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Broadbent Maths - creative primary maths

Do we need textbooks to teach primary maths? And if so which ones?

Wednesday, 4 May 2016
Some schools are looking at textbooks and teachers have asked me for advice on this. I've put together a number of things to consider for those thinking about using maths books to support their teaching.  Does your school just need Teacher's Guides or is a textbook also necessary? Is it a Practice Book you're after or do you need problem solving ideas? To help with this I've also looked at some of the features of a few of the new maths books recently published.
These are two questions that I've been asked recently:
We have worked closely with a school that is training others in mastery, I agree with the concept, however I'm unsure about following the Maths No Problem books. I believe in the creativity of Maths. I feel I need to know more, so can you help?
I have just been comparing Shanghai maths books to Singapore maths and saw your name in one of the books. They seem quite challenging for Y1&2 and how do they differ?

Most of the new textbooks are advocates of a mastery approach, so the main elements of this are worth considering first.

I am the author of the practice books for the new Rising Stars Mathematics as well as being a consultant on the series. I have also been involved in the Shanghai Maths Project material with Professor Fan, reading through his translations from the Chinese to check they made sense and had a reasonable match to our curriculum.

An outline to the mastery approach:

  • class working together on the same topic

  • challenge provided by going deeper not accelerating

  • teaching is focused, rigorous and thorough

  • speedy teacher intervention to prevent gaps

  • more time on teaching topics - depth and practice

  • carefully crafted lesson design - scaffolding

  • engaging pupils in reasoning
As you can see from the list, teaching primary maths with a mastery approach is not dependent on using a textbook, it is a whole approach that needs to be incorporated into all aspects of your planning and teaching.

Teaching a unit of work in a sequence of lessons with a clear focus, with shared LOs and expected outcomes is something I feel is important and children should always be given time to grasp a concept before moving on. Flexibility is important - if an extra few days or week is needed for the class to gain a full understanding then use the time, it shouldn't be constrained by a fixed daily plan. Depth, not acceleration and good use of models and images is also important.
For those of you using my Planning Menu, the two week unit usually gives enough time on a topic and this can be shortened or lengthened as needed and, of course, if you prefer you can stay on the same topic and teach the next unit straight after teaching in a larger block.

The important thing in all this is that the teacher knows the class and is the decision maker in ensuring the maths builds on what the children already know, is taught effectively and engages them in a purposeful and enjoyable way.

Using textbooks in maths has been given attention following the Policy Paper from Tim Oates in November 2014 and follow-up articles by the NCETM Director, Charlie Stripp. It is relatively easy to implement (although expensive for schools) and they can be a useful resource. As a textbook author I'm obviously very pleased that they are back in favour in England. I have written a lot for the Middle East and Africa where they have always been seen as an essential element of good practice. 

However, textbooks aren't the most important ingredient in a mastery approach - it is simply about great teaching and this is dependent on a teacher's own subject knowledge. It may be that a good textbook or teacher's book will help teachers with this. For example, my Planning Menu includes specific small steps of progression within each teaching unit which teachers have found invaluable in supporting their own subject knowledge. A textbook (which includes a teacher's guide) should have elements that help teachers with their pedagogical subject knowledge.

I believe there are two key places where a maths textbook may be useful:

1   to 'clarify' part of the lesson where a new concept or skill is being taught

2   for 'practice', especially if there is good variation within the practice tasks

I suggest using an explore, clarify, practice, extend, review lesson structure.

The most important thing is for teachers not to become over reliant on textbooks. This was something that happened back in the 80s and early 90s. This can diminish teacher's creativity and decision-making and result in maths lessons that are less engaging for children. I have written many maths books and the creative element is problematic in a published scheme. The context needs to be relevant to your children and school, anything over prescriptive can limit creativity. I try to encourage the schools I support to think about a 'hook' to engage the children and a 'product' to aim for at the end of a unit - this could be a made item, a poster, a menu, a performance or simply the answer to a really tricky problem - something that gives the maths purpose.

So which new textbooks are available?

This is not a particularly extensive list, there are other maths schemes and books, but these are the books I have been involved with myself or have been specifically asked about by teachers. All textbooks are now expected to meet the NCTEM quality criteria.

Shanghai Maths Project (Collins)

The Shanghai books  are purely practice workbooks - there are no teaching materials (yet) or textbooks. They include a lot of practice activities for each number and calculation topic, but far less for shape and measures. Topics are taught over longer periods with less emphasis on a spiral curriculum.

It builds up in difficulty very carefully and cleverly, with an emphasis on understanding each step and uses procedural variation very well to help with the understanding. Problem-solving and reasoning is included. Once the basic skills, procedures and concepts are mastered, the maths moves on very quickly and it looks very challenging in places. It relies on the children having a good grasp of the concepts before moving on and is an advocate of 'one lesson, one concept' to keep the learning focussed. These have been written as a 'project' for schools to use to support their teaching in whatever way they choose. They look a bit basic - single colour and simple artwork, but they wanted it to be as close as possible to the original books they were copied from.

Maths - No Problem
Inspire Maths (OUP)

These are both based on the Singapore approach and are much, much more of an all-encompassing scheme for teachers to follow. They have lots of paper resources - teachers books, textbooks, workbooks - and expect schools to follow the daily, weekly and termly programme. The maths is based on a spiral curriculum, re-visiting topics and building on the previous steps, and they make very strong use of concrete-pictorial-abstract representations (e.g. bar model) to help with understanding. The teaching element is very detailed with a lot of explanation, children listening and discussion. They mix variation with variety in the practice activities - and there is a lot of practice that children are expected to complete.
Both Inspire Maths and Maths - No Problem were chosen by NCETM and the DfE as the maths books for schools taking part in the maths hub initiative.
I know one school that is planning to use some of the Maths - No Problem materials as a resource alongside my Planning Menu unit structure for ‘clarifying’ and ‘practice’, with teachers planning their own lessons and not following the structure of the series.

Rising Stars Mathematics
This new series follows a mastery approach and provides teachers books, textbooks and practice books. Like the Singapore books it is an all encompassing scheme based on a spiral curriculum. They also make strong use of concrete-pictorial-abstract representations (e.g. bar model) to help with understanding and there is a lot of explanation and teacher support in the textbook, teacher's guide and CPD videos, so very good for pedagogical subject knowledge support. I wrote the practice books and there is procedural and conceptual variation when it aids children's understanding. Unlike the Singapore and Shanghai books they are not translations or close copies of existing Chinese materials but have been written by UK writers following the principles of mastery. 

My own personal view?

Well, I would want to plan my own lessons and not follow anything too prescriptive.

I would probably look for a good practice book for each child, that is well presented and includes variation. This would replace the need for so many loose worksheets and they would only complete the parts that support my own teaching objectives - not something to be 'worked through'. Towards the end of the year, when you've used the parts needed for your teaching, children could complete the sections not used, in spare moments or at home as consolidation. 

A teacher's book and even a textbook, from perhaps two different series, could be useful as resources to help support teachers' own subject knowledge, show different ways to represent the maths and provide other teaching ideas, especially for problem solving and reasoning. 

Tips for choosing maths books

Ask yourself and other teachers in your school:

• In which part of a lesson do you need extra support?
If it is your subject knowledge and what content to teach then you will need some support with the structure, progression, expected outcomes, AfL questions and perhaps other areas such as language and modelling. My Planning Menu provides this, and a good Teacher's Guide should also give support in this.

• Where do you currently find maths resources?
Where are you finding your teaching ideas, problem solving and practice activites? How long does it take you to find appropriate materials? If you struggle for ideas then a good Teacher's Guide or textbook could help.

• What aspects of your maths do you feel you deliver well? 
This can be really important - as you will want to keep the elements of your teaching that are working. Often a new approach can be given to all the teaching staff, and unlesss it is flexible, it could perhas mean some teachers will be replacing teaching methods that work well with a system they don't feel so comfortable with. 

Give it a try

You should give them a try in the classroom and get one copy of all the books available. To keep costs low, buy only one book from a series for a specific year group, then a different book from another series for different year group.

Ask teachers to look/use the book when they are planning for the next few weeks to see how or what they can find from these resources that they could include in their planning and teaching. 

Teachers can then review and feedback their views on the books they used to the whole staff. 

You can never have too many resources in a school, so the expense of buying these books should not go to waste as they can be used as reference books in the future. 
Related articles

Some thoughts on the NCETM mathematics textbook guidance
A list of criteria has been sent to publishers and schools to show the expected features of maths textbooks.

'Teaching for Mastery' will you use the new NCETM assessment material?
These are free, so worth a look and would work well alongside my Planning Menu AfL questions

Mental Arithmetic Practice books published
A list of all the features I would look for in a practice book

Mastery in Maths - how can primary schools plan for this?
6 suggestions to help you plan for a mastery approach

Further reading

Five myths of mastery in mathematics
Interesting views from the National Association of Mathematics Advisers (NAMA)
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