M AT H E M AT I C S
MEET THE TEACHERS AND JOIN A MATHEMATICS MASTERY LESSON
WELCOME TO MATHEMATICS MASTERY
My name is Helen Drury, I’m a maths teacher and Director of Mathematics Mastery
We believe that the UK needs a new approach to teaching maths. So we’ve drawn on the best of existing practice from all over the world to create Mathematics Mastery. Initially developed with teachers in the ARK network of schools, we are now partnered with over 100 primary and secondary schools in the UK and we’re excited to be bringing new schools to the partnership
At its heart Mathematics Mastery is simple – maths at any level, be it aged 5 or 35, can be broken down into a few core principles. Mathematics Mastery ensures pupils have a deep understanding of mathematical concepts; they explore these using objects, pictures and through conversation as well as written symbols and numbers. Mathematics Mastery puts problem solving and language at the centre of every maths lesson and we make sure that our pupils are resilient learners. Read on to sample a Mathematics Mastery lesson to find out how this works in practice.
We also believe that excellent maths teaching doesn’t begin and end in the classroom. Teachers both need and want professional development and support that flows seamlessly into every aspect of their teaching. Mathematics Mastery encourages teachers to develop their lessons and teaching techniques for themselves. We believe in our teachers as contributors and researchers as well as practitioners – Mathematics Mastery is driven by the schools and teachers within the partnership. Read on to hear one of our teachers explaining how her school’s membership of the Maths Mastery partnership helps her become a better teacher.
ACTION LINKED TO EVIDENCE
Mathematics Mastery has grown out of respected research and we will continue to learn and adapt as the partnership develops. We want to demonstrate the possibilities for mathematics teaching and learning in UK schools and show that the UK can be great at maths.
SO WHAT’S IT REALLY LIKE?
So what’s it like to be a Mathematics Mastery partner? The best people to help you with that are our schools, teachers and pupils…and I’m delighted to introduce just a few of them to you…
MEET A HEADTEACHER Miles Chester New King’s Primary School
I’m a Headteacher at a primary school in West London. We became a Mathematics Mastery partner school in 2012 – the very first cohort. We joined Maths Mastery because we’re always looking for new approaches that will have an impact on our pupils. I liked the fact that Maths Mastery was cutting edge but would be monitored closely and is based on educational research. Maths attainment in our school was already good but I wanted to find ways to accelerate progress. It’s not easy introducing a new classroom approach and I didn’t take the decision lightly. It was helpful that we were able to introduce it just to Year 1 to start with. It gave us a chance to get to grips with the principles without having to commit the whole school. Maths Mastery asked us to show that we were committed to the programme for the whole year – turning up to the cluster sessions and putting time and effort into making the school visits worthwhile. Like making any improvements, it certainly takes extra resources and time to make it work. It’s been worth it though and I understand why there is such an emphasis on engagement and commitment. I don’t teach Maths Mastery myself, but I’ve got a great Maths Mastery School Lead. The Year 1 teacher worked really hard and enthusiastically at introducing the programme. She spent a lot of time liaising with the Maths Mastery core team to make sure that the programme worked for the school. What’s been interesting for me is seeing how really experienced teachers and more junior teachers can both use the materials and support in the way that works best for them. It’s worked well with very different teachers. As a Headteacher I’m always trying to make sure that my staff are supported and getting interesting training and I’ve enjoyed seeing the teachers develop their teaching. One area of concern for me was how we would manage our Ofsted visits. I was worried that to people who aren’t familiar with the Maths Mastery approach, the units at the beginning of Year 1 can look a bit easy. I was concerned Ofsted would think we weren’t stretching the pupils enough. However when you see what that initial teaching enables the pupils to do by the end of Year 1, then it’s really impressive. Now I’d be very happy to show off Key Stage 1 to Ofsted. We’ve had measurable improvement in maths attainment. For the first time ever, our Year 1 class are all on track with expected progress – that has never happened before. My Year 2s (who studied Maths Mastery in Year 1) now make faster progress in maths than any other class in the school. And perhaps even more importantly, my pupils seem to be enjoying maths more. They get really excited when they find out that maths is next!
MEET MORE HEADTEACHERS “Over 80% of my pupils speak English as an additional language and I know how important it is to have a real emphasis on language and vocabulary – I was impressed by Maths Mastery’s focus on language and developing understanding through talking. I also believe that the concretepictorial-abstract approach is key to maths teaching and I liked the way this was embedded at every stage of Maths Mastery. As an inner London school we also have an inevitable turnover of staff and Maths Mastery ensures that our maths curriculum is stable, consistent and well-established, despite staff changes.” Suzanne Parry, Headteacher St Augustine’s Primary School “We joined Mathematics Mastery because we were interested to find out more about the SE Asian ‘mastery’ approach but we didn’t just want to purchase a scheme.What attracted us was the support package: the professional development, school visits and the academic/research approach. We haven’t followed it to the letter but we have merged it with our already excellent practice. Even as an outstanding school, it has really helped develop our pedagogy and practice for the better.” Kate Frood, Headteacher Eleanor Palmer Primary School
MEET A TEACHER Rebecca Carver ARK Conway Primary School
I’m a Year 1 teacher at a primary school in Hammersmith. I was an NQT when I started teaching Mathematics Mastery in 2012 and I was the first teacher in the school to work with the Maths Mastery approach. I was a bit apprehensive joining a new programme as an NQT. But I’m so pleased I did – I love teaching maths. One of the hardest things about being a teacher is making sure that you keep developing and learning whilst also fitting in a busy teaching schedule. Maths Mastery makes it easy for me to bring my own new learning into the classroom. When we signed up, I went for a day’s launch training. We had really intensive sessions on the principles of the programme and I was there with teachers from other schools. At first I was a bit daunted trying to implement everything we’d been taught. But because the principles are developed so strongly in the curriculum and teaching materials, I’m always drawing on the training when I teach. I’ve found the online tutorials particularly helpful. It’s like having a really keen teaching partner – a particular treat for me as my school is one form entry! I revisit the tutorials frequently during the unit so that I’m constantly reinforcing the principles. I’ve been a regular at the cluster sessions, where we meet up with teachers in other schools to discuss different aspects of the curriculum. It’s been reassuring and inspiring to find out what other people are doing. I’m also still in touch with some of the teachers I met at launch training and we’ve been to visit each other in our schools and observe each other’s lessons. It’s been great to make a new network of colleagues. Collaborating is effective because we understand each other but can bring new ideas. We’ve also had school visits from the Maths Mastery team. I’ve had some informative feedback and I like that they come to see us in our personal teaching environment.
“I like that I’m part of a new approach to teaching maths that gives you the time, space and tools to really understand not just what you’re teaching, but why you’re teaching it.”
At first I tended to plan my lessons one at a time. Now that I have more experience I plan all the lessons for the week in one go. I log in to the online toolkit and find the learning objectives and lesson principles. I go through and add my own success criteria specific for my pupils. I adapt and differentiate the tasks to suit my pupils and I write notes for the teaching assistant as to how to support different children through the lesson. I also have an ongoing bank of extensions that I create for the unit. I definitely have more confidence now than when I started. It’s always been clear that the whole point of the Maths Mastery principles and materials is to provide a framework for each teacher to adapt creatively for their own pupils. I’m now much more flexible and inventive about the way I teach. I like that I’m paart of a new approach to teaching maths that gives you the time, space and tools to really understand not just what you’re teaching, but why you’re teaching it. It’s been great working with other Maths Mastery teachers in the school. The Year 2 teacher is a much more experienced teacher than me and I’ve enjoyed working collaboratively. We have discussions about Maths Mastery everyday – it’s definitely a team effort!
JOIN A YEAR1 LESSON Numbers within 100 Comparing numbers
MEET SAM DAVIES AND HER YEAR 1 CLASS FROM KING SOLOMON ACADEMY My class has 30 children with a really broad spread of low and high attaining pupils. Most of them don’t have English as a first language. They have been learning with the Maths Mastery approach for around 8 months. Today’s lesson is all about comparing numbers within 100. They all know the numbers to 100 from previous lessons and we’ve done lots of work on place value, adding and subtracting numbers up to 40. They’re all confident using dienes blocks and number lines because we use them in every lesson. The children always sit at their tables at the start. First we go through the lesson objectives so I explain that we’re comparing numbers within 100 and they tell me that comparing numbers means working out if a number is bigger or smaller. We also look at the key words for each lesson – here they’re greater, smaller, tens, ones and compare.
Maths Mastery lessons follow a 6 part structure. This keeps the lesson pacey, gives flow and allows more opportunities to teach creatively, give feedback and assess learning.
1 DO NOW 2 NEW LEARNING 3 TALK TASK 4 DEVELOP LEARNING 5 INDEPENDENT TASK 6 PLENARY
Whilst the principles are always the same, no two Maths Mastery teachers are! Check the speech bubbles for ideas from other Maths Mastery teachers!
1 DO NOW
A warm up task to get the brain working quickly and effectively
SPOTLIGHT ON TRANSITIONS Every second counts in maths lessons. So between tasks the children sing songs or do call and response with the teacher. It helps keep them focussed and keeps the lesson flowing.
This is a warm up task which the children do independently at their tables. The material is a recap of previous learning and every child should be able to do it. To get them all started I’ve given them each a 100 square. I ask them to put a counter on a number greater than 59. And then on a number less than 15. And I do a few more examples. They’re already familiar with “greater than” and “less than” so this is a great way to remind them of previous learning and make sure they’re all concentrating for today’s new learning. The Do Now task lasts about 5 minutes and at the end the children will all come together for the lesson’s New Learning. They’ve all got spaces on the carpet in the centre of the classroom. Whilst the children are moving to the carpet, they will do a TRANSITION song – the song for today’s lesson is the Days of the Week Song!
“I would bring in a task from a previous lesson. A game where they have to work out which number out of 100 is missing would work well to remind them of previous learning.” Jasbir Mahey, Gilbert Colvin
“I might ask them to make the numbers that we need for the next task on place value charts. It makes sure they’re all on track for the new learning coming next.” Stephanie Lester, ARK Atwood
2 NEW LEARNING To introduce the main maths concepts for the day’s lesson
All the children sit in rows on the carpet. I’m using the interactive white board. We’re learning that to compare two numbers you can look first at the tens column and then at the ones column. I’m using two big place value charts which they’re all really familiar with. 10-15 MINS
SPOTLIGHT ON CONCRETE, PICTORIAL AND ABSTRACT Dienes are concrete objects. Pictures of objects are pictorial. Written numbers are abstract. Mathematics Mastery uses all three throughout each topic. FULL SENTENCES Pupils learn to express and explain concepts by always talking about maths in full sentences. This improves their understanding and helps them become more articulate.
I start off using CONCRETE manipulatives - dienes blocks. I put 6 ten rods in the tens column and 9 ones in the ones column. We all count them out together – “there are 6 tens and 9 ones, we’ve got 69!”. I then put 7 ten rods in the other chart. I ask one of the children to tell me what number I’ve made. “70!”. And please tell me how you know? “Because I count each rod 10, 20, 30, 40, 50, 60, 70!”. I ask them to talk to their partners about which number is biggest. I walk around the classroom listening in, reminding them to talk in FULL SENTENCES and checking their understanding. I then say that when you compare numbers you always have to look at the tens column first. We look at the tens column in 69 and count that there are 6 tens. And we do the same for 70 and count that there are 7 tens. I emphasise that 7 is bigger than 6 and so we know that 70 is bigger than 69 just by looking at the tens column. Then we make two different numbers on the charts: 57 and 59. We count the tens in each and find out that they’re the same. So I say that we don’t know which is bigger just by looking at the tens column – we need to look at the ones column too. We count the ones and we say together than 9 ones is bigger than 7 ones. And so we’ve worked out that 59 is the biggest number. I then do two more examples and I get the children to come up and make the numbers themselves, so that they are participating in the New Learning. We’re now 15 minutes into the lesson and it’s time to transition – this time we sing their Secret Number song – back to their maths tables.
“I would also put 69 and 70 up on flashcards as written numbers so they’ve got the abstract representation as well as the dienes blocks.” Stephanie Lester, ARK Atwood
“I also ask them questions like “Is it better to have 69 or 70 sweets?” to make sure they’re also understanding why comparing is important in real life.” Jasbir Mahey, Gilbert Colvin
3 TALK TASK
To practice the new learning and talk about maths
The pupils are back at their tables ready for the talk task, which they’ll do in pairs. This part of the lesson is really valuable as it helps me check progress and assess understanding. 10 MINS
SPOTLIGHT ON ADAPTING Maths Mastery has core principles and they work best when teachers are creative and adapt the suggested tasks so that they work for their pupils.
“I love the emphasis on language. I’ll give stars out when I hear pupils using the star words correctly.” Stephanie Lester, ARK Atwood
“I’ll vary the task so that the winner is sometimes the person who gets the lowest number.” Jasbir Mahey, Gilbert Colvin
The main focus here is on the children working together and talking in full sentences about maths. They’re all on mixed ability tables here and the task is essentially the same as the New Learning but in the format of a game. I’ve ADAPTED the suggested task slightly to fit it to my class – I want them to keep using dienes blocks and not introduce dice just yet. Each child picks a number card and then makes it on their place value chart using dienes blocks. Then one of them tells the other one which number is bigger and how they know. The person with the biggest card wins and keep the card. Then they pick some new cards and the other person explains which is the biggest. They love playing games – introducing the competitive edge keeps them all engaged. As they play I walk around and check how they’re doing. If I notice that anyone is behind I flag to my teaching assistant that they need to be given some small group attention for the next part of the lesson. After about 10 minutes I ask the children to transition back to the carpet, counting in tens.
4 DEVELOP LEARNING To build on the new learning and develop a deeper understanding
The Develop Learning segment mirrors the New Learning segment earlier in the class but aims to take their learning on a bit further. In this lesson we’re doing this first by introducing another resource – a number line. And then by introducing a problem solving element. 10 MINS
SPOTLIGHT ON QUESTIONING Smart questioning is key. The right questions get pupils to explain themselves in different ways and encourage a deeper understanding of concept. Pupils are encouraged to ask questions themselves.
Children sit in pairs and I give each pair a number line with 100 beads on it. We’re about to play a Mystery Number game – my pupils love this game – so I introduce them all as detectives with a puzzle to solve. We go through a list of mystery number clues, after each one eliminating numbers that can’t be the mystery number. The clues focus on “greater than” and “less than” so they’re using the new learning from earlier on. As we go through I keep asking them QUESTIONS about how they know which numbers to eliminate and whether they know the mystery number yet. I’m so pleased that my pupils can follow this activity. It’s pretty demanding for Year 1. But because the FOUNDATIONS were so well laid during the Autumn term, the pupils are really starting to show that they can use what they’ve learnt to tackle quite complex concepts.
FOUNDATIONS Maths Mastery focuses on depth of understanding. If children have a good foundation they’ll remember what they’ve learnt and be able to apply it to more complex concepts.
“I would give them a small selection of different apparatus so they start learning to use the one that suits them.” Stephanie Lester, ARK Atwood
“I would give each child a laminated 100 square and marker pen so that they can eliminate the numbers themselves as we go along.” Jasbir Mahey, Gilbert Colvin
5 INDEPENDENT TASK To practice their learning independently by solving problems
The pupils now transition back to their desks singing the Secret Number Song again. This next task is a chance for them to practice their Develop Learning independently. They are given their own mystery number clues along with a number line. 10 MINS
SPOTLIGHT ON DIFFERENTIATION Differentiation is not about accelerating pupils through the curriculum or holding them back. For higher attaining pupils it’s about pushing for increased depth and exploration. For lower attaining pupils it’s about scaffolding tasks but not putting a ‘cap’ on their learning.
The suggested task is a great basis and it needs to be adapted to make sure that it’s challenging everyone in the class. I’ve adapted the exercise suggested by Maths Mastery so that it is DIFFERENTIATED for high, middle and lower attaining pupils. My lower attaining pupils are given only 3 mystery numbers with 2 clues to work out each number. My middle attaining pupils are given 5 mystery numbers with 3 or 4 clues for each number. My higher attaining pupils are given 4 examples with all 6 clues. I’ve added in some unhelpful clues to see if they can spot them. I go round the room at the same time as the teaching assistant and mark over their shoulders as I go round. I give individual assistance if I hear children that need it. And I remind them to always use their number line and record the answers they get. I expect my higher attaining pupils to finish their mystery numbers. So for those that finish I’ve put an extra task in the middle of the table with a challenge to create their own mystery number and clues to go with it.
“I’d give my lower attaining pupils some extra scaffolding and ask the TA to read out the clues for them.” Stephanie Lester, ARK Atwood
“I’d link this to another class topic—for example, if we were also learning about the beach that week, I’d say that one of my 100 beach balls had gone missing and ask them to find which one.” Jasbir Mahey, Gilbert Colvin
To recap on the lesson, check understanding and celebrate success Our ONE HOUR lesson is nearly over and it’s time for the final part—the plenary. I’m using this segment to sum up what the children have learnt and to assess their understanding. 5-10 MINS
SPOTLIGHT ON TIMING The suggested timings are all based on a recommended one hour lesson. But if a school needs to have shorter maths lessons then timings, like all other aspects, can be adapted to fit.
I ask the children who created their own mystery numbers to come up to the front and present their number to the class. They take the whole class through the clues and we check the answers as we go along still using our number lines. We’ve also got a maths wall at the back of the classroom which shows all the maths learning objectives for this week. At the end of the lesson I ask the children to say what they’ve learnt and then it gets written up on the wall.
“Sometimes I use the plenary to introduce a topic for the next maths lesson. So here I could introduce ordering numbers” Stephanie Lester, ARK Atwood
“I would play a game with my TA at the front of the class, where we’d both pick a number and say which one we thought was bigger/smaller. Only one of us would be right and I’d ask the class to decide who.” Jasbir Mahey, Gilbert Colvin