Guidance, ideas and examples to support schools in developing their curriculum, pedagogy, enrichment and support for more able learners, within a whole-school context of cognitively challenging learning for all. Includes ideas to support curriculum development, and practical examples, resources and ideas to try in the classroom. Popular topics include: curriculum development, enrichment, independent learning, questioning, oracy, resilience, aspirations, assessment, feedback, metacognition, and critical thinking.
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Posted By Stefan Pearson,
04 April 2018
Updated: 07 August 2019
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Stefan Pearson, Teacher and Challenge Coordinator at Bradford’s Copthorne Primary School, shares five key takeaways from this year’s English for the More Able conference…
Last month I attended the English for the More Able conference in York, run by NACE in partnership with Rising Stars. The conference explored a range of approaches to support, engage and challenge more able learners in primary English, with an opening keynote from author Anne Fine, interactive workshops, and opportunities to share ideas with fellow primary teachers, coordinators and school leaders.
Like most delegates, I left the event with a pile of notes and a head buzzing with ideas – some of which I’ve already begun to test out in my own classroom. Here are five of my main takeaways from the day – offering fresh perspectives to keep primary English relevant and engaging for learners of all abilities.
1. Oracy skills can – and should – be taught in schools.
Among the keynote speakers for the day was Neil Mercer, Emeritus Professor of Education at the University of Cambridge and Director of Oracy Cambridge. Professor Mercer’s talk reinforced my belief that oracy skills are an essential foundation in learning and life, which can – and should – be taught in schools.
To communicate successfully, young people need to develop language and skills to reason and reflect, express ideas clearly and confidently, listen carefully, and talk and work well in a group. Most children’s home experiences will not provide opportunities for them to develop all the oracy skills they need, making it even more important that oracy is taught in schools.
The aim, Professor Mercer believes, should be to engage children in “exploratory talk” – characterised by active listening, asking questions, sharing relevant information, challenging ideas and giving reasons for doing so, and building on what has already been discussed. In exploratory talk, all participants are encouraged to contribute, ideas and opinions are treated with respect, and the group works within an atmosphere of trust and with a shared purpose, seeking agreement and joint decisions.
2. We need to talk about listening…
Just like skills for effective talk, listening skills also can and should be taught in schools and discussed with learners from an early age. For me, a key takeaway from the conference was the decision to talk more about listening in my classroom. The most effective types of listening are attentive listening – in which the listener is interested, takes in facts, and checks information – and active listening – in which the listener responds with questions and relevant comments, gathers facts and ideas, and attempts to understand the feelings of the speaker.
3. … and provide effective Talking Points.
Dr Lyn Dawes, also a member of Oracy Cambridge, shared her work on Talking Points – thought-provoking statements that encourage children to talk about a topic, promoting discussion, comparison, analysis, reasoning and negotiation. Through participation in Talking Points discussions, learners explore a curriculum topic in depth, generating shared understanding and establishing areas for further investigation. Most importantly, they develop skills for effective group discussion, practising sharing their opinions and giving reasons, listening and responding to others, and collaborating to ensure everyone has a chance to contribute.
Talking Points can be used across any curriculum area and can be created by both teachers and learners – a fantastic resource to support effective learning and develop oracy skills, which can then form the basis of written work.
4. Grammar really can be fun!
NACE associate Christine Chen ran a workshop on grammar games, sharing lots of practical ideas. One of these involved writing a six-word sentence and numbering the words 1-6. Learners are then asked to roll a dice, identify the word class of the corresponding word, and replace the word so the meaning of the sentence alters.
I’ve already tried this with my class and the children really enjoyed it. This kind of game also builds in differentiation, providing scope for challenge while reinforcing learners’ understanding of the different parts of language.
Another idea from this session which I’ve also tried out is the challenge of writing descriptively without using adjectives – meaning other word types must be carefully selected to convey mood, pace, emotion and so on. This prompted my more able writers to rethink their approach to description, and they really relished the challenge.
5. Engaging parents can be as simple as this.
My fifth and final key takeaway from the conference is in fact a resource developed by my own school. During her plenary talk, headteacher Christabel Shepherd mentioned our reading mats for parents. These proved in-demand amongst conference delegates, with many schools recognising the importance of engaging parents in developing children’s reading and comprehension skills.
We give the reading mats to parents and carers as laminated resources to use at home. They provide explanations and examples of different question types – for example, questions to retrieve information, to comment on language choices, or to relate texts to wider contexts. The sheets include question frames, which can be adapted for any book.
At Copthorne, where 98% of our learners are EAL and many families speak little English at home, we’ve found these reading mats very effective in supporting parents. In addition to encouraging shared reading at home, the mats enable parents to make effective use of questioning to develop their children’s understanding.
How does your school support more able learners in primary English? Contact us to share your approach.
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Posted By Alex Pryce, Oxplore,
21 March 2018
Updated: 08 April 2019
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Looking for ideas to challenge your more able learners in science, technology, engineering and mathematics (STEM)? In this blog post, Alex Pryce selects four “Big Questions” from the University of Oxford’s Oxplore project – providing rich starting points for debate, investigation and independent learning…
Oxplore is an innovative digital outreach portal from the University of Oxford. As the “Home of Big Questions”, it aims to engage 11- to 18-year-olds with debates and ideas that go beyond what is covered in the classroom. Big Questions tackle complex ideas across a wide range of subjects and draw on the latest research undertaken at Oxford. Oxplore aims to realise aspirations, promote broader thinking and stimulate intellectual curiosity.
Our Big Questions reflect the kind of thinking students undertake at universities like Oxford. Each question is accompanied by supporting resources – including videos; quiz questions; possible answers, explanations and areas for investigation; and suggestions from Oxford faculty members.In the classroom, these four STEM-related Big Questions could offer super-curricular enrichment spanning a diverse range of subject areas. Teachers could ask students to design a mini research project on a particular aspect of the question, or extend their learning by challenging them to create Big Questions of their own.
Provoke debate around the Big Bang, chaos, laws of probability, and where explosions fit into this as examples of order and disorder. Students can learn about the history of explosions, and positive examples of the things that wouldn’t exist without them. Delve deeper into the science behind the nuclear bomb and take a closer look at creatures that could survive one.
Perfect for: a wide-ranging subject discussion.
What does it mean to be a human being? Examine the nature of intelligence, language, creativity and the law with your students. You can debate the role of artificial intelligence within society and explore the boundaries between computers and consciousness – now and in the future.
Perfect for: debating future technological developments.
We all travel forward through time, but what happens if we change how we do this, or the speed in which we travel? Inspire your students to explore special relativity in action – through GPS, electromagnets, and TV and PC screens.
Perfect for: Doctor Who fans!
Is it right to interfere with nature? Introduce your students to the science of stem cell research, therapeutic cloning, and create neuroethics debates. Discuss whether humans should be allowed to “design” new animals, and explore the development of cloning: from Hans Spemann’s original 1902 experiment that split a salamander embryo in two, to the first successful human embryos cloned in 2008.
Perfect for: discussions of the weird and wonderful.
Alex Pryce is Oxplore’s Widening Access and Participation Coordinator (Communications and Engagement), leading on marketing and dissemination activities including stakeholder engagement and social media. She has worked in research communications, public engagement and PR for several years through roles in higher education (HE) and the Arts and Humanities Research Council (AHRC). She holds a DPhil in English from the University of Oxford and is a part-time HE tutor.
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Posted By Victoria Burrill,
09 March 2018
Updated: 09 April 2019
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Next week NACE and Rising Stars are hosting the English for the More Able conference in York, bringing together educators, researchers and advisers from across the country to explore strategies to challenge more able learners in primary English. In this blog post, Victoria Burrill, author of Rising Stars’ English for the More Able activity book series, picks out 10 texts with a lasting power to engage, inspire and challenge young learners – plus recommendations of what to read next…
The Twits by Roald Dahl
I am yet to meet a child who doesn’t love Roald Dahl’s stories and I think it’s because they make you laugh, cry, grimace, cower and cheer all at once. You will meet characters like none you’ve met before and you will want to read this book over and over again.
If you like this, try: Fizzlebert Stump: The Boy Who Ran Away from the Circus (and joined the library) by A. F. Harrold
A Boy and a Bear in a Boat by Dave Shelton
This is a simple tale of adventure and friendship. The relationship between the eponymous child and his ursine companion will enchant you and teach you that not all adventures are the same.
If you like this, try: Kensuke’s Kingdom by Michael Morpurgo
Fantastic Beasts and Where to Find Them by J. K. Rowling
If you want to experience the power of imagination, this almanac of wondrous beasts will whisk you away and hopefully encourage to create your own incredible creatures.
If you like this, try: The Hobbit by J. R. R. Tolkien
The Miraculous Journey of Edward Tulane by Kate Di Camillo
This charming tale will take you around the world, both under and over the sea. The protagonist, Edward, will enchant you and show you how some characters can capture your imagination and your heart.
If you like this, try: Because of Winn Dixie by Kate Di Camillo
Oranges in No Man’s Land by Elizabeth Laird
This is a story to make you think, to make you feel grateful and safe, and to help you understand that good can come from tragedy. It will open your eyes to the lives of others.
If you like this, try: The Garbage Kid by Elizabeth Laird
Wonder by R. J. Palacio
A story like no other. Told from a number of perspectives, this is a story of facing difficulties and finding friends. This book will make you feel something that you won’t forget.
If you like this, try: One by Sarah Crossan
The Graveyard Book by Neil Gaiman
Prepare to be spooked! This book is beautifully written and will teach you the power of words in creating atmosphere.
If you like this, try: Coraline by Neil Gaiman
The Selfish Giant by Oscar Wilde
An old story with a message which remains current and important. This simple tale is full of storytelling power. It has a moral to which we can all relate, whether we are the children or the giant.
If you like this, try: The Little Prince by Anton de Saint-Exupéry
Tuck Everlasting by Natalie Babbitt
This story offers its readers the ultimate “What if?” It will make you think and wonder about things you may have never wondered about before. Join the protagonists in making the ultimate life or death decision.
If you like this, try: Peter Pan by J. M. Barrie
The Unforgotten Coat by Frank Cottrell Boyce
This book uses words and pictures in an usual way to tell a very human story and one which is very relevant to our modern, global society. It will make you think and might open your eyes to the experiences of others.
If you like this, try: Coming to England by Floella Benjamin
Victoria Burrill is Head of English at Newton Prep School in Battersea, London. She teaches Years 5 to 8, preparing children for pre-tests and entrance exams for London day schools at both 11+ and 13+ and Common Entrance at 13+. She has written for both Rising Stars and Galore Park for the past four years and her catalogue includes the English for the More Able series, 11+ Practice Papers and Revision Guide, and the Galore Park English textbook series for Years 3 to 6. Her particular passion is to instil a love of literature in her students and she plans her lessons around whole novels, using them to teach key skills and to evoke a love of a good story.
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Posted By Amanda Moorghen,
07 March 2018
Updated: 08 April 2019
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Earlier this week, the English-Speaking Union (ESU) hosted a meetup for NACE members on the topic of cultural capital – including the importance of providing opportunities for young people to explore and develop oracy skills. In this blog post, the ESU’s Amanda Moorghen shares five reasons to teach oracy skills for learners of all ages and abilities.
At the ESU we believe every child can and should be taught oracy skills. Just like literacy and numeracy, at one level oracy is a basic skill that no one can go without – whether on the stage, in the boardroom or in everyday conversation, all of us need to express ourselves and listen to others. But, as with literacy and numeracy, oracy is also so much more than this basic skill: it’s the key to incredible intellectual and emotional experiences. No one should be locked out of opportunities in life for fear of speaking in public, or inability to rise to the challenge of an interview or presentation.
1. Oracy supports learning
Many great lessons include talk. In particular, challenging open-ended tasks often have a discussion element – exploring new ideas, questioning, analysing and synthesising. Explicit oracy instruction ensures all pupils have the tools they need to access talk-based learning, stopping these lessons from being dominated by a few more confident characters. Talk can also precede writing – stronger oracy skills can help develop the creativity and critical thinking pupils need for their written work.
2. Oracy is vital for social mobility
Some children receive a lot more oracy practice and instruction than others. This impacts their learning at school, but also their ability to fulfil their potential later in life. For some, interviews, presentations or seminars present barriers to success. Explicit oracy instruction for all pupils narrows that gap, giving everyone the change to flourish. In later life, whether in higher education (lectures, seminars) or the workplace (interviews, meetings, presentations), oracy skills help people to make the best of the opportunities they have.
3. Oracy is good for social and emotional learning
Teaching oracy skills helps children who may be struggling to work or play well with others. For example, teaching rules and conventions around turn-taking in small-group discussions helps involve pupils who find free-flowing, “chaotic” discussions off-putting. Developing oracy skills can also boost children’s confidence and self-esteem. Some teachers worry that shy children will be left out of oracy activities, but at the ESU we find it is precisely explicit oracy instruction that helps them to overcome their nerves: clear expectations and guidelines help everyone to find their voice.
4. Oracy opens doors to opportunity
Extracurricular activities such as debating, youth parliament and volunteering bring a wide variety of benefits. Oracy education helps students to access these opportunities: for some, a debate in class might help them to find a passion for politics, whilst for others, formal oracy instruction gives them the confidence they need to volunteer in the community.
5. Oracy is empowering
Oracy instruction helps young people to develop the skills they need to speak out about what matters to them. At the ESU, we’ve worked with young people who are a voice for change, whether on the world stage, in their school or in their local community. The demands of democratic life require us all to speak up – teaching oracy means everyone is equipped to do so, not just those who began life with the loudest voice.
Join the conversation…
To celebrate our centenary, the English-Speaking Union is inviting you to use your voice and tell us what you’d like to speak out about and why. Find out more at 100.esu.org/speak-out, and have your say on Twitter or by posting on our Facebook page. Don’t forget to use # ESUspeakout with your post.
Amanda leads the Research and Resources team at the English-Speaking Union. Before joining the ESU, she studied philosophy at the University of Birmingham, which is also where she discovered the joys and benefits of debate, speaking, judging and coaching around the world. Having seen how transformative debate and discussion can be, Amanda joined the ESU to help support teachers in bringing oracy skills to the classroom.
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Posted By Lesley Hill,
27 February 2018
Updated: 23 December 2020
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Lesley Hill, headteacher of NACE member Lavender Primary School in North London, explains how the school’s approach to marking and feedback has evolved alongside the development of a strong learning mindset culture.
Our marking and feedback policy cannot stand alone. It only works because we have embedded the learning culture on which it depends.
About five years ago, we were proudly using assessment for learning (AfL) strategies, such as no hands up, colourful cups, and thumbs up, thumbs down and thumbs somewhere in between. None of this was particularly useful for those learners who were unable to be honest about where they were in their understanding. This became apparent to me during a Year 2 literacy lesson. I shook my lolly-stick pot and was ready to pick a child to answer my question, when a higher achiever visibly shuddered. That said it all.
We turned to the work of Carol Dweck and immediately introduced growth mindset, understanding that higher-achieving children can often be those with the most fixed mindsets, causing barriers to learning.
Developing skills for effective learning
We knew that embedding a growth mindset culture was essential, but we also realised very quickly that the skills of being a good learner had to be taught too. A school full of determined children chanting (albeit sweetly) “We can do it!” doesn’t necessarily mean better outcomes. We introduced themes around Guy Claxton’s work, Learning to Learn, and our children learnt to be resourceful and reflective, as well as resilient.
We also understood that if children were truly going to understand where they were as learners, we needed to examine our success criteria. Hours had been spent trying to put English success criteria into a hierarchical order with a must, a should and a could. Whilst our lower-achieving children stayed safely with the “musts”, some of the higher-achievers completed the “should” and “coulds” and missed some basic “musts” altogether. We ditched MSC for toolkits, after attending a Pie Corbett course.
Giving children ownership of their learning
The same training also prompted us to establish cooperative reviews, which offer a focused and structured peer assessment strategy. We have trained our children to give effective feedback and to have useful discussions around their learning. This is key. Our current marking policy includes lots of peer assessment and reflection, which begins to give ownership to the child. We firmly believe that ownership of learning impacts positively on children’s motivation to challenge themselves.
This ownership was previously promoted by allowing learners to choose their own level of maths tasks, where they would be encouraged to make decisions about the levels of challenge they could manage. We have since bought a Singapore Maths scheme; the reflective approach and decisions around which strategy to use to solve a problem fit perfectly with challenge and ownership.
Learners also have ownership over the marking of maths. The answers are on the tables and learners check after solving a few problems. If they have some wrong, they will unpick the steps they have gone through to understand where they have made an error or have a misconception. This deeper-level thinking can enable them to change their approach to get a solution. Should they not be able to see where they have gone wrong, the teacher will step in to guide or re-teach through a face-to-face conference.
Moving on from written marking
Conferences have taken the place of written marking. It was apparent to us for some time that reams of written marking or rows of ticks and dots, carried out away from the learning context and delivered back the next day, was, at best, hard for children to relate to and, at worst, a meaningless waste of time. With teacher workload high on the agenda, our decision to stop written marking altogether, for every subject, was not difficult to make. Our children already owned their learning, they knew how to self- and peer-assess effectively, and they were reflective, resilient and skilled learners. It was an easy step to hand over the pen.
Our marking and feedback procedure is simple. Children mark their own work according to the success criteria and they write a reflection on their learning – commenting on their understanding, successes and difficulties. They are also challenged to consider how they have approached the work and what they might do differently. Teachers look at the books every day and identify where there is a need to support or extend children’s learning. They plan in targeted 1:1 or group conferences for the following day, or hold spontaneous conferences, to address misconceptions, clarify points and extend thinking. During conference discussions, children are encouraged to consider where they have met their targets and to choose new ones, and to talk about the reflections they have made.
Children’s reflections are a window to their understanding, not just of concepts, but of themselves as learners. They provide teachers with far greater insight than a piece of work on its own and thus teachers can cater far more effectively for each child’s needs. Our approach to marking is not a stand-alone. It is an extension to the learning culture we have worked to create: a culture of learners who can recognise and be honest about where they are, who know where they need to go, and who are not afraid to share the responsibility for getting there.
Lesley Hill is headteacher of Lavender Primary School, a popular two-form entry school in North London, part of the Ivy Learning Trust and a member of NACE. She has taught across the primary age range and has also worked in adult basic education and on teacher training programmes. Her current role includes the design and delivery of leadership training at middle and senior leader level, and she also provides workshops on a range of subjects, such as growth mindset and marking. Her forthcoming book, Once Upon a Green Pen, explores approaches to create the right school culture.
Read more: log in to our members’ area to access the NACE Essentials guide to learning mindset, and the accompanying webinar.
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Posted By Ems Lord,
19 February 2018
Updated: 08 April 2019
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Ems Lord, Director of the University of Cambridge-based NRICH project, explains how one primary school developed learners’ conjecturing and convincing skills through the challenge of solving live maths problems – and the motivation of seeing their solutions published on the NRICH website.
What’s the problem?
Imagine the scene: your carefully planned problem-solving activity has completely engaged your class. They’re busily applying their mathematical skills in a real-life context and the higher attaining learners are being suitably stretched too. Towards the end of the session, you gather the class together to share their solutions. One of your high attainers raises a hand and suggests the correct answer. In response, you ask the inevitable question, “How do you know?” Instead of launching into a convincing argument, they simply shrug their shoulders and say “I just knew the answer!”
What are the three levels of conjecturing and convincing?
Developing the skills to conjecture and convince are essential components of our mathematics curriculum. Nevertheless, even high attainers sometimes struggle to explain their thoughts to others. They might have convinced themselves about their solution, but they are not yet able to convince another person. They need time to explore others’ solutions and develop their own convincing answers too. In Thinking Mathematically (1982), John Mason talks about three levels of convincing: convincing yourself, convincing an enemy and convincing a sceptic.
Submitting solutions to "Live Problems" on the NRICH website
As learners make the journey from being a novice to an expert at mathematical reasoning, they will progress through several distinct stages. To begin with, their solutions might simply describe how they went about solving their problem. “We do train them that it’s either right or wrong, don’t we?’ noted a teacher.
Following a visit from the NRICH team, which focused on using solutions to develop reasoning skills, the school’s mathematics subject leader set every class the challenge of submitting their own solutions to a Live Problem. The teachers began the process by exploring examples of learners’ work already published on the website, ordering the solutions according to their level of reasoning and comparing their different content. This session was supported by the article The Journey from Novice to Expert.
Back in class, the teachers introduced their classes to the various Live Problems on the NRICH site, explaining that the learners could submit their own solutions. This was incredibly motivating for learners. “There was a real reason for doing it, a bit like when you’re writing in English and you want a real reason,” explained a teacher.
Let’s look at one of the Live Problems explored by the learners. In Number Detective, learners need to identify a mystery number by following a list of clues:
- The mystery number has two digits.
- Both of its digits are even.
- The digit in the tens place is greater that the digit in the ones place.
- The ones digit is not in the three times table.
- The tens digit is not double the ones digit.
- The sum of the two digits is a multiple of five.

By focusing on explaining rather than describing their mathematical thinking, the learners developed their solution:
- Amelia says, “8 and 120 are not the number because 8 is one digit and 120 has three digits.”
- Aironas adds, “It can’t be 18 or 83 because they have odd digits.”
- “46 and 22 don’t have a tens number greater than the units number, so it can’t be them,” suggests Matas.
- Jessica states, “86 is not it because it has 6 in it (the 3x) and the rest are not.”
- Tommy D says, “It isn’t 42 because the tens digit is double the ones digit.”
- There are now only two possible answers left: 64 and 80.
- Lastly, Tommy C goes for it! “I think 64 is the answer because 6 + 4 = 10 and 10 is in the 5 times table.”
As you can see, the learners carefully explained their thinking. “I thought it would be daunting for them to be able to justify why they’d chosen a certain answer, why they’d decided on a certain thing and made a statement, but I was really surprised by how many wanted to stand up and justify themselves,” noted one of their teachers. Seeing their solution on the NRICH website created a buzz around the school and beyond: “They couldn’t wait to actually go home and tell their parents all about it.”
How can this be developed further?
Whatever their current level of reasoning, learners can also try writing their own problems for others to solve. One very successful approach is using the NRICH problem as a template. Here are two new versions of Number Detective submitted by learners from the school, which have since been published by NRICH:
As the learners progress through their schooling, they will be able to start justifying their solutions by providing a correct logical argument that has a complete chain of reasoning to it. Their improved solutions will include words such as “because”, “therefore”, “and so”, “that leads to”...
Having seen some of their learners’ work published on NRICH, I asked the teachers if they encourage their learners to try more Live Problems . “Yes, I would love to, definitely. It was fun,” one of them told me. More Live Problems are uploaded every half term and learners can also challenge themselves with some unsolved Tough Nuts problems.
If you would like to develop the reasoning skills in your classroom, make sure your class know about the latest Live Problems by subscribing to our free NRICH newsletter.
Ems Lord has been Director of NRICH since 2015, following a previous role leading one of the country's largest Mathematics Specialist Teacher Programmes. Ems has taught mathematics across the key stages, from early years to A-level Further Mathematics, and has worked in a variety of settings, including a hospital school. She’s supported schools as a leading mathematics teacher, local authority consultant and Chartered Mathematics Teacher, and has taught mathematics education on both BEd and PGCE teacher programmes. She is currently working on her PhD thesis, which explores approaches to improve support for those learning calculation skills, and is President-Elect of the Mathematical Association for 2019-2020.
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Posted By Ems Lord,
07 February 2018
Updated: 08 April 2019
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NACE is proud to partner with the NRICH project at the University of Cambridge’s Centre for Mathematical Sciences, which offers free online resources to enrich the mathematics curriculum, provide challenging and meaningful activities, and develop mathematical thinking and problem-solving skills. In this blog post, the project’s director, Ems Lord, explains why and how NRICH is developing resources designed to get GCSE students seriously interested in Further Mathematics…
Entries for the Further Mathematics A-level have tripled in recent years, from around 5,000 students in 2005 to a staggering 15,000 by 2015 (source: JCQ). But one of the greatest recent success stories in mathematics is under threat.

Figure 1: Entries for Further Mathematics up to 2016 (source: JCQ)
The transformation of Further Mathematics has all the ingredients of a great news story, yet the latest figures are alarming. Anecdotal evidence from both schools and colleges indicate a staggering 50% drop in the number of students opting to study Further Mathematics this year.
Recent changes in national policy promoting the study of three A-levels have hit Further Mathematics – often regarded as a fourth option – harder than most subjects. The NRICH team at the University of Cambridge has joined up with colleagues at the University of Oxford to address concerns regarding the current decline in Further Mathematics entries. The realisation that many GCSE students do not appreciate the opportunities offered by Further Mathematics led to our new set of free resources for schools, which we’ve called Adventures with Complex Numbers.
Why focus on complex numbers?
The current GCSE mathematics curriculum offers learners very limited insights into some of the most exciting topics awaiting them with Further Mathematics, such as complex numbers. The topic offers a terrific opportunity to give students interested in a range of different subjects a real taste of Further Mathematics well before they make their A-level choices. Complex numbers is an engaging topic for potential artists, engineers and scientists, as well as future mathematicians.
Figure 2: The Mandlebrot Fractal, a very popular concept with artists, who frequently exploit the level of detail and complexity revealed by zooming in on the original image.
What resources are available?
The key here is remembering that the resources created by NRICH are aimed at GCSE students; they are not intended for A-level teaching, although teachers may recognise their potential for those students too.
The materials adopt two straightforward approaches towards complex numbers. First, they explore the day-to-day applications of complex numbers in the real world. Learners can hear first-hand accounts about the crucial role that complex numbers play in the electricity networks that power our daily lives and how they help engineers keep structures safe and stable – as well as some spectacular examples of what can go wrong!
Figure 3: A dramatic clip from Professor Ahmer Wadee’s video Complex Numbers – Strength
The second approach encourages learners to explore complex numbers for themselves. The team have devised a range of animations which encourage a very hands-on approach, letting learners ask themselves “What if?” and giving them the tools to explore their ideas:
Figure 4: Screenshot from Vanishing Roots
So, they’re interested… What next?
We very much hope that learners enjoy the interactive resources and first-hand accounts exploring the uses of complex numbers. But the resources go much further than that. Learners can access a range of articles which take the topic much deeper, allowing them to discover how Heron of Alexandria missed his chance to explore the unknown mathematical land of complex numbers, as well as exploring the role of complex numbers in movie animation. For learners considering signing up for the Further Mathematics A-level, there’s also a live link to the national Further Mathematics Support Programme.
We’re not suggesting that this set of new resources will halt the declining numbers of Further Mathematics entries. Clearly, other agencies need to get involved too to arrest the decline. But we do hope they will offer an excellent starting point for engaging learners with the ideas they’ll encounter when studying Further Mathematics, and that they will be tempted to learn more about the possibilities offered by the subject.
Ems Lord has been Director of NRICH since 2015, following a previous role leading one of the country's largest Mathematics Specialist Teacher Programmes. Ems has taught mathematics across the key stages, from early years to A-level Further Mathematics, and has worked in a variety of settings, including a hospital school. She’s supported schools as a leading mathematics teacher, local authority consultant and Chartered Mathematics Teacher, and has taught mathematics education on both BEd and PGCE teacher programmes. She is currently working on her PhD thesis, which explores approaches to improve support for those learning calculation skills, and is President-Elect of the Mathematical Association for 2019-2020.
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Posted By Nicola Morgan,
31 January 2018
Updated: 20 August 2019
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Think you understand what makes young people tick? Think again. Award-winning author and expert on teenage brains Nicola Morgan shares five factors which are often overlooked, but which hold the key to effectively supporting today’s young learners.
I’m delighted to be giving the keynote speech at this year’s NACE Cymru Conference, in Cardiff on 28 June. I’ve been asked to write a blog post introducing some of my ideas. I’ve thought of “five things we forget at their peril” – ideas which underpin my philosophy and which will, I hope, resonate both with those of you who can’t come to the conference and those I’ll be talking to on the day. I will explain everything in detail in my speech, with fascinating science!
1. Young people know a lot about a lot... and very little about a lot
Today’s teenagers know far more than I did about the “big wide world”. Thanks largely to the internet, social media and globalisation, they’ve interacted with people from different backgrounds and cultures, been exposed to wide-ranging ideas, breathed diversity, celebrated difference. They are often streetwise, worldly wise and knowledgeable in ways I couldn’t have imagined.
But we should not overestimate their knowledge of basic psychology, biology and life skills. They often don’t know that headaches and stomach aches can be a symptom of stress or that sleep and calories are necessary for learning and brain function. They don’t always know about metacognition or growth mindsets and far too often have too much done for them by their parents.
2. Young people do not have our life experience – they do not know that “this too shall pass”
How young people’s bodies and brains react to stress is almost identical to our own: they feel the same; they are the same; prick them and they bleed, stress them and their bodies flood with alerting chemicals. But they arrive at these pressures new. They do not know, because they have not experienced, that how they feel about something today is not how they will feel tomorrow or next week or next month.
We need to tell them, often – just as we remind our own friends in pain or turmoil – that everything changes, passes, morphs into something manageable and often something forgettable. In my keynote, I’ll talk about the brain difference that underpins this, but let me just say now that they are in the moment because the moment is big and new and dramatic and all-consuming. They are less able to look ahead and to rationalise. But they will learn to do so faster if they have the chance to try and if they are guided.
3. Failure is the greatest risk our students face, and the lucky ones will fail soon
We want our young people to be resilient, to cope with setbacks. Resilience grows from experiencing difficulty and being supported, with empathy and metacognition, to pick ourselves up and try again. To get back in the saddle.
Too many parents and schools raise the stakes until failure is The Worst Possible Thing. But failure only means that you aimed high enough. Real success comes from being ambitious, understanding “what went wrong” and keeping on trying, but trying better. Too many of our brightest children don’t experience failure at school and are failure-phobic, coming to a crashing fall later. Ditto their parents, who helicopter in to prevent the failure.
4. Stress is life-saving and dangerous, performance-enhancing and performance-wrecking
Don’t be afraid of stress: it enhances your life and gives you the physical and mental state for super-performance. The key is to know your triggers and symptoms and learn how to feel stress when you need it and not when you don’t. My course Stress Well for Schools teaches all this in detail.
5. Digital natives do not have specially evolved brains
They were born with the same brains as the rest of us. They’ve spent a lot of time on screens so they have learned those skills. The more time we spend doing something the better we are at it. It’s very simple: use it and don’t lose it. There are skills you have that “digital natives” don’t have but which they could learn, too. They’re not special.
“But, surely, they’re better at multi-tasking? They do it so much, no?” Ah, no. The opposite. In my keynote, I’ll explain exactly why and exactly what they are better at… Trust me: the science on this is fascinating, revealing and important. And relevant to us all.
Tags:
adolescence
mindset
myths and misconceptions
neuroscience
research
resilience
technology
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Posted By Chloe Maddocks,
29 January 2018
Updated: 22 December 2020
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London’s renowned Saatchi Gallery is known for championing the work of previously unheard-of artists, offering a springboard to fame. Living up to this reputation, in March this year the gallery will feature work by some of the UK’s youngest and least-publicised artists – displaying creations from a cross-disciplinary project completed by Year 4 learners at NACE member and Challenge Award-accredited Pencoed Primary School.
Titled “Creating our Welsh identity”, the project started with a focus on learners identified as at risk of underachieving, including the more able – but its success led to elements being rolled out across the entire year group, and the school.
Class teacher Chloe Maddocks, who coordinated the project, explains more…
The context:
Promoting creativity and creative thinking is part of our school vision, and we recognise these as key life skills. However, this was an area we felt we could develop further.
We developed the “Creating our Welsh identity” project with the aim of raising academic attainment, improving learners’ self-esteem and confidence, and developing their creative skills – combined with a focus on numeracy and links to the year group topic. We also wanted to explore learner and staff perceptions of what it means to be creative, and to develop this thinking and awareness of broader creativity.
Having scoped out the project, we successfully applied through the Arts Council of Wales for a grant of £10,000, to be split between Year 1 (2016-17) and Year 2 (2017-18).
The project:
Running for the duration of the spring term, the project was linked to the Year 4 theme, The Stuarts. Initially, we selected 18 learners, targeting those at risk of underachieving. Due to the project’s success, we subsequently adopted some of the broader approaches across the rest of the year group and throughout the school.
At the start, learners did some research around the history of the Union Jack. Exploring symmetry, measuring and shapes, they then created their own version of the flag using fabric and donated materials, incorporating aspects of their own identity. Members of the community volunteered to teach learners to use a sewing machine, so they could stitch on their initials. The group also created personal identity drawings, based on research into the history of their family, incorporating words and symbols that represented them inside an outline of their body.
Numeracy was embedded from the start, right through to the end. We incorporated this in planning so all 60 learners within the year group were also taking part in the numeracy tasks. We looked at which National Literacy and Numeracy Framework (LNF) strands we could include, as well as planning our maths, language and topic lessons around the project. Focusing on real-life problems and tasks that reinforced specific numeracy strands – pricing activities, comparing costs from different supermarkets, profits and budgeting – allowed learners to relate to the importance of numeracy in everyday life.
More able and talented (MAT) learners were selected to act as leaders of certain parts of the project and were given the task of planning and coordinating the celebration event. All activities were differentiated to provide appropriate levels of challenge, and weekly evaluations allowed staff to tailor sessions to meet learners’ needs.
Learner engagement:
During the project we worked alongside Haf Weighton, a textile artist from Penarth. Haf brought some lovely ideas and had a wonderful working relationship with both the adults and children involved. She was selected by the learners themselves through an interview process, inspiring them with her style of art and her passion and love for her work.
Throughout, the learners were a key influence in determining the project’s direction, and were particularly active in devising the final outcome – the afternoon tea party. I had weekly conversations with them, in which they were able to evaluate their own work and the work of Haf, as well as discussing ways for the project to develop.
Celebration and exhibition:
To celebrate their work, learners hosted an afternoon tea party for parents and carers, sharing the project outcomes and showing off what they had learned throughout the topic. Around this event, learners had the opportunity to:
- Work alongside a candle maker
- Work alongside members of the community to create cushions and print
- Research what types of foods would have been served at a Stuart tea party
- Research the history of afternoon tea
- Take a trip into Pencoed village to purchase food
- Work out pricing, budget and profit
- Be filmed and interviewed by Heno, S4C
On the day of the party, parents and carers had the opportunity to sit in on either a literacy or numeracy lesson, tailored to the theme of the Stuarts.
Through Haf’s connections, we’ve also been able to reach a much wider audience. The artwork created was displayed in our very own exhibition in the HeARTh Gallery at the Llandough Hospital. Haf also shared details of the project at the Knit and Stitch Show in London, and – after the success of the project was shared online through our school website and Twitter – the prestigious Saatchi Gallery was very interested to work alongside Haf and to share the learners’ work.
Impact:
The impact for learners was far greater than we initially anticipated. All made progress with their weekly Big Maths scores and overall numeracy skills. They were also able to see the benefits of numeracy in everyday tasks, benefitting from the cross-curricular approach.
As well as developing a multitude of literacy, numeracy and creative skills, there was also an improvement in learners’ general confidence, wellbeing and self-esteem. For MAT learners, independent thinking and problem solving improved, and all learners felt a strong sense of pride and achievement in their work. Opportunities to see their work displayed, and to share their learning with parents and carers, provided inspiration to broaden their horizons and aspirations for the future.
There’s also been a wider impact, as we’ve shared the excellent practice across the school. In addition, the project has raised awareness about the importance of creativity among learners, staff and parents, showcasing how much can be achieved.
Next steps:
We are now in our second year of this project, and intend to continue running projects in this way. We’ve also been involved in school-to-school collaboration and shared our experiences in networking events across the Central South Consortium to promote this project to other schools. And of course we’re also planning to take the learners to the Saatchi Gallery in March, so they can experience the exhibition first-hand!
Chloe Maddocks has been a full-time teacher at Pencoed Primary School for four years, teaching Years 3 and 4. As coordinator of the “Creating our Welsh identity” project, she’s enjoyed opportunities to develop her leadership and project management skills, learner engagement, and share expertise with peers at other schools. She’s passionate about showing how creative skills can be incorporated into cross-curricular learning.
Pencoed Primary School has been a NACE member since 2014 and achieved the NACE Challenge Award in July 2015. With approximately 600 learners enrolled, the school is dedicated to developing networks of good practice and continually reviewing and improving its provision for all learners within an ethos of challenge for all.
Do you have an inspiring project to share with the NACE community? Contact us to share a case study.
Tags:
arts
creativity
enrichment
KS2
Wales
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Posted By Mike Sheridan,
24 January 2018
Updated: 08 July 2019
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In this blog post, Mike Sheridan, Ofsted’s regional director for London, gives an update on Ofsted’s research into the curriculum – emphasising the importance of staying focused on quality of education, rather than qualifications.
In my last blog post, I talked about Ofsted’s forthcoming research into the curriculum. Since then, the Chief Inspector, Amanda Spielman, has published a commentary which set out some of our initial findings. If you haven’t had a chance to read it yet, I’d encourage you to do so. In it, Amanda challenges us to think about the substance of education. She writes:
“What do we understand to be the real substance of education? When we think about what the core purpose of education is, what comes first to our minds? In recent years, we have thought a great deal about the role of leaders and the importance of teaching. We have also given a great deal of our collective time to exam grades and progress measures. These are undoubtedly important. However, at the very heart of education sits the vast accumulated wealth of human knowledge and what we choose to impart to the next generation: the curriculum.”
The final sentence in this quote resonates with me, as I’m sure it will with many of you, because it challenges schools to think about why they do what they do. Let me explain.
Qualifications versus quality of education
I sometimes wonder if some schools have become so driven by end of key stage measures that they’ve lost their focus on the substance of education. I’d like to encourage teachers and leaders to focus honestly on this and consider if tests and examinations have become an end in themselves, rather than a measure of the quality of education a pupil is receiving.
Put another way, when schools are making curriculum decisions, are they primarily concerned about the knowledge and experiences a learner will glean, or the examination outcomes the learner and school will record?
Let me be really clear here. I’m not suggesting for a minute that examinations and accountability measures aren’t important. They are both vital and necessary. But where schools are “gaming” the system to the point where the education learners receive is compromised – and we have seen some evidence of this – pupils are the ones losing out.
What needs to change? Well, we need to make sure every school’s curriculum is focused on substance (the stuff learners know as a result of their schooling), not “stickers” (qualifications for the sake of qualifications, which add little to their broader knowledge and understanding).
There have been some well-rehearsed examples of practice designed to get the “sticker” at the expense of the experience of learners. For example, learners being entered for easy qualifications which add little, if anything, to their knowledge or ability. Or being entered early into mathematics GCSE to secure a grade C, when two years’ study rather than one would give them a deeper understanding, and perhaps prepare them to study mathematics at a higher level.
Make every key stage count
These examples are, thankfully, much less commonly seen in our schools today than they have been in the past, and pupils are getting a better deal because of their demise.
However, there are still examples of practice in schools which, despite stemming from good intentions, focus on the importance of qualifications at the expense of experiences. One of these, and the one I really want to highlight, is the narrowing of a broad curriculum to spend more time preparing for tests.
We see this happening in two ways. First, in some schools the Year 6 (and sometimes Year 5) curriculum focuses too keenly on passing the tests. I can’t imagine the boredom and frustration some children must feel in this situation, and the missed opportunity to develop their knowledge across a full range of National Curriculum subjects.
The second is the shortening of Key Stage 3 and early start of Key Stage 4. While I can see the arguments for this, we shouldn’t lose sight of the importance of KS3, and the rich range of subjects studied during this time. For some learners, this is the last time they will study important subjects such as history, geography or the arts. Are we really saying that losing this breadth early is serving them well? I believe we should be focusing on making KS3 a period in a young person’s life where they are enthused across a full range of subjects, taught well by teachers who are passionate about what they are teaching. At the very least, I would hope those schools that are lengthening KS4 stage have a good reason for doing so.
If we are serious about teaching a rich, knowledge-based curriculum, surely we need to hold our nerve and make decisions with this at the forefront of our minds. At Ofsted we are continuing our research into this, and will publish fuller findings later this year.
Tags:
curriculum
Ofsted
policy
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