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Some thoughts on the NCETM mathematics textbook guidance

Tuesday, 3 March 2015
A list of criteria from the NCETM/DfE has been given to publishers and sent to all schools to show the expected features of a maths textbook, largely based on the type of textbooks seen in Shanghai and in Singapore. So for the first time it looks like we could be going down the road of DfE approved textbooks.  

There is obvious anxiety about the impact this will have on the publishing industry, with one current author, in particular, up in arms about it. I have some sympathy for the views of Ruth Merttens, but disagree with some (not all) of her concerns. I certainly don’t think it is necessary to ‘kite-mark’ textbooks, but it is useful to have a list of features to look out for and, most importantly, it will give teachers the green light to actually go ahead and confidently use textbooks to support their teaching rather than relying on producing their own worksheets. This is long overdue. 
The aspect of this textbook guidance that could be very restrictive for schools (and equally terrible for publishers and authors) is if the criteria for textbooks is too tight and does not allow for creativity or flexibility. A Government approved list would be even worse, particularly if there are only a few NCETM/DfE approved textbooks to choose from.
Don’t confuse using textbooks to support teaching with only teaching with textbooks. They can be a useful resource used alongside practical demonstration, modeling, problem solving and applying maths to real-life situations. The Broadbent Maths Planning Menu, for example, provides the framework, philosophy and planning support; teachers could also use textbooks alongside it to support each unit, if it was felt to be useful.
Schools each have their own unique culture for learning, with the strengths of the teachers and headteachers in their schools driving their approach and pedagogy. I am pretty sure that schools wouldn’t want to choose from a small number of maths textbooks that are a clone of each other – there is no choice in that. Likewise, authors and publishers don’t need to be told what to publish. They should be free to take risks – publishers know the educational market and authors should know what works in a classroom.

The real concern, in my opinion, is that publishers will no longer publish maths textbooks that are ‘different’ to the set criteria – perhaps a series based on stories, or just on measurement, or a problem-solving series of textbooks based on a historical context, or… well anything that has a spark of creativity. These books may not meet the criteria, but could be hugely valuable to some schools that want to teach in a different way to the ‘Singapore’ or ‘Shanghai’ approach.
It is worth outlining the nine criteria points from the NCETM to see how useful their recommendations may, or may not, be to schools.
The NCETM’s principles of a well-designed and well-written textbook are:
Mathematical coherence
·       The learning sequence set out in carefully organised sections

·       Clear lines of progression and connections made between maths ideas
Mistakes, misconceptions and misunderstandings
·       Explicit use made of mistakes, misconceptions and misunderstandings
·       Aspects of difficult mathematical ideas explored in depth
Mathematical tasks and exercises
·       Careful thought given to the nature, structure and sequence of tasks
·       Tasks provide the appropriate level of challenge 
·       Some use of relevant, engaging and appropriate contexts
·       Varied tasks involving pupils in a range of cognitive processes and intelligent practice
Representing mathematics
·       Appropriate use of representations of mathematics to provide understanding
·       Models, pictures and diagrams used to help pupils make sense of mathematical ideas
·       Relevant and appropriate Illustrations and contexts used
Use of technology
·       Any online materials linked to the textbook, mirroring its structure
·       Calculators not used to replace essential mental and written calculation skills
Outside the classroom
·       Focused homework and out of school activities for practice and application
·       Meaningful opportunities to apply maths to everyday contexts and other curricular subjects
Assessment and review
·       Both formative and summative assessment incorporated
·       Assessment activities allow pupils to review the key ideas and concepts
Educative teacher material
·       Teacher professional development available to support effective use of the materials
·       A comprehensive teacher’s guide accompanies the textbook
Textbook authors
·       Only authors with expert knowledge, skills and credibility should be selected

·       Authors must draw on research evidence and accrued professional experience
·       Materials must be trialled and refined in the light of trial data
This list could be useful for providing reminders when writing textbooks or as guidance to schools to assess textbooks - there is nothing on this list that is wildly off the mark or new. If I think back to my first maths scheme, Longman Primary Maths (written with Peter Patilla and Ann Montague-Smith back in 1996) all these features were present. Most of the current textbooks available should also meet the majority of these criteria points.
However, all the current textbooks are varied and don’t have the look or format of a Shanghai textbook or a Singapore textbook (quite rightly so – we teach in the UK). This list of criteria doesn’t explicitly push that style either, but if the DfE decides to approve some textbooks and not others then publishers will be focused on producing books that are more likely to get on the approved list.

So it is not this list of criteria that is a concern, but the idea of a DfE approved list of books for primary maths.

If, as Ruth Merttens suggests, the message from the DfE is that, “the only model for textbooks were the Chinese and Singaporean ones on show and a list of criteria would be drawn up to which all textbooks would have to conform”, then it is likely these will be the only ones on the approved list and this will have a very limiting consequence on the books available to schools.
At the moment it is the individual differences between textbooks and other approaches to maths, that give schools the choice to use the approach and resources best suited to their situation. That choice should remain with schools, not constrained by the DfE.
Experienced UK maths authors are creative and base their writing on current research and we can obviously learn from the Shanghai and Singapore systems bringing in any aspects that would be effective in our school. Perhaps a longer time on single concepts or increased practice using more variety would be something to include. However, coverage of the content within the current NC could be an issue if longer time is spent on single topics. 
This could be a great time for educational publishing, for authors, and for schools, with opportunities out there for some exciting new resources. We just don’t want to take our eyes of the ball by looking to the East too much.

I’ve been writing maths books in various forms for over 20 years and for just about all the major educational publishers. I have also written core textbooks for other countries, unsurprisingly where textbooks are valued. For one of my MA modules I looked at the reasons for the negative view of textbook use in UK primary schools from a historical perspective. 
It compared our use of textbooks to the use made of them in schools in Nigeria. Here are the first few paragraphs – if you wish to read further click on the file:

Decline in textbook use.docx
There has been a major decline in textbook use in UK primary schools from the mid-1990s onwards. The decline started with the findings of the Bierhoff Report (1996), which compared primary mathematics textbooks used in Switzerland, Germany and the UK. It reported that German and Swiss textbooks included mental calculation strategies as a priority, but that there was an over-emphasis in UK textbooks on formal written algorithms, with little support for language and mental reasoning. The report actually named the most popular mathematics scheme in use at the current time, pointing out weaknesses in the textbooks. This small report had quite an impact, influencing the Numeracy Task Force (DfEE 1998) and the National Numeracy Strategy (DfEE 1999) with the emphasis on mental calculation strategies and direct teaching within a 3-part lesson of starter, main and plenary.
An earlier report from Ofsted (1993) had indicated that, in many primary classrooms, pupils predominantly worked independently through a textbook to learn their mathematics. Brown (1999: 7) considered that the main reasons for this included a lack of confidence of teachers in their own mathematics and an increasing emphasis on pupil autonomy, with children expected to work at their own pace and ability level. However, with the advent of the National Numeracy Strategy there was now an expectation of whole class interactive teaching (DfEE 1998: 54, Straker 1999: 42). 

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