To date, her career has spanned early years, primary, secondary, HEI and advisory roles. She is passionate about ensuring all children and adults learn and love mathematics. She is an active participant of the mathematics community and is chair of the Primary ATM/MA Group, a member of NAMA, ECMG and BSRLM and an invited member of the Primary Contact Group with The Royal Society. Follow her on Twitter (@easternmaths), find her on LinkedIn or visit her website: www.alisonborthwick.co.uk

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There is a new scheme on the block, and I was invited to take a look!

Oxford University Press have been designing and writing a new digitally-led resource that supports the teaching of mastery in the UK. With a fantastic team of writers and editors, I was keen to see what a ‘scheme of the future’ might look like.

MathsBeat is a scheme that makes you think! It is not for the teacher who is looking for a quick win, a pile of lesson plans to follow, or a reduction in planning time. Good! It is a scheme that you need to put effort in and use as a framework to scaffold your thinking. If you want a resource that really supports children to think, reason and understand mathematics, this is for you.

While most of the scheme is online, each year group (Y1-Y6) also has a Teacher’s Handbook (Y1-Y2 are currently available as printed handbooks). I like this. This means I can use both the online materials (via Kerboodle) but also flick through a book too. The Teacher’s Handbook offers selected examples of some of the tasks (one or two per strand). This really helped me to then navigate the online resources with more determination that perhaps I would have otherwise.

MathsBeat contains all the usual elements you would expect to find in a scheme (e.g. objectives, activities, assessment questions, etc). However, this is no ordinary scheme. At the heart of this scheme is understanding – for both the teacher and the pupil. Instead of pages and pages of what to do, what to say, what to ask etc, the authors expose the structure of mathematics by suggesting key manipulatives to use, by encouraging teachers to pose misconceptions and to offer non-examples which prompt pupils to think and reason, and, by going deeper, to really understand mathematical structure. Working systematically, predicting and verifying and asking pupils to convince are all part of the suggested pedagogy.

Here are a few of the elements you might expect:

• Unit maps, overviews and strands (which reflect the national curriculum for England mathematics curriculum)
• National Curriculum for England objectives (sub-objectives are included for each term)
• Aims of each strand (with a short video to watch if you wish to), key ideas and models and apparatus (MathsBeat uses a core set of manipulatives)
• Learning tasks (notice the word learning, not teaching!)
• Mathematical vocabulary (this includes both content and skills vocabulary)
• Differentiation in the form of ‘on track’, ‘needing support’ and ‘going deeper’. Each phase is also followed by ’what next?’
• Assessment for learning opportunities (‘on track’ helps you to know what features children should be displaying if ‘on track’; the ‘look and listen for’ gives advice about what to notice if children are not on track, and is followed by ‘if so …’ suggestions). Super helpful!

There are also a few additional features, which I like and which I suspect will become particularly helpful as technology becomes ever more present in our educational lives.

• Digital planners – these are helpful. Teachers can select the appropriate strand, tasks, videos, practice sheets, manipulatives etc quickly and then store in one place. There are also ‘front-of-class slides and downloadable practice activities’ (useful but quite typical with any scheme).
  
• Virtual manipulatives (including Numicon, of course!). Although real manipulatives are encouraged throughout, there is also a bank of virtual ones to use too. This is helpful, particularly when we find ourselves in situations where children can’t use real manipulatives, or we want to demonstrate something to the whole class. And of course, children are getting very good at using technology, so it is helpful to draw on these skills too!
  
• CPD – in the form of short videos. Both Mike Askew and Robert Wilne (the two editors) offer short videos to help you navigate your way through the scheme, draw your attention to different elements and support your subject knowledge when teaching for mastery. This element is particularly helpful. We know that any book, scheme or resource is only as good as the professional development that sits alongside it. These videos can be used to either support you as the teacher or as PD opportunities to use with all teaching staff in your school.
  
• Authentic conversations and examples of children’s work. I often want to ask: ‘So what does this look like?’. For me, this is perhaps the most powerful part of this scheme – being able to see children’s work, what they did and the conversations that took place between the teacher and the child. This really exposes the mastery element of going deeper and focusing on understanding, not just getting the correct answer. Notes, questions and reflective comments that sit alongside these vignettes really do make you feel as though the authors are sitting on your shoulders, guiding you through all of this. As I said earlier, this scheme will make you think!
  
• Exposing misconceptions and non-examples. We all know this is good practice, but it is really helpful to see how we can do this in a structured way. As well as providing the task to try out there is also a running commentary offered, in the way of statements and questions, to prompt thinking and reasoning with children but also for teachers too. This part really does help to develop teachers’ subject knowledge.

As you would expect there is a teaching sequence. This is organised into three phases:

1. Pre-emptive teaching suggestions and launch tasks
2. Learning task
3. Bigger thinking

Phase 1 encourages teachers to take opportunities to use formative assessment to find out what children do and don’t know before heading straight into the topic. It also serves as a reminder to children about some of the mathematical content they will have covered previously, but forgotten about until now! This is all presented in a launch task.

Phase 2 contains the four learning tasks offered for each week. As well as the actual task, prompts, actions and questions are a key part of this section. I really do like how examples of the way in which children tackled the tasks are included here. It is a privilege to be able to parachute into a lesson and see how it could unfold. The comments that are offered alongside the example are highly informative too. You could take any one of these and use in a PD session with teachers. Here are a few examples:

• Why is confidence with 10-frames necessary before working with base-ten apparatus?
• Which of the methods you tried do you feel is the best approach for this calculation? Can you explain your reasoning?
• Are children confident with partitioning all numbers to 10? If not, what could you do to improve their conceptual understanding and rapid recall?
• What is the same and what is different about the arrays and calculations?
• What common error is shown by this child?
• Why do you think the teacher asked the child to check with a different method?

Phase 3 focuses on ‘bigger thinking’ where children are encouraged to think, and think harder. The task is offered to all children and helps to summarise the learning for that week. Because of the open-ended nature of the tasks all children can access these tasks and it is great to see that fluency, reasoning and problem solving is central to these tasks.

Often, one of the criticisms of schemes in general is that teachers feel obliged to follow it – almost to the letter. But with MathsBeat you are encouraged to ‘adapt and use what is appropriate’. One of the two key principles of MathsBeat is that ‘no two classrooms are the same’. So, if you want to use the script, you can, but the message throughout is to do what your children need, not what the scheme tells you to do. This is a good mantra!

The other principle centres around mathematical thinking. While all children can and do solve problems, it is our job to help them to figure out the most efficient way to solve each problem. While one method may work for one pupil, it will be different for another pupil. MathsBeat reminds us of this through the inclusion of children’s mathematical thinking to problems and the accompanying prompts and questions in the text.

The scheme is well structured and relatively easy to follow, although I suspect (as with anything new) it will need some investment (in time) to really get to understand and use it effectively. There is a lot of content. However, because this is a digitally-led scheme, rather than having to flick backwards and forwards between pages and books, the tabs do help here.

Another feature I like about MathsBeat is the attention to detail. You really do get the sense that all involved in this scheme really do know how to teach effectively and for understanding. For example, 4 x 5 is explained as ‘4 multiplied by 5, or 5 groups of 4’. Often this is misrepresented in mathematical documents, but in MathsBeat it is mathematically correct and also highlighted to support those using the scheme. Another example is when the authors talk about over-generalization. This is helpful as it reminds us that all children can and do need to be able to generalize, but they can sometimes make links that are mathematically incorrect. For example, addition is commutative, so subtraction must be too. Not only are these misconceptions highlighted, but guidance is offered in how to address this usefully in the classroom.

This is a scheme for confident teachers. Its purpose? To support the teaching of mastery by teaching for understanding. The different phases remind us that mastery is about having an inclusive expectation that all children are capable of learning mathematics and that we are capable of teaching all children. Teaching mathematics well is about teaching children to work fluently and flexibly, to think and reason and, of course, to problem pose and problem solve. MathsBeat has captured how to do this brilliantly.