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Using a high quality textbook to support teaching for mastery

Created on 23 June 2016 by ncetm_administrator
Updated on 14 March 2017 by ncetm_administrator

Using a high quality textbook to support teaching for mastery

The school mathematics textbook has a long history and something of a reputation to shake off:

Fierce, gown-clad schoolmaster strides into the classroom. ‘Turn to page 68 and proceed!’ then watches hawk-eyed over quaking students.

Even beyond this historical picture, textbooks have often been seen to occupy the less creative side of mathematics teaching. But this is all changing in some primary classrooms, where teachers have been engaged in a trial [read about initial findings here] involving new textbooks, adapted from one of two examples used in Singapore, and designed to support a mastery approach to mathematics teaching.

Interim findings have been encouraging with teachers reporting positive effects on their own confidence and on children’s confidence, understanding and progress.

Hannah Gray, who teaches Y2 at Thorn Grove Primary School in Bishops Stortford, and works with the Matrix Essex and Herts Maths Hub, is one of the teachers involved in the trial. At the start of the NCETM visit, children are sitting on the carpet and involved in an animated discussion over a problem displayed on the whiteboard:

‘How can Amira share 12 key chains equally between 2 children?’

A class discussion, facilitated by Hannah, follows. The children’s explanations of how the question might be tackled are detailed, confident and lengthy – no one expects that ‘6’ might be an acceptable response. It is incredible how much can be drawn from a single, apparently straight-forward problem. Beyond verbal explanations of how children had reached their answer, one child suggests a diagram that Hannah starts on the board and is finished off by another pupil:

Hannah guides in the direction of ‘operations’ and a child suggests that this is a problem that uses division. When asked for ‘number sentences’ to describe the situation, the pupils suggest:


And 6+6=12

And finally 12÷2=6

They agree that the division number sentence best fits the problem. At which point Hannah asks, ‘So why are the other two not wrong?’

A pupil responds, ‘Dividing is just the opposite of timesing. And the other one shows the two groups added together’.

It is clear from their thorough explanations and their subsequent work on whiteboards, that the class have excellent understanding of the relationship between the four operations. Potentially this will enable them to approach division without the commonplace fear it evokes.

Following the discussion on the carpet, Hannah sets another problem:

‘Ruby has 15 marshmallows that she is packing into bags. She packs 5 marshmallows into each bag. How many bags does Ruby need?’

Children return to their desks to work on this problem using whiteboards. Again their responses show their depth of understanding – not just that the problem is a division problem, but how it can be checked and understood using multiplication and addition too.

Click to enlarge

Some children are still struggling with exactly what to draw. There are those that have confused ‘bags of 5’, with ‘5 bags’:

Click to enlarge

But all are confident to put pen to whiteboard and draw pictorial representations of the situation that show at least an emerging understanding of division, and for some a complex and rich understanding of connections between division, multiplication and addition.

How has Textbook Use Changed Mathematics Teaching in Hannah’s Classroom?

This sort of mastery approach to teaching is by no means achieved solely with a textbook. Rigour and skill characterise Hannah’s teaching. So what is new in Hannah’s teaching since she became involved in the textbook project?

  • Teaching Style

    ‘I always knew that developing understanding in maths was important and tried to plan lessons accordingly. However the textbook project has given me deeper understanding of effective maths teaching and given me strategies and tools to implement and develop my own skills and knowledge for teaching maths.

    ‘I have also moved away from “trying to get the correct answer” to exploring all the different strategies to solve a problem and choosing the one which best suits you. For example, there is only one answer to 2+3 however there are many ways to get to the answer, draw dots, use cubes, doubles (3+3 =6 so 2+3=5) etc and whichever one you use is right. This is also good for teaching a mixed ability class.’

  • The importance of pupil talk

    Hannah has been impressed by how well her class have learned to talk mathematically.

    ‘There is a lot more discussion and conversation in maths than ever before which I feel has helped children consolidate learning and have deeper understanding. Within the discussion there is also a greater focus on the language of maths and using it in our discussions. The textbook project has highlighted to me how discussion and conversation are crucial to teaching for mastery and for teaching maths effectively. Previously, I would have said to children “you can speak with your partner if you’re stuck.” However now discussion is a focus of teaching and I will give a problem and ask children to tell their partner how they would solve it then come together and discuss all the strategies as a class.’

    Hannah’s class now sit in all-attainment groupings of 6 children round a desk, and she keeps the class together as much as she can. Talk pairings across an attainment gap can deepen understanding for the child searching for best ways to explain a concept as much as for the child listening to understand the explanation.

  • Using the textbook as a teacher-support tool.

    Hannah finds the online teacher guide that comes as part of the textbook package to be very useful in offering lesson suggestions, questions to ask and material for projection onto whiteboards. To begin with she used the class set of textbooks but found that each child having a book was cumbersome and took up too much space on the table. Now she uses the textbook pages online so that she can project the question and, only later, display a variety of possible methods for solving.

    The textbook programme also offers Hannah confidence that she has covered everything and in a mathematically coherent order.

    ‘The textbooks give a clear and concise sequence of work which covers all the outcomes in the curriculum. Within each chapter the lessons are in a sequence where one builds on from the next.’

  • Workload

    Hannah is clear that using the textbook has eased her workload, and moreover, allowed her to spend preparation time on tailoring the material to the needs of her class, adapting and adding her own material as she sees fit.

    ‘I don’t need to; decide what to teach, check the curriculum outcomes, gather resources for teaching and plan a sequence of lessons and activities for the week. Obviously there may be some adaptations to be made but this is small (workload commitment) in comparison to before.’

  • Training

    Hannah’s involvement in the textbook project—like all those teachers working with both textbooks-- included 5 days training from the textbook publishers, which she feels was essential to successfully understanding how to use the material successfully.

    ‘I think the training’s very important. You couldn’t just give a school the textbook. When we first got all the stuff through, I was having a look before the training and I didn’t know how I was meant to know what to do.’

How has Textbook Use Changed Mathematics Learning in Hannah’s Classroom?

Reflecting on the changes that have taken place in the children’s approach to mathematics, Hannah comments on their improved understanding of mathematical connections. Topics that might previously have been taught distinctly now have the relationships between them drawn explicitly.

Hannah also mentions that children now understand the = sign as signifying the equality of both sides of the equation, rather than as a signal to write the answer.

Children are now able to use and understand an increased number of different strategies and their work is less procedural, based more on thorough understanding.

Any reservations?

There are still some issues that Hannah feels are holding back development of textbook use in her classroom. One of the difficulties she has encountered is with the pace. In Singapore, children start school a year later than in England, so they encounter concepts when they are a year older. Hannah believes therefore, that younger English children take a little longer to pick up the ideas than their Singaporean counterparts. To allow for this, Hannah sometimes has to spend more time on a topic than intended by the textbook.

Routine practice and drill around times tables and other number facts, emphasised by the National Curriculum, is not something that is explicitly stressed by the textbook, so Hannah has had to add in some time to deal with this.

Finally , the CPA approach (using a mixture of concrete, pictorial and abstract representations of each concept), that Hannah and the textbook authors advocate so strongly, appears to conflict with Y2 SATs in which children are not permitted to use manipulatives.

‘From the training they said the concrete should always be available – even higher ability (children) can use concrete (representations) to help them work it out and that’s fine. But that doesn’t lend itself to SATS because they’re allowed nothing (in the exam) – so I focus on drawing (pictorial representations) a lot. It (the textbook) doesn’t quite match with the curriculum.’

Interim Findings from the Textbook Project

Hannah’s enthusiasm for the Singapore-style textbook is consistent with the majority of teachers involved in the Maths Hub National Collaboration Project trialling their use.

Interim findings (Jan-July 2015) suggest that being involved in the textbook project has had the following benefits for teachers and their pupils:

  • Improved teacher subject knowledge and confidence in teaching maths
  • A positive impact on children’s attitude to learning maths, and their attainment in the subject
  • Some teachers reported reduction in workload –others said that the focus of their planning had altered, allowing them more time to focus on children’s learning.

Debbie Morgan, NCETM’s Director for Primary, emphasises the coherent learning journey constructed by the textbook. Teaching for mastery relies on very carefully chosen examples and questions that highlight key mathematical structures. One aspect of variation theory (a key component of teaching for mastery) is to represent concepts in a variety of ways in order to extract the essence of the concept and develop a deep understanding. This includes linking concrete, pictorial and abstract forms. Intelligent practice requires that children do not just repeat multiple questions on the same topic, but that the questions change, one feature at a time, to expose mathematical structure. Debbie Morgan points out that teachers do not have time, even where they have the expertise and confidence, to think up all those carefully chosen examples. Having a rigorous and thoroughly checked textbook frees up teacher time to analyse and think deeply about the resources rather than spend time hunting for them.

‘It’s a very different pedagogic approach (to traditional textbook use). The textbook is a support for the teacher. It doesn’t dominate the journey. There is a flexibility (and indeed the textbooks encourage that flexibility) for teachers to come up with some contexts of their own to support the core material, and indeed, to take ideas from the children.’

Hannah agrees:

‘The longer I work with these textbooks, and use the ethos for mastery the more natural it becomes. I find it easier and quicker to understand the pedagogy and implement lessons. I think the mastery approach could be planned into every lesson even without the textbooks, however I believe the textbooks and online planning are vital in decreasing workload and providing teachers with a clear and logical sequence to teach the curriculum. Also, I believe proper training over a period of time is needed as well as time for teachers to practise and become familiar with the teaching for mastery ethos.’

If you’d like to offer your views, or experiences, on any aspect of teaching for mastery, please contribute to the discussion threads in the NCETM’s Maths Café Community. NB: To access and make posts in the Maths Café Community, you need to be registered with the NCETM and logged in.


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04 May 2017 16:41
Which whole school textbooks are you using to support this approach?
13 September 2016 22:39
I'm a year 2 teacher in a school that is adopting the mastery approach. We have one of each textbook and workbook in each year group and use them for planning (Maths No Problem). We have started to plan all lessons on the smartboard and I create my own using the ideas from the books. Sometimes I put the tasks purely on the smartboard and children copy things into their books or on whiteboard, at other times I print off the individual tasks for the children to complete which reduces the amount of recording and leaves more time for reasoning. It does take time to prepare but the ideas are all there and there isn't any money! I figure that it will make things alot easier next time - I already have a fractions unit and an addition unit from last year which I am looking forward to tweaking and using again! I am using lots of interactive elements of smartboard (eg reveal answers and the question tools) which means I can focus on getting quality explanations from the children and maintain pace rather than trying to write on the board at the same time.- this is working particularly well with the first units-Counting to 100 and Place value. Hope this helps.
By hpar22
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11 September 2016 17:44
So, out of interest, how much have you spent and what, if anything will your ongoing future costs be?
By bears1404
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11 September 2016 17:25
I'm the maths leader at the school where Hannah is trialling the project. We tried to buy just the online licence and work books (we don't use the text books as it is more user friendly to show the anchor task on screen), but unless you buy the startup pack, you can't get a discount, so it works out just as expensive. The online training vidoes that come with the startup pack are useful - I've used them for staff training sessions. They exemplify open questioning that really stimulates pupil discussion and mathematical thinking.

We're now using the books in years 1 - 4. Ensuring teachers get adequate training is the key to success.

This year I've bought one of the work books for year 5 and 6 to give me some inspiration in setting "mastery" type tasks for pupils. Not sure yet how useful they will prove to be.
09 September 2016 20:06
Would anyone out there be prepared to share their experiences of buying just one MNP textbook and workbook for each year group to use as a support for planning, rather than ploughing £10,000 we simply do not have into a textbook project? Would we really miss the online materials to which Gwen Tresidder refers in the message above? I can't seem to find the cost of an online licence on its own. When Gwen refers to the "reference copies" are these the textbooks or something different?
By mcurtis3.313
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02 August 2016 06:57
@bears1404 @paris123 Regarding the cost - When I interviewed Hannah, it was clear that she didn't find the 'one textbook per child' model very helpful and basically had a stack of rarely used textbooks in her classroom. It was the reference copies, and even more importantly, the online material (@crickard) that she found most helpful. So this could lower the cost - though I believe the online licence alone is costly.
01 August 2016 12:06
Whilst, as Debbie says, a text book helps to provide some coherence to the learning journey through providing carefully designed examples etc, I can't help thinking a series of powerpoints (or equivalent) would actually be more user-friendly than a text book.
By crickard
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15 July 2016 11:24
Thanks for sharing this Blog. I was saddened to read that Hannah tends to choose pictorial representations rather than concrete becuase the pupils' won't be able to use them in a test. The test is a couple of days of KS1. The CPA aproach is about building understanding the resources are not tools they are a vehicle for revealing the concepts of mathematics as the pupils are assimilating their understanding (Piaget). If the pupils have enough experience and exposure then the imagary remains when the concepts are accommodated. (Piaget). Being able to translate this to any situation is when pupils' have mastered an idea and therefore enabling the assessment to be more reliable if the children no longer need the concrete. The pictorial can be taken with them but this is the conceptual step from the concrete.
13 July 2016 12:24
How will this follow through to senior schools? I teach in FE and find myself going back to the CPA structure to helpstudents gain understanding, but of course they believe it is childish even if it does help. The barriers are lack of belief and adapting materials to suit the age of students as well. Love the concepts and they make total sense to me, especially to create the mathematical discussion
By Annettsj
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12 July 2016 18:17
Surely one of the main points of Singapore/Shanghi maths effectiveness is quick intervention in the afternoon with the pupils who did not 'get it' in the morning. This is usually done in very small groups by a qualified maths teacher. It is this that won't be able to be replicated due to lack of funds, never mind the cost of the text books.
By RedLeicester
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12 July 2016 17:45
I agree cost of textbooks would be a major problem without specific extra govt funding. DEAN
By paris123
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12 July 2016 15:07
The evidence is very compelling. However, in many, many schools the cost of text books is prohibitive. I investigated use of text books (Inspire) in my school (420 pupils) and was quoted initial cost of £10,000 then £8,000 annually ongoing. For schools without significant pupil premium this makes it a non-starter - especially in current climate with schools facing real term cuts of 5%-8%. If govt really do believe in this I hope they will fund ALL schools appropriately.
By bears1404
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