teach, School of Education, University of Michigan, Ann Arbor, MI 48109, mtlt@umich.edu

a coat costs £80. The shop then offers 30 per cent off. Work out the new cost.

Knowing that most students prefer to calculate 30 per cent first, then subtract it, would be KCS (knowledge of content and students). However, knowledge of content and teaching (KCT) is knowing that one way to encourage students towards the one-step method is to set ‘undoing’ problems – 70 per cent of a number is 56; what is the number?

Finally, knowledge of content and curriculum (KCC) helps us focus our teaching on what is really needed. For example, students in (AQA) Core Maths and A level, both need to know about exponential functions.

But Core Maths students will only meet e²x or e-x while A-level students could meet e²x+3.

Starting with mathematical content knowledge, the framework proposes three sub-categories: common content knowledge (CCK), specialist content knowledge (SCK) and horizon content knowledge (HCK). These are all forms of mathematical knowledge, but they are distinguished by their purpose.

CCK is what you learn by taking mathematics A-level or an Open University mathematics module. It is mathematics for its own sake, to help you understand your subject.

SCK is the kind of mathematics that you need precisely because you are a teacher. For instance, being able to put mathematical expressions into words.

HCK is the mathematical knowledge that lies outside the curriculum, but which helps make sense of it by showing its developments or its applications.

These kinds of teacher knowledge are closely interlinked but they are all mathematical. One way of enriching professional learning is to use these categories to audit the outcomes, making sure you have covered something in each of these areas.

MENTORING SWAPPPING GOOD IDEAS HELPS TEACHERS ALL ROUND Mentoring can help those new to teaching who may find it a particular challenge to motivate learners taking GCSE resits or studying Functional Skills.

Emily Spall, a maths tutor at Develop Norwich – part of the Develop group, a not-for-profit organisation delivering education and training in Eastern England – and John Greenwood, head of the Norwich centre, talk about the benefits of mentoring.

iStock

HOW TEACHERS CAN EXPAND THEIR KNOW-HOW TO TEACH POST-16 MATHS INSPIRINGLY

Emily As a new teacher, it was overwhelming trying to apply the freshly learnt theories, research, policies and procedures to the everyday environment of my classroom.

Maths has such a bad reputation. I often found it difficult to face a class full of students who had become disengaged with maths due to their previous experiences.

John helped me translate my enthusiasm for maths into my lessons. He reminded me that I wasn’t going to convert every student into a mathematician, but I could give them a supportive environment where they could learn.

I would always come away from meetings with John feeling like I had come up with a solution that I was excited to try. In this way teaching became more about testing and trialling things instead of searching for a winning formula.

John While technical aptitude in your specialist area is essential, there are so many more strands to teaching that have to be experienced in order to develop.

Passion, creative thinking, acting, organisation, being flexibly personable and being able to critically reflect are all fundamental attributes of a successful teacher.

Mentoring is about the: ‘what if’; ‘that was a great idea’; ‘don’t worry, start fresh tomorrow’ and numerous other discussions.

The key point I try to pass on to mentees like Emily is that teaching does not have a set template for success.

Refining practice is one of the most satisfying parts of the profession.

Mentoring is also a two-way process. It can sometimes be easy to become complacent, but the role of mentor forces you to reimagine and review; as well as bringing to light new developments in teaching theory.

Dr Cathy Smith is a senior Lecturer in the School of Mathematics and Statistics at the Open University, and leads the Mathematics Education team.

InTUITIONMATHS • SUMMER 2018 7

EMBEDDING

HELP LEARNERS TO DEVELOP THEIR MATHS THROUGH EFFECTIVE EMBEDDING Vocational tutors can really make a difference to learners’ maths skills and their overall success on courses. Gail Lydon discusses some practical steps and how teacher teamwork is so important

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e continue to debate the embedding of maths into programmes because it is a complex issue.

Have vocational and other non-maths tutors the skills they need to support learners’ maths skills? Are they already busy enough getting through their own course objectives? Isn’t it the job of the maths specialist staff to do this?

There are even discussions about the word ‘embedding’ itself. Some prefer supporting and developing.

What we do know from research is that vocational tutors (often a shorthand for all those who are not maths specialists) can have a significant impact on learners’ maths skills. We also know that when vocational tutors support maths skills development their learners do better in their vocational courses too.

So what to do? Remember, said Dylan Wiliam, that “small changes are better than big changes because when you make big changes things go wrong, classroom discipline falls apart and you go back to doing what you know how to do, so you have to make very small REFERENCES •W iliam, D, (2006) Assessment for Learning: why, what and how. IOE. •V isit Jo Boaler’s website at www.youcubed.org •T he ETF’s assessment for learning guides can be accessed here goo.gl/7ayFhv •Y ou can read the former Institute for Learning’s report, IfL research to inform the work of the Commission on Adult Vocational Teaching and Learning, at goo.gl/qjkTFE 8 SUMMER 2018 • InTUITIONMATHS

incremental changes and not change more than one or two things”.

Embedding may mean some of the following: •P resenting positive messages to learners about maths within their courses and in their future careers.

When maths is seen as an important element of a learner’s programme, then learners perform better. To give positive messages a tutor must be positive themselves and many non-maths specialists are nervous about their own maths skills.

•M aths and vocational tutors sharing their schemes of work – a collaborative approach.

•V ocational tutors being clear about the maths skills their learners need to be successful in their vocational context (and sharing this with the maths specialists).

•V ocational tutors using learners’ maths initial and diagnostic assessment results to ascertain where learners may need support in their vocational course because of maths content.

Jo Boaler, professor of mathematics education at Stanford Graduate School of Education, suggests four boosting messages about maths: everyone can learn maths to high levels; believe in yourself; struggle and mistakes are really important (this is when learning happens); speed is not important.

Vocational tutors know their learners and have a special relationship with them because of their vocational expertise, so they can help their learners overcome

the fear of maths that is often present.

Vocational tutors are natural problemsolvers and can support their learners to persevere when the going gets tough. The Assessment for Learning: effective practice guidelines can be used to support these key messages.

But here is a word of warning about embedding, taken from a 2013 research report from the former Institute for Learning (IfL) that fed into the Commission on Adult Vocational Teaching and Learning (CAVTL).

“Embedding, for many vocational tutors, means teaching by stealth, disguising the functional skills – this carries a strong possibility that the skills disappear altogether.”

Maths skills need to be made explicit if learners are to be able to apply them in a range of contexts. This is where the teamwork of vocational and maths specialists is key.

If you are concerned about your maths knowledge and skills and feel you need to brush up, then visit Foundation Online for a list of courses.

Gail Lydon is the Yorkshire and Humberside Regional Specialist Lead (RSL) for maths and English, and she has supported teachers in the development of maths and English since 2000.

CASE STUDY FIGURING IT OUT IN A FUN AND INFORMATIVE WAY

CASE STUDY MAKING MATHS ACCESSIBLE FOR BLIND SCHOOL LEARNERS

By Nicola Tomlinson Adult Education Wolverhampton has a strong culture of staff development and quality improvement.

Many opportunities to develop English skills in a natural way are already available to staff and students. Staff can clearly see where English is present in everyday life. However, this is not the case with maths.

We decided to work on making maths relevant with our CPD module, ‘Maths and Where to Find it’.

Sessions are activity based and include: • Descriptions of shapes using maths terms • Identification and exploration of a favourite number – is it odd or even, is it a prime, a square or a square root?

• The use of photographs depicting everyday situations such as retail car parks and food preparation.

Through these activities teachers are able to recognise that they have maths knowledge which they can share with students in a fun and informative way. The teachers no longer see maths as “I can’t do maths”; they are now thinking of how they can introduce maths seamlessly into technical classes. Staff are now asking for additional training, resources and glossaries to develop their maths language skills.

By Albert Pitcher When I first went to the Royal National College for the Blind (RNC) Hereford in 2016 to find out more about being a mathematics teacher for the visually impaired, I asked how you teach a blind student about quadratic waveforms.

Kate Stevenson (my future mentor) smiled and, without fuss, demonstrated how it was done with the tactile method, using a raised centimetre grid, pins, corkboard, elastic bands and wiki sticks.

Simple but effective, and it appealed to my technical background. I duly applied for the maths teacher job and got it. Kate and the team then set up a very steep learning curve for me to be able to enhance my teaching and technical skills to the level needed to assist students access and succeed in mathematics at RNC. Mathematics is taught from entry level to A level at RNC and it is fair to say that each student has their own unique challenges to access, understand and successfully use the maths they are learning.

VI (visual impairment) ranges from students who have some useful sight to those who have no sight.

Some students also have other challenges in the form of being on the autistic spectrum, hearing impairment and physical impairment.

So the challenge at RNC is not just helping students learn and use the mathematics, but also adapting standard texts and resources into a medium they can use to learn from.

Here are a few approaches.

• Producing paper resources in large print up to font size 36 (Arial is the normal font used).

• Using adaptive software like Jaws, Supernova, zoomtext and NVDA. • Producing tactile diagrams that interpret mathematics diagrams.

• Producing models of 3D shapes.

• Producing text resources in Braille.

It is common practice to have a class of five students who use a range of adapted resources as the lesson progresses.

The same approach applies when examinations come around and it is a major logistical exercise to ensure the students have all they need (including readers and scribes) so they can have the best chance of success.

Yes, it is very busy, but totally worth it as the students want to succeed and very often do. In fact we have one student (having gained A* in maths last year) potentially going to Oxford University after this year.

CASE STUDY ‘THE MORE WE KNOW, THE MORE EFFECTIVE WE CAN BE AS TEACHERS’

By John Cooper Being a busy maths teacher, I was rather trepidatious when the opportunity arose to engage with research through the Education and Training Foundation (ETF) and SUNCETT. But once I started to speak with people who understood how young people learn, and read a little about the theories surrounding learners’ perceptions of maths, I was able to implement simple changes in the classroom. As a result, we’ve improved outcomes for some of our learners and it’s enabled us to understand why our working harder in the classroom might not always equate to a better lesson.

Discovering the mastery concept of teaching maths and developing our ‘Essential 8’ programme have enabled me to connect with colleges using the resources and to present our research in the UK and Finland.

Differentiating by depth, rather than difficulty, means learners can move forward together collaboratively. It can transform the learning experience and even reduce maths-anxiety for some. Thanks to research, I understand more about my learners and appraise teaching approaches in an informed way. Take a look at Dr Helen Drury’s work on mastery as a start. The more we know, the more effective we can be.

And that has to be a good thing for our learners.

Go to cooperstutors.com for more about the Essential 8 programme.

Nicola Tomlinson is teaching, learning and assessment manager (Integration and Initial Assessment) at Adult Education Wolverhampton.

John Cooper teaches GCSE maths at Sussex Downs College. He is a Year 2 student on the ETFSUNCETT MPhil course.

Albert Pitcher is a lead mathematics teacher at the Royal National College for the Blind.

InTUITIONMATHS • SUMMER 2018 9

SPECIAL EDUCATIONAL NEEDS & DISABILITIES

A PARTNERSHIP TO HELP STUDENTS WITH THE MOST SEVERE NEEDS

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ince January 2015 Achievement for All has been working with 22 further education colleges, including specialist provision, sixth form and general FE colleges.

Our Achieving Further Programme is specifically designed for the post-16 sector and focuses on students with the most severe and complex needs, students whose life chances may otherwise be limited and those who have disengaged with education in some way.

Delivery is through a strong partnership between an achievement coach and a nominated college leader, working closely with the staff teams and developing teaching and support practices.

Key findings in maths teaching and learning:

•M aths can be affected greatly by language and comprehension difficulties.

Effective communication between deliverers of both maths and English is essential to learners’ success.

• Teachers must learn about their learners’ needs and deficits early on to plan delivery and support. If learners have

NOTES Achievement for All is a not-for-profit charity that aims to improve outcomes for children and young people regardless of their background, challenge or need.

The Achieving Further Programme framework is structured around four interdependent and interrelated elements: •L eadership and Management •T eaching and Learning •E ngaging with learners, their parents or carers and others •W ider outcomes and opportunities including employability skills.

10 SUMMER 2018 • InTUITIONMATHS

a disability or learning need hindering sequencing, logical reasoning and spatial awareness, these can impact on maths ability and learning strategies.

• Your speed of delivering is crucial to understanding. But if learners have comprehension challenges and/or delayed language, then this really is a basic need for learning.

• Learning support should be supportive but also encourage as much independence as possible. Often if learners look as though they are struggling to solve a problem, a learning support assistant (LSA) can step in too quickly or give too much help, which can hinder learning/progress and give a ‘false reading’ of capability (in both directions).

• Absence and missing vital building blocks in maths can render all other lessons useless. The gaps need to be filled, and you must not assume learners will be able to pick it up.

Generic findings:

• LSAs vary greatly in ability and we need to focus on this area. Support goes from too hands-off to too hands-on. Learners, particularly in post-16, need to gain as much independence in all areas of their education and life as possible, especially if we want them to progress further in education and training. Many senior leaders feel this is an area of concern.

• Written work needs to be adapted appropriately for learners with poor hand function both in handwriting and use of a keyboard. This can slow learners down, and often the correct equipment may not be accessed. Negotiating education, health and care plans (EHCPs) at the outset is essential. The set-up for a learner with SEND must

start from pre-enrolment. But too often mainstream or vocational teachers are nervous of adaptations and their uses as they are not trained or fully supported.

• Verbal communication for some learners may be challenging and teachers tend to learn as they go, with little training in speech and language therapy (SLT) or communication techniques. This can leave learners and teachers frustrated.

Evaluative feedback

Here are a couple of comments from nominated college leaders involved in the Achieving Further Programme.

“In a very large, two-campus FE college, the only students achieving target results in maths in the last academic year were the ones working with us. All other students were below target and we are repeating this with new students this year.” Assistant principal “In a sixth form college where the team had lost motivation, student progress, achievement and retention had slipped and the team were stuck. After we spent a year working with them they reported 100 per cent achievement, 100 per cent progression and 100 per cent retention.”

Assistant principal To find out more about the Achieving Further Programme, and other Achievement for All programmes, visit goo.gl/SXmzA4

Derwen College

The Achievement for All charity is working to develop teaching practices that benefit young people whose life chances may otherwise be limited

By Professor Sonia Blandford and Lainy Russell

CASE STUDY BOOSTING ‘SEND’ LEARNERS’ SKILLS

CASE STUDY A THEMED MATHS WEEK

By Iain Evans and Tim Galashan The mainstream maths curriculum assumes that all children on entering the education system already have an innate sense of number value which is used to underpin further acquisition of numeracy skills.

Within our Functional Skills sessions at Derwen College we have recognised that many adult learners with SEND do not possess this innate sense of ‘numerosity’, and have significant gaps in their basic maths skills. This impacts significantly upon their confidence and resilience when working with numbers.

These learners struggle to work with number skills beyond counting using fingers or objects and rely heavily on these strategies to accomplish any given calculation. This limits development of higher-level number skills such as grouping, comparing, doubling and multiplication – limiting learners’ ability to develop many transferable skills required in independent life.

For the past two years, we have been involved in Education and Training Foundation (ETF) research projects with Sunderland University, trialling the Numicon system as an approach to boost basic maths skills for learners with SEND. Commonly used within the primary curriculum, Numicon is designed to strengthen learners’ understanding of basic mathematical concepts through the use of different coloured shapes used to represent numbers. Each number from 1 to 10 has an individual shape, colour, size and weight, which the learner can internalise more readily than the abstracts of digits and the linked words we use to name them.

There are only 10 Numicon pieces, which makes internalisation of the system simpler. Any number higher than 10 is a combination of the pieces, which helps to reinforce how larger numbers are made up (adding, doubling, multiplying).

We use scales to reinforce value, as learners can place pieces in each side and see which one is worth more or less. Learners can also progress on to adding, and checking their adding, using the scales.

For example, Jimmy thinks 5 and 4 make 10, so we put a 10 piece in one side and try to balance it with a 5 and 4. This way he can see that he has come up short and needs to try again, or experiment.

This exploratory approach is much better than the failure of incorrect counting or the answer ‘no’.

By Ruth Perry Each year, during the spring term, Natspec (the national membership association for organisations offering specialist further education and training for students with learning difficulties and/or disabilities) runs a themed Maths Week.

The event offers post-16 specialist providers the chance to share ideas and effective practice. Learners from across the sector are also invited to enter a competition, as individuals or groups, which allows them to showcase their maths skills.

Now in its fourth year, our Maths Week was originally introduced in response to providers’ concerns that, at times, they were struggling to make maths meaningful and accessible to learners with SEND, and to find creative ways to embed maths into the curriculum.

A themed week, where the spotlight is turned on maths, allows practitioners to promote maths across their organisation and the curriculum, making colleagues more aware of the rich opportunities for maths learning.

It also helps learners understand the relevance of maths to their learning and their lives.

The focus this year is on developing maths skills in and for the workplace. We wanted to use the week to get three broad messages across: • Maths skills are invaluable in the workplace; • Being effective in a work-related context can help learners realise that they are capable of ‘doing maths’; • If more young people with disabilities are going to gain employment, providers need to equip them with a wide range of skills for work – including maths.

The week, called ‘Work it Out!, ran from 5 to 9 March and practitioners used social media to share what they and their learners were up to. The range of maths skills and work-related contexts on display was richly varied.

They included interpreting timetables, handling money at the till, and counting and sorting eggs from a chicken coop.

Over the four years Maths Week has been running, practitioner confidence in developing learners’ maths skills has grown, and the event is now as much about celebrating the diverse range of good practice in the sector as it is a chance to tackle challenges together.

Congratulations to this year’s winners of the Maths Week competition, who were students from Royal College Manchester, part of The Seashell Trust.

Providers interested in taking part in next year’s Maths Week should send their contact details to info@natspec.org.uk

Iain Evans is a Functional Skills teacher and Tim Galashan is a Functional Skills maths lead. Both work at Derwen College, which is a specialist independent college for learners with learning difficulties and disabilities. In 2016, Derwen became the first specialist college to receive an Ofsted Outstanding Grade 1.

REFERENCE Professor Sonia Blandford is chief executive of Achievement for All. Lainy Russell is their post-16 programme manager.

• Sir Peter Williams (2008). The Independent Review of Mathematics Teaching in Early Years Settings and Primary Schools is available at goo.gl/SdMkq6 • Some free resources on Numicon from the Oxford University Press are available at goo.gl/ufh8dY

Ruth Perry is policy officer for Natspec. She previously taught in schools and has worked for the Qualifications and Curriculum Authority (QCA).

InTUITIONMATHS • SUMMER 2018 11

MOTIVATION

TURNING RESITS INTO A REWARDING EXPERIENCE Students facing having to retake GCSE maths need a big boost to their confidence, so teachers must make lessons enjoyable and inspiring, says Fiona Allan

S

tudents who are resitting GCSE maths often arrive at their new further education and training providers feeling pretty demoralised about the subject.

They probably spent the last year being told that they must pass this GCSE. They may have spent some of the Easter holiday in school having extra lessons.

Their parents may have paid for coaching.

Then they receive disappointing news when the GCSE results arrive in August.

Added to this, when they had their interview to decide on their post-16 course they were told that they would need a pass at GCSE for their hoped-for career. So what do we do to them? We test them. The test often tells us that they aren’t even a 3 or a D, and it tells the student that they are even more inadequate than they thought.

So, why give them a test during the first few days? Instead, why not assess them before starting the first topic by giving pairs or trios a large sheet of paper and asking them to tell you everything they know about your first topic. Listen to their discussions, ask questions and look at the posters. You may be surprised by how much they already know!

Here a few more ‘don’ts’ for the start of the year.

Don’t timetable their lessons so they have one long session on one day – try to persuade senior management that your

students need to have frequent maths lessons. You can do a lot in a maths lesson, even in a 30-minute lesson!

I found it best not to expect the students to do exercises in short lessons – this was when we did quickfire questions or a whole class activity.

Don’t attempt to teach the whole syllabus again or tell the whole class everything from first principles. You won’t have time – assess them at the start of each topic and then teach them the parts they all need. You can then concentrate on teaching small groups while the others do routine questions or tackle exam questions.

And some do’s: Let them enjoy success early on in the term – give them a fairly easy test in which they will score high marks. Praise them! Tell them that research shows that everyone can improve in maths when they work at it. Show them that maths is useful by looking at pictures or videos and finding the maths that’s being used.

Make maths lessons interesting/fun by including maths jokes, fun videos etc Remember to find out what they know before starting each topic, and confront their misconceptions.

Finally, make them work hard by giving the class activities in which everyone has to take part.

REFERENCES •A nne Watson, et al (2013). Deep Progress in Mathematics. This resource is available from the STEM Learning website at goo.gl/UjpTet •T he NCETM’s Maths in Work videos are available at goo.gl/zpZPrB 12 SUMMER 2018 • InTUITIONMATHS

Fiona Allan is assistant director of the National Centre for Excellence in the Teaching of Mathematics (NCETM).

CASE STUDY PUZZLES COULD BE THE ANSWER

CASE STUDY HOW COLLABORATING ACROSS THE CURRICULUM CAN UNLOCK LEARNING

CASE STUDY RIPPING UP THE RULE BOOK WITH A DIAGNOSTIC APPROACH TO RETAKES

By Emma Bell Engagement in maths in further education is a problem. The students who are working towards a GCSE maths resit or Functional Skills are not, on the whole, there by choice. They would rather be anywhere else but a maths classroom, especially when they see their peers working solely on their main vocational subject.

Our aim at Grimsby Institute of Further and Higher Education is to change perceptions about maths, for students, for staff, and for the public as a whole.

Using the hashtag #MathsMatters, I have begun a social media and marketing campaign. I post puzzles on our internal social platform, Yammer, for staff to enjoy. These puzzles have proved popular, and staff have been overheard talking about them in the cafeteria queue.

The puzzles aim to show that we can have fun solving a problem. I’ve been sharing the puzzles on Twitter, Facebook and Instagram too, and now they are being used in schools and colleges around the country.

Our Friday puzzles are just the start.

The Chartered College of Teaching is supporting me to start a #MathsMatters network where I hope to share research and good practice on a national scale.

I’m visiting college departments to investigate how I can support embedding maths in vocational areas.

I’m the lead for initial teacher training in our university centre. This means that the #MathsMatters agenda is embedded in our TILLS PGCE course – our next generation of teachers will be able to continue spreading the message as they embark on their future careers.

By Lisa Jane Ashes As a vocational teacher, you know only too well the real-life industry situations that can allow your former students to finally understand the purpose and importance of mathematics.

But how do you support your students during their course when they ask the age-old question: “When am I ever going to use that?”

If mathematics is a required part of your course, stop tagging it on as an added extra and look for ways to bring it to life in the work that students are preparing to do every day.

At the very least, make a regular habit of asking the question, “Where’s the mathematics in that?”

Cross-curricular communication between mathematics tutors and tutors of vocational subjects is the ideal. Clear, electronically accessible course plans are also helpful. Being able to see what is being taught in mathematics can help you make links between mathematics teaching and what exists in your course.

For example: Catering involves ratios and food portions, pricing and profit margins, event running costs and competitor comparisons.

Plumbing involves measurements, area, volume, ratios, the effect of radius on pressure, force per metre, pipe density, fitting costs.

Collaboration between maths and vocational departments can support confidence and understanding. And collaboration works both ways as mathematics tutors can also link back to your course for concrete examples to support their teaching.

Where the maths exists, highlight it! Make it obvious to your students when and where they are using mathematics. Look beyond the requirements of your final assessment and bring in inspiration from their potential futures.

By Martin Newton The GCSE results for the 16 to 18 cohort at Stoke on Trent College were below national average in the 2016/17 academic year.

This was due to a variety of external and internal factors and influences. However, it did offer us the opportunity to rip up the rule book and start again from scratch. Our searches for a ‘silver bullet’ had drawn a blank.

We had been working with MEI (Mathematics, Education, Innovation) on a more individualised approach, funded by the Stoke Mathematics Excellence Partnership.

I found Mr Barton’s ‘Diagnostic Questions’ (DQ) online.

A colleague, Dave Walker, and I trialled the diagnostic questions resource with great success.

We split the curriculum into five areas: number, proportional reasoning, geometry, algebra, and statistics & probability.

For each area I compiled a pre-topic test and a posttopic one. When the pre-topic test was completed, the data was presented by DQ in such a way that we could use it in an assessment for learning (AfL) approach.

We then planned five or six weeks’ work based on learners’ gaps and misconceptions, thus teaching only the skills that most of the group needed. The learners set themselves individual targets specific to their needs.

The learners, teachers, senior leadership team and Ofsted like the process. DQ concentrates on misconceptions, cuts marking and gives teachers flexibility, moving away from a linear scheme of work.

A typical question might be:

Emma Bell is the maths enhancement manager and a teacher educator at Grimsby Institute of Further and Higher education. The institute won the Association of College’s 2017 Beacon Award for Staff Development, sponsored

by City & Guilds. belle@grimsby.ac.uk @maths_matters #MathsMatters

isa Jane Ashes is a self-employed teacher and L learning coach. She is the author of a book called Manglish, bringing English and Maths together, which is published by the Independent Thinking Press.

FURTHER READING • The ENiGMA project at Manchester College is a practitionerled initiative that includes collaborative thinking to approach English and maths across the curriculum goo.gl/188QfB • Ideas for teaching communication skills in other subjects goo.gl/Qrpb37 • There are a number of case studies here, detailing how numeracy and literacy can be embedded in vocational subjects goo.gl/PDvjTg

3+1=?

5 6

A

B

C

D

4 30

4 11

23 30

31 56

Questions are designed to identify common misconceptions that learners hold. This enables us to know learners’ thinking behind their incorrect answer; they also write an insight into their reasoning.

Learners have made an average improvement of a grade from pre to post-test over all five units.

The proof of the pudding will be in the GCSE results. If our predictions are correct most learners will be making progress through the grades and there should be an improvement in high grades for grade 3 learners.

Martin Newton is maths development lead at Stoke on Trent College.

InTUITIONMATHS • SUMMER 2018 13

LEARNING TECH

EXPLORING THE OPPORTUNITIES OF DIGITAL TECHNOLOGY A one-day ETF-funded course shows teachers how to develop digital techniques in Maths. But using technology needs to be shaped by good teaching practice, not just trying to engage ‘reluctant learners’. By Bob Read

I

n the past two years the Education and Training Foundation (ETF) has funded the development and delivery of a one-day course for maths teachers, Digital Technology: Developing Your Practice, as part of their Maths and English Pipeline programme. This article reviews some of the key tools and teaching approaches on the course and the impact they have had on practitioners.

Throughout the course participants are regularly prompted to consider how the use of technology needs to be shaped by good practice in maths teaching, and not just by a concern to tick a box on an Ofsted checklist or by a desperate attempt to engage ‘reluctant learners’.

They are encouraged to reflect

REFERENCES •F or information on the ETF English and Maths pipeline visit goo.gl/KTLomK •C oe, R; Aloisi, Cesare; Higgins, S; Elliot Major, L. (2014) What makes great teaching?

Review of the underpinning research.

Read online at goo.gl/sRRxgn •V isit the Diagnostic Questions website at goo.gl/xhVmGu •F ind out more about Padlet at goo.gl/v87puv •C heck out Hegartymaths at goo.gl/oyXc6A •C heck out Corbettmaths at goo.gl/PeXMSu •V isit Edpuzzle at goo.gl/AghcBb •F ind out more about Triptico at goo.gl/8jjwf6 •F ind out more about GoConqr at goo.gl/JNHQkN •G oogle Forms goo.gl/szmcQB •T o find out your ETF regional specialist ;ead for maths visit goo.gl/uzRwk9 •T o watch Liam Alderton’s video click the play icon below, or watch it on YouTube via the following link goo.gl/4NH7kY 14 SUMMER 2018 • InTUITIONMATHS

critically on established research

by Malcolm Swan, and more recent findings in cognitive psychology, when considering the value of digital tools and websites. For example, the importance of exploring common misconceptions in maths is highlighted when participants are introduced to the Diagnostic Questions website and its extensive bank of online resources. Participants also evaluate different ways in which collaborative problem-solving can be enhanced and captured by the use of online ‘corkboards’, such as Padlet, which enable learners to share ideas using their smart phones.

At the same time, for those topic areas where direct instruction and the modelling of calculation strategies are valuable, there is now a wealth of video material available on YouTube and websites, such as Hegartymaths and Corbettmaths, which can be used as the basis of blended learning delivery models.

The course provides participants with opportunities to evaluate such resource banks and explores ways in which teachers can give learners easy access to online material by using QR codes on worksheets and posters. It also demonstrates how teachers can convert video tutorials into interactive teaching resources using annotation tools such as Edpuzzle.

But what does this all look like in practice?

A recent ETF video case study (see References, left) features Liam Alderton, a Functional Maths teacher at East Coast College, who explains how his use of

digital technology has greatly enhanced the collaborative atmosphere of his classroom and provided new forms of revision opportunities for his learners.

The video shows how Liam uses Padlet to organise his course materials in an online format that learners can easily access with a single click on a mobile device and without time-consuming log ins and passwords.

It features some of the whiteboard resources Liam creates using tools on the Triptico and GoConqr websites to promote classroom interaction. But he also explains how he uses Google forms to develop quizzes for learners to complete between sessions as they provide valuable data on learner performance that he can use to plan follow-up lessons.

If you would like to find out more about using digital technology in maths teaching, contact your ETF regional specialist lead for Maths, who can provide you with more information about courses and other support opportunities in your area.

Bob Read is the ETF regional specialist lead for maths and English in the East of England.

Bob is a training and development adviser for ACER, the Association of Colleges’ Eastern Region organisation.

RESOURCES WRAPAROUND MATHS RESOURCES FOR TEACHERS AND TRAINERS

RESOURCES MATHS REGIONAL SPECIALIST LEADS

A range of resources and benefits are available from the Education and Training Foundation (ETF) to support practitioners delivering maths courses.

Each year 4,000 of them complete face-to-face, online and blended courses to improve their teaching and assessment approaches in maths and English.

Support and courses are available to help with effective teaching of maths for teachers of GCSE, Functional Skills, apprenticeships and study programmes.

Many practitioners start with the ETF’s self-evaluations tools. There is one for the GCSE pathway and for Functional Skills. These are designed to identify which areas of your mathematical knowledge need updating.

A range of maths modules is available from Foundation Online Learning covering topics such as algebra, geometry, the language of maths, measurement, numbers and probability. There are also guidelines for assessment and tracking.

The maths exhibition site on the Excellence Gateway provides a portal to a range of tools, resources and case studies which you may find useful.

Teachers and trainers can contact their regional specialist maths lead for more advice, guidance and support (see Specialists panel, right).

Practitioners are also invited to join the ETF’s Professional Exchange Networks (PENs) to explore regional challenges and reflect on effective practice in the sector.

Education and training providers can also engage with our dedicated team of specialists to receive a maths strategic support visit to identify high-level areas of need.

To discuss a strategic visit, please contact the ETF’s Head of Maths and English, Imke Djouadj, at: imke.djouadj@etfoundation.co.uk To find out more about the PENs visit goo.gl/9cjjk9

If you have questions about the type of support and professional development you feel you may need in maths, then the Education and Training Foundation’s (ETF) regional specialist leads are here to help.

They are all experienced practitioners and can advise you on, and signpost you to, courses and activities that will best suit your needs.

EXCLUSIVE DISCOUNTS Don’t forget that SET members are eligible for an exclusive 15 per cent discounts on most Maths courses (and many others) run by the Education and Training Foundation (ETF).

For information on all member benefits visit the SET website and click on ‘Membership’. https://set.et-foundation.co.uk

RESOURCES

East of England Bob Read bob.read@acer.ac.uk East Midlands Norma Honey nrmhon@aol.comLondon London Sonia Thomas sonia.thomas@etfoundation.co.uk North East Lianne Abraham lianne.abraham@ncl-coll.ac.uk North West and Cumbria Sue Lownsbrough sue.lownsbrough@gmx.co.uk South East Judy Maguire maguire.judy@zolitayre.co.uk South West Alison Pearson alisonpearson1@yahoo.com West Midlands Steve Pardoe s.d.pardoe@warwick.ac.uk

Yorkshire and Humber Gail Lydon gaillydon@me.com

• The Professional Standards for Teachers and Trainers reflect and support the efforts of practitioners to help learners overcome the barriers to maths and English learning. Read the standards at goo.gl/KgH1iL InTUITIONMATHS • SUMMER 2018 15

UNPARALLELED PROFESSIONAL CAREER SUPPORT One of the many benefits of SET membership As the only membership body for professionals working across further education, teaching and training, we are here to support you in your career. Membership grants you access to the latest research in maths and English in addition to opportunities to achieve excellence and to gain recognition in your profession and community.

Not yet a member? Join now at set.etfoundation.co.uk or call 0800 093 9111