In this second of two blog posts, mathematics consultant Belle Cottingham outlines five approaches to ensuring more able learners are effectively challenged within a maths mastery curriculum.

In my previous blog post, I argued that a maths mastery approach holds the key to ensuring our more able learners develop the creative problem-solving skills they need for success – not only in exams, but in life more generally.

Of course, this is all great in theory, but how do we effectively achieve differentiation in maths mastery? There isn’t a strict right or wrong answer, but here are five approaches to try…

1. Anticipate and adapt.

Good teachers anticipate. They know their learners and anticipate what they may say, what mistakes they may make, what answers they may give. All learners are different, with different strengths. Just because a learner is more capable at calculation, doesn’t necessarily mean that s/he is also more able at problem-solving or shapes.

Anticipating answers is not easy; it takes years of experience and constant growth and development from the teacher’s point of view. However, the more accurate the anticipation, the better the tasks and the more appropriate the challenges the teacher can set.

2. Use skilful questioning to promote conceptual understanding.

Mastery is not about doing repetitive questions. In fact, the beauty of mathematics itself, with or without mastery, is that it is infinitely stretchable. Questions can be solved in more than one way. Questions can be asked in more than one way.

For example, let’s imagine a group of children are learning the 8 times table. Some will be quicker than others. Some may already recall the tables. Just because they can recall them, however, doesn’t mean that they understand why.

“Why is 8 x 3 the same as 3 x 8?” “What does 8 x 6 look like?” “Is 8 x 6 > 6 x 9?” These are just some of the ways the question can be asked or extended.

Each of these questions will make learners think beyond the simple calculation. A calculator can calculate; a brain can reason, question, explore… Brains were built for exactly that!

3. Use problems that can be extended for more able learners.

The choice of tasks and questions used in the classroom should be carefully considered and selected. The questions should be set so everyone in the classroom can readily attempt them, falling within the overall knowledge bracket, but they should also be suitable for simple extension to challenge and deepen understanding.

Continuing the tables theme, a question like “Find different ways to calculate 12 x 4” can be very rich in answers.

Some students may add 12 + 12 + 12 + 12, making links between addition and multiplication.

Others use the multiplication facts that already know. The 2 and 10 times tables are taught before the 12 times table. Hence, they can calculate 2 x 4, 10 x 4, then add the results.

Or they can simply use the properties of multiplying by 4, double, then double again. 12 x 2 = 24 and 24 x 2 = 48.

There are many ways to think about multiplying two numbers, and each of them can link to other ideas, concepts and applications.

4. Use concrete pictorial and abstract (“CPA”) representation.

More able learners can benefit as much as their peers from the use of CPA representation to visualise and represent mathematics in different ways.

Providing concrete material for everyone will facilitate more able learners’ need to meet problems which are presented in different ways, in different contexts and with use of more varied vocabulary. Using the table question, more able learners may use counters or marbles to explain to a partner what 6 x 8 looks like. Being able to articulate the mathematical thinking is a very important skill that we need our future mathematicians, engineers, teachers and doctors to have.

More able learners may also be encouraged to work in mixed-ability groups and asked to write a question based on a picture they see, or write a question that has a mistake in it… The options of extending a mathematical task are limitless and the more it happens, the more robust the mathematical foundation in our learners will be.

5. Allow time to explore, think and reflect.

This is very important for all learning to happen. The mastery approach provides this. Reflecting on mistakes that a learner has made herself, or that someone else in the classroom made, is a very good strategy that can be used to clear any misconceptions, and is particularly effective through the learners’ own voices. Having time for reflection is crucial in creating maps of knowledge that can be used in developing future concepts or embedding the roots of the existing ones.

Mathematics consultant Belle Cottingham has a Masters in Mathematics and Learning, and a decade’s experience in teaching and tutoring maths for all ages and abilities. A member of the Mathematical Association, Association of Teachers of Mathematics, National Association of Mathematics Advisers, and Japan’s Project Impuls, she writes for the Mathematical Pie Magazine and has authored teaching guides and textbooks, including contributions to the Rising Stars Mathematics range. You can follow her on WordPress and Twitter.

Lesley Hill, headteacher of NACE member Lavender Primary School in North London, shares her school’s approach to ensuring the curriculum remains broad, engaging and meaningful – alongside a successful focus on good outcomes for all learners.

“Lavender” School conjures images of a delightful school in a leafy suburb. It is a delightful school, but we have our challenges. The number of children with English as an additional language, and of those eligible for FSM, are both above national averages. We also have a high number of children with need. However, challenges are not just about closing gaps, and when it comes to curriculum one particular challenge is to hold on to what is important.
 
In the late 80s, I was an advocate of themes, of helping children see links in learning and maximising creativity. Although I understood the need for a national curriculum (to avoid children potentially repeating the same topic year after year!), I had serious concerns about a rigid, dictated and narrow curriculum that would merely feed standardised tests.
 
A few decades (and curriculum reviews) on, and I don’t believe that prescription has to stifle creativity, or that children have to learn within a narrow framework to get results.

Empowering learners to make choices… and mistakes

For some years, most of our subject teaching has been done through cross-curricular topics and we insist on at least one pupil choice topic per year. Classes or year groups vote on different themes and teachers ensure that the statutory knowledge and skills are covered within the topic. In KS2, we aim to include children in the planning process by asking them to consider how the required topic content could be taught.
 
Our use of pupil voice helps to engage and motivate our learners, but we also want them to have ownership over their learning. The introduction of growth mindset five years ago made a marked difference in terms of attitude, and was particularly empowering for those higher-achieving learners who find it so hard to “get something wrong”.

Developing skills for self-evaluation and reflection

Learning to learn strategies were also embedded and this culture enabled us to introduce fast, effective feedback a year ago. Teachers do not write in any books, but mark verbally during lessons, through 1:1 or group conferencing. Children peer- and self-assess and write reflections on their learning against success criteria. The self-evaluative process needs higher-order thinking, and allows learners at all levels to develop those skills.
 
Meta-cognition is promoted through peer work and is particularly successful for higher achievers when working with lower achieving or younger children (such as through our Reading Buddy scheme). Talk partners are therefore picked randomly to allow a range of peer-work experience. Group and paired feedback has been successful across the curriculum. I opened a sketch book recently and read, “I spoke with my partner and we thought that I should put more shading and detail on the petals.” Our “drafting and crafting” approach is used across the curriculum, enabling children to reflect on all learning, not just the core subjects.

Encouraging creativity at home

The fact that we value all subjects is visible in our homework policy. Learners have the usual spellings and number facts to learn, but also work on given topic themes. Because the titles are quite open (such as “Enfield Town”), children can access them and deepen their learning according to their own starting points. On home-learning day, you might see children carefully manoeuvring a model volcano, clutching a home-made booklet about local history or a USB stick with a slideshow about chocolate. They might just have a sheet of notes that have been prepared for a “lecture”. They share these projects at school, paying special attention to their presentation skills, which are then peer- and self-evaluated.

Extracurricular experiences and engagement

Visits and outings are built into our curriculum. We develop enterprise and aspiration through trips to businesses and institutions, such as Cambridge University, and by inviting in key people. We value working with others, getting involved with school cluster creative projects wherever possible. Last year, we were able to buy in a British Sign Language (BSL) teacher from a partner school to teach sign language to every class from nursery to Y6. We also encourage entries to events such as the annual Chess Tournament and Mayor’s Award for Writing, and are in the process of organising a spelling bee across our partner schools.
 
Home-school partnerships are important to us. Family days, where parents come in and work alongside their children, as well as exhibitions and information fairs, help us to share our wider curriculum. One event saw parents being led on a tour through the WWI trenches and, last year, families came in to learn the school song (written by the children themselves). We also work to build wider community links through events such as bulb planting with the local park group, or charity choir performances. Our School Council representatives are confident and vocal when considering local and wider issues and how we can support others.

What does it all mean?

Lavender's results are very pleasing across all key stages. Our GLD, phonics, KS1 and KS2 combined outcomes remain above national figures, with progress data of our higher-achieving children being better than national in all subjects.

OK, so Year 6 do have to do practice tests and more homework than most, but you'll still catch them sneaking into my office during a unit on mystery texts, going through my bin, and desperately trying to work out if I'm actually a spy. Despite budget pressures, I will continue to find the money for Herbie's insurance (our school dog's work with the most vulnerable children is priceless) and I’ll always value our subject leaders for the passion and drive they bring to our curriculum.

Data will always be top of my agenda, but it's there alongside breadth, depth and enrichment. A broad and balanced curriculum doesn't have to be at the expense of good outcomes for our children.
 
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 book, Once Upon a Green Pen, which explores creating the right school culture, is due to be released early next year.

In this blog post for the NACE community, Mike Sheridan, Ofsted’s regional director for London, previews upcoming research commissioned to identify and share good practice to ensure all learners benefit from a broad and balanced curriculum. 
 
Alongside my reflections on changes to school accountability measures – to be published in the upcoming edition of NACE Insight magazine – I want to make a point that I hope many of you will agree with. Examinations are an important measure within education, but they shouldn’t be seen as the sole or driving purpose of education. Examination results give an indication of the quality of an education, but there is a worry that schools sometimes focus more on the exam itself, rather than the knowledge and skills it is testing.
 
Earlier this year, the Chief Inspector expressed her concern that too many schools aren’t giving pupils this broad and balanced curriculum, instead focusing very narrowly on exam subjects to ensure the best possible grades. In light of this, she commissioned a piece of research on the curriculum.
 
This piece of work is looking at how schools interpret the curriculum, to see what is effective and what isn’t. We will share the good practice we find (of which there is much!), but where students aren’t getting a good deal, we want to ensure this is made clear as well. We will publish our initial findings soon.
 
Rather than being seen as a threat, I hope this research will help calm the anxiety some feel is created by an excessive focus on tests and exams. My belief is that a great curriculum leads to well-rounded individuals who get good grades because they have the knowledge, skills, character and resilience to do well in exams and in life. If you believe the same to be true, perhaps now is the time to be brave so that we can transform our good education system into a world class one. One which fully equips our young people to confidently compete on the world stage.

Watch this space for Mike’s commentary on Ofsted’s upcoming research publication on this topic, and contact us to share your own school’s approach to delivering a broad and balanced curriculum.

Keren Gunn, senior assistant principal for teaching school and staff development at Sir Christopher Hatton Academy, explores the challenges and opportunities of the new top GCSE grade.

Sir Christopher Hatton Academy is an outstanding (Ofsted 2015) mixed comprehensive, the lead sponsor in the Hatton Academies Trust, a teaching school and lead of the Hatton Teaching School Alliance. It achieved its second accreditation with the NACE Challenge Award in 2015, and is working towards its third. 

As we review and renew our practice for all learners, I have been reflecting on what the change to the new 9-1 GCSEs means. What will a grade 9 look like; what are the qualities of “grade 9-ness”? How will we teach it effectively, and will we recognise it when we see it? 

We know that according to Ofqual and the DfE, about 20% of the number of students achieving grade 7 or above will achieve a grade 9, and this means about 2.9% of students who would have got an A* would be getting a grade 9 this time round. 

Opportunities and challenges across the curriculum

We see the new grade 9 as a real opportunity, as well as a challenge. From speaking to middle leaders across the academy, the challenges and the opportunities sound remarkably similar across the subjects. The grade 9 system provides huge opportunities for stretching and challenging students, and could allow for real progression and mastery within the curriculum. There are significant opportunities to exploit creative links with business, industry and higher education, for example in food technology or computing and beyond. 

Examples of the innovation taking place include the use of authentic materials in MFL to ensure the language is of a sufficiently high register; adaptation of teaching methods and materials previously used at A-level; and a significant awareness of the need to explicitly teach higher-level thinking skills. The changes also offer an exciting opportunity to re-shape our Key Stage 3 curriculum to develop learners earlier on.

And the challenges? First, the lack of quality exemplar materials from exam boards to guide on the difference between a grade 8 and 9 – particularly significant in subjects like English where we have long been used to a subjective mark scheme, but equally so in mathematics and science, where there are new uncertainties in how questions are likely to be worded. There is also the challenge of delivering additional knowledge-based requirements, while ensuring the skills needed for sophisticated evaluation and analysis are fully developed. 

Developing “grade 9” qualities and skills 

The very quality of being a grade 9 learner is to be independent, enquiring, analytical, critical – and teachers need to be given the best tools, materials and CPD to ensure they can meet these students’ needs. 

One area I have been working on in my own English teaching is the enhancement of targeted academic writing skills, to develop the quality of expression and lexical choices required at grade 9, as well as building contextual and cultural capital as students explore texts. I’ve also used open investigative approaches to poetry, encouraging learners to explore both creative and analytical responses, as well as more formal analysis. After initial work on the Ted Hughes poem “Bayonet Charge”, one student’s response in a first-person piece of creative writing read:

“As the bullets rained down on us the mud caught my feet and held me there as I stumbled frantically. That tear in my eye was not of bravery or patriotism, but of shock and pain. How could our country do that to us? Why would it push us to pain and anguish? I couldn’t comprehend.”  

She had been given time to explore themes, concepts, attitudes and values, enabling her to form independent ideas about the poem, which she will then be able to translate into more formal academic analysis. 

In realising that the message is about challenge for all, we can maximise the opportunity presented by the new GCSEs and embrace the vision of excellence for all students.  

This blog post is based on an article first published in the summer 2017 edition of the NACE Insight newsletter, available for all NACE member schools. To view all past editions of Insight, log in as a member.

Anna Wynd, head of modern foreign languages at North Oxfordshire Academy (NOA), explains how the school approaches language learning through a “menu of challenge”.

In our approach to modern foreign language teaching and learning at North Oxfordshire Academy, we strive to nurture and encourage our pupils’ enthusiasm and curiosity, offering a varied menu of challenge.

Interactive games such as the “horse race” allow pupils to work in differentiated teams to solve tasks that will move their horse closer to the finish line, while allowing opportunities for self- and peer-assessment. Our KS3 homework involves a variety of interests, skills and pupil choice at different levels, such as recipes in the target language.

Preparing for the unexpected

The current MFL Programme of Study details the importance of pupils having the opportunity to read literary texts in the language (such as stories, songs, poems and letters) to stimulate ideas, develop creative expression and expand understanding of the language and culture.

NOA’s MFL library, which includes books, DVDs and magazines, allows the MFL department to continue to support the Academy’s drive on literacy by encouraging reading for pleasure in the target language and an exploration of intercultural understanding.

In addition, the films act as an effective and enjoyable way of developing pupils’ listening skills, particularly in training them to deal with “the unexpected element” of languages – a skill required for outstanding achievement according to Ofsted. Furthermore, the longer texts have been challenging yet purposeful, and act as a great stretch for our most able language learners.

A varied menu of challenge

We also include the following in our menu of challenge for language teaching and learning:

• A bank of authentic resources which are planned into schemes of work (maps, brochures, receipts, magazines).
• A whole-school approach to Assessment for Learning (AfL): “Find the gap, teach the gap.” Every student has a knowledge organiser for every subject, and uses them to revise the vocabulary and grammar that is studied in each lesson for the memory platform test. Every lesson begins with a memory platform that assesses prior learning. Pupils then self-assess in green pen. The main aim for this is to improve memory recall.
• Using sixth-form students to support Year 11 in small study groups to go through exam skills. The Year 11 cohort enjoy hearing from a peer about how they dealt with the exam, revision and stress.
• French Club, attended by able language learners in Year 8. Activities include board games in the target language; discussion of festivals and traditions in more detail, and comparison with the UK or with the home country of the students who attend; pupil-created quizzes either on cultural facts or what they’re currently learning; listening to French songs and talking about art and artists.

This case study was originally published in the Spring 2017 edition of NACE’s Insight newsletter. To view past editions, log in as a member.