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 Hilary Lowe,
11 December 2019
Updated: 03 December 2019
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NACE Education Adviser Hilary Lowe goes in search of the perfectly pitched challenge...
Building on NACE’s professional development and research activities, we continue to explore and refine the concept of ‘challenge’ in teaching and learning for high achievement – the central tenet of much of our work and the heart of provision for very able learners.
What do we mean by challenge?
The notion of challenge is multi-faceted and goes further than designing individual learning and assessment tasks. It merits a subheading which makes it clear what we mean. As a provisional and necessarily evolving definition:
“Challenge leads to deep and wide learning at an optimal level of understanding and capability. It encompasses appropriate learning activities but is more than that. Its other facets include, for example: the learning environment, the language of classroom interactions, and learning resources, together with the skills and attributes which the learner needs to engage with challenging learning encounters. These encounters may take place both within and beyond the classroom.”
Some of these building blocks coincide with pedagogical approaches and theoretical perspectives which enable challenging learning for a wide group of learners. It is important therefore that we also interrogate these perspectives and adapt related classroom practices to ensure relevance and application for the most able learners.
Our work on challenge in teaching and learning is part of a wider campaign that will also explore and promote the importance of a curriculum model which offers sufficient opportunity and challenge for more able learners.
Below, we focus on the design and delivery of challenging tasks and activities in the classroom which are likely to enable more able learners to achieve highly and to engage in healthy struggle.
Pitching it right: keep the challenge one step ahead
If teaching for challenge is providing difficult work that causes learners to think deeply and engage in healthy struggle, then when learners struggle just outside their comfort zone they will be likely to learn most. Low challenge with positive attitudes to learning and high-level skills and knowledge can generate boredom within a lesson, just as high challenge with poor learning attitudes and a low base of knowledge and skills can create anxiety. Getting the flow right, ensuring the level of challenge is constantly just beyond the learners’ level of skills and knowledge and their ability to engage will then create deeper learning and mastery.
By scaffolding work too much and for too long, and stealing the struggle from learners, we can undermine expectations and restrict the ranges of response that our learners could potentially develop unaided.
Implications for planning and teaching
What then are the implications for planning and for using every opportunity inside and outside the classroom to “raise the game”? Challenge should involve planned opportunities to move a learner to a higher level of achievement. This might therefore include planning for and finding opportunities in classroom interactions for:
- Tasks which encourage deeper and broader learning
- Use of higher-order and critical thinking processes
- Demanding concepts and content
- Abstract ideas
- Patterns, connections, synthesis
- Challenging texts
- Modelling and expecting precise technical and disciplinary language
- Taking account of faster rates of learning
- Questioning which promotes and elicits higher-order responses
When considering the level of challenge in your classroom, ask:
- Do you set high expectations which allow for the potential more able learners to show themselves?
- Have you reflected on prior learning and cognitive ability to inform your plans?
- Is your classroom organised to promote differentiation?
- Do you plan for a range of questions that will scaffold, support and challenge the full range of ability in your class?
- Can you recognise when learners are under- or over-challenged and adapt accordingly?
- Are you using examples of excellence to model?
- Will learners be challenged from the minute they enter?
Share with your learners your expert knowledge, your passion, your curiosity, your love of the subject and of learning. Have high expectations – and resist the urge to steal their struggle!
Challenge in the classroom: upcoming NACE CPD
New for 2020, NACE is running a series of one-day courses focusing on approaches to challenge and support more able learners in key curriculum areas. Led by subject experts, each course will explore research-informed approaches to create a learning environment of high challenge and aspiration, with practical strategies for challenge in each subject and key stage.
Details and booking:
An earlier version of this article was published in NACE Insight, the termly magazine for NACE members. Past editions are available here (login required).
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Posted By Sarah Carpenter,
16 January 2018
Updated: 03 November 2020
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Getting to grips with mastery doesn’t have to be hard work – far from it. In this blog post (originally published on schoolsimprovement.net), NACE associate Sarah Carpenter outlines a simple but effective use of mastery to improve primary English provision for all learners, including the more able…
While teachers and schools are at different points in the maths mastery journey, it’s now fairly clear what that looks like and what’s expected. When it comes to English, however, there’s relatively little guidance on how to use mastery effectively.
Inspired by Michael Tidd’s advocacy of longer literacy units, covering fewer texts and focusing on writing for a social purpose, over the past three years I’ve worked with schools to develop a mastery approach for primary English. This is certainly not the only approach to mastery in English, but it is an approach that I and the schools involved have found effective.
The concept is simple: each half term the teacher selects a central “driver text”. This is paired with a range of supplementary texts, including fiction, poetry, non-fiction, multimodal texts, and cross-curricular links. The unit is planned around the driver text, building in curriculum requirements and a broad range of writing opportunities.
This approach gives all learners the opportunity to develop a secure understanding of the driver text, subject matter and key skills – as well as the scope to work in greater depth and to explore and showcase their creativity and writing abilities.
Here are six reasons to try this mastery approach in your primary English provision:
1. It works for learners of all abilities
First and foremost, mastery is about providing support and opportunities for learners of all abilities to develop at their own pace. This approach allows time for all learners to become familiar with the central text and subject matter, and to practise specific skills such as predicting, comparing, making connections and synthesising.
For learners working below age-related expectations, you’re not moving on too quickly, and there are opportunities to consolidate skills through repetition. At the other end of the spectrum, more able learners have opportunities to broaden their knowledge and understanding of the writing purpose, bring together multiple texts, and deepen their subject knowledge.
The inclusion of poetry in each unit helps to expand learners’ vocabulary and get them thinking creatively about the choices they’re making. The use of non-fiction and cross-curricular texts provides opportunities for the more able to make clever use of sources, and to play with their writing styles, taking the audience and purpose into account. They have a bigger toolbox to draw on, allowing them to really show off their finesse as writers.
2. It engages even reluctant writers
When choosing a driver text, I try to choose one that will capture the interest of everyone in the class, particularly keeping boys in mind. Then I plan the unit to incorporate a wide variety of writing opportunities – short, medium and long – so even reluctant writers face something manageable and interesting, that breaks the mould in terms of what they’re usually asked to write.
3. It develops deep subject knowledge
Bringing in supporting texts with a shared theme allows learners to develop a deep sense of subject knowledge, so they can write as experts in the field. Just as a published author wouldn’t start writing without doing their background research first, we’re setting the same expectation for our pupils. This approach resonates very much with highly able learners in English.
4. It makes more effective use of time
This approach takes up no more or less time than would already be used for literacy sessions, but makes more effective use of that time. Covering fewer texts in a more focused way means more time to get deeply into the full range of curriculum requirements – in terms of reading, writing, drama and spoken language. You can even use the driver text or an accompanying text for guided reading sessions, so everything is working together.
In terms of planning, you do need to allocate more time at the beginning, because you’re essentially planning out the full half term in skeletal form. You can adapt as you go along, but you need to plan ahead to ensure you extract everything you can from the driver text and stop at the right points, building up that sense of mystery and anticipation, and allowing for reading and writing opportunities along the way.
Once you’ve chosen the driver text, you’re looking for those opportunities to bring in non-fiction, and searching for appropriate poetry connections. Once you’ve done this groundwork, you should find you spend less time on weekly planning, because you’ve got the framework in place.
5. It works for all types of text…
…even (or especially) picture books! I often choose picture-based story books or graphic novels, such as David Wiesner’s Flotsam or Shaun Tan’s The Arrival – which can be interesting when you tell people the unit is going to improve children’s vocabulary and grammar! Other driver texts I’ve used include Robert Swindells’ The Ice Palace, Rob Biddulph’s Blown Away, Helen Cooper’s Pumpkin Soup and Alexis Deacon’s I am Henry Finch.
Essentially, you’re looking for a text where you see lots of potential to go off at all sorts of different angles, and bring in cross-curricular links. For example, with I am Henry Finch, there are lots of links to be made with PSHE.
6. It’s fun!
Last but certainly not least, this mastery approach is fun. I’ve developed units for KS1, lower KS2 and upper KS2, with positive feedback from all. Not only have schools got some fantastic writing and reading responses from learners, but the children have really enjoyed it. They appreciate the opportunity to get deeply into one particular text – but not to the extent where they get bored, because they’ve got the addition of other texts of different types, and the scope to show off just what they can do.
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Posted By Belle Cottingham,
28 November 2017
Updated: 08 April 2019
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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.
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Posted By Belle Cottingham,
27 November 2017
Updated: 21 March 2019
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In this blog post, mathematics consultant Belle Cottingham argues that a maths mastery approach holds the key to ensuring more able learners develop the creative problem-solving skills needed for success – not only in exams, but in their future careers.
“We don’t do differentiation now, we do mastery instead!” I was recently told by a school teacher.
The more I discuss mastery with teachers, the more I encounter a general misunderstanding in the application of it. It seems to be a commonly held belief that when using a mastery approach, all learners must be doing the same work and move through the programme at the same pace. It therefore follows that those considered “more able” suffer from a lack of differentiation.
Is that what mastery is about? Shouldn’t the more able be accelerated? What should learners do in a mixed-ability class if they have finished the question? How can a teacher manage learners’ work when some complete the task quickly and others need more time to grasp the concepts?
These are challenging questions for most teachers and educators, and at present there is little clear guidance.
Depth, not speed
Of course, the answer is simple: yes, there should be differentiation. But how can this be achieved in a mixed-ability class where teachers are often already maxed out in terms of time and resource?
Prior to the mastery approach, more able learners were usually accelerated by moving through the curriculum faster than others. For example, if most of the class was learning how to multiply, accelerated learners who knew how to multiply were taught how to divide.
Is learning a tick-box exercise? Does teaching someone to drive make them immediately a driver? Is the breadth and depth of a question important too?
Learning takes time.
When mastery is truly applied as it was intended, learners get the opportunity to explore and deepen their understanding beyond the boundaries set within the national curriculum.
There is always more to learn; there are always new ways to look at a concept. Learning is not a linear concept; it’s a curve that moves up and down, constantly changing. A process of evolution. Learning is not about memorising steps, or reeling out answers parrot fashion. It’s about developing ideas, making connections, clearly understanding the why behind the question, rather than racing straight to the answer.
Why we need maths mastery
In 2017 the pass boundary in GCSE mathematics (grade 4) for our learners was 17%.
17%! That’s what young people – our future nurses, dentists, architects, plumbers – needed to pass the exam. There was still a drop in the number of students that passed the exam. To achieve the maximum grade possible (grade 9), our most able learners had to achieve only 80%.
I wonder how we compare with our neighbours? Or other developed countries? Sometimes I think it is best not to know the answer, and this may be one of those times. In my view, 17% to pass and 80% to achieve the maximum grade is simply not good enough. Were the exams that difficult? Was the mathematics used so advanced? What is happening to our brightest learners from primary schools when they enter secondary school?
I recently worked with a group of 20 students in Year 11. Their GCSE grade targets were 7 and 8. I gave them the second question from a GCSE specimen paper. The first few questions are usually the ones everyone can access, but that’s not what I found at all.
Out of 20 learners in the group only three managed to solve the question independently. The other 17 said they were unsure what “proportion” was. They were considered “good” students in school (based on previous results). They wanted to do well in their GCSEs. They wanted to solve the question. They just didn’t know how. So where are we failing?
Developing creative problem-solving skills
Why are our more able learners unable to solve a question unless we ask them specifically what we want and tell them how we want it? What happened to initiative, taking risks, trying things, not being afraid?
There is no point asking learners to think critically, extend their knowledge and problem solve in exams if we haven’t invested time and energy teaching them how to do this. We can’t expect our learners to solve a question in different ways if teachers have been trained to explain a concept in only a single way.
Change doesn’t happen overnight. For teachers to embed new practices they need to see evidence that they work, and they need to know that they will have the time to implement change and see it through without external meddling. They need to buy into the idea.
This summer I was lucky enough to observe seven primary and secondary schools in Japan. They were all mixed classes of 30-40 students. All the lessons I saw were based around a single task. If the learner solved the task in one way, s/he immediately moved to a second method and then a third and so on. I was surprised to see that the more able learners didn’t look bored when they had solved the task in one way. They knew exactly what was expected of them – they just kept going, trying, drawing graphs, using algebra, exploring...
If this was possible in a classroom of 40 learners, it’s certainly possible in our schools. Frankly, Japanese results speak for themselves. Japan is consistently ranked in the top five countries for mathematics, according to TIMSS results.
What is particularly impressive when you analyse the TIMMS results is Japanese learners’ aptitude for solving questions they have never seen before. As can be seen from the illustration below, though only 54% of the material from the test had been taught in Japanese schools (different countries have different curricula), learners in Japan achieved an average of 69%. They could solve questions they hadn’t been taught because of their mathematical thinking/reasoning ability.
Is this an important skill in life? Well, a problem wouldn’t be a problem if we knew the answer beforehand!
Instead of accelerating children through the curriculum, the maths mastery approach supports deeper understanding and exploration – allowing more able learners to develop creative problem-solving skills that will serve them well not only in exams, but in their future careers.
Continuous improvement
All these ideas may be simple to apply, but knowing when to use them and how to use them can be challenging. Our teachers need the right resources, support and training to be able to adapt and grow themselves. It is simply not good enough to roll out a concept and expect people to organically learn. For our learners to solve tasks in multiple ways, they must be taught by teachers who themselves are capable of using different approaches to solve tasks. This may sound obvious, but a lot of teachers will have grown up in an education system where learning through repetition was rife. Consequently, structures must exist to provide guidance where this is needed.
For the maths mastery approach to be successful in the UK for children of all ages and abilities, we need to allow time for that to happen. Countries like Singapore and Japan have been working throughout the 1980s and 90s to shift their national approach gradually to a mastery model. What we see now is the result of years of relentless work from teachers, authors, parents and learners. Importantly, this process remains ongoing in these countries with frequent reflection and improvements/adjustments being made – which is of course consistent with mastery. There is always room to improve and learn more!
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.
For Belle’s advice on how to challenge more able learners within a maths mastery approach, click here.
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