Publishers are feverishly producing complete new sets of text books for English schools using consultants and academics from Shanghai and from Singapore. This comes on the back of a Nuffield Foundation report suggesting that the poor quality of text books is a key issue for schools in England. The overwhelming demand to teach to the test is now accepted, with even Ofsted saying there was; “too much teaching concentrated on the acquisition of disparate skills that enabled pupils to pass tests and examinations but did not equip them for the next stage of education, work and life.” So, in a major crisis of confidence for English maths educators, we look to the successful TIMMS nations. But what are the key elements of the Shanghai Maths ‘Mastery’ and Singapore Maths? Well certainly in Singapore they are keen to assert that this is a reworking of what was best in maths education in the UK from the early days of the ATM with Dienes, Gattegno and Cusienaire. The work of Bruner, Piaget and Vygotsky most significantly underpin their thinking. Physicial manipulative and iconic presentations proliferate. Bruner’s *enactive*, *iconic* and *symbolic *modes of representation and his notion, built on Vygostsky of *scaffolding* are the basis of the approach. However, in Shanghai, the key point is to ensure all students succeed together. Charlie Stripp on the NCETM site tells us that differentiation, by giving easier work to students identified as less successful can be “very damaging”. So, to those of us old enough to held the flame, ‘mixed ability’ teaching may be set to return. Notably, in Shanghai everyone practices but with “procedural and conceptual variation” i.e. well structured exercises developing the mathematical ideas by focusing on the key variation. An idea that would be familiar to those involved in the best text books from an earlier era.

I was sent a complete set of eight volumes of WOW maths from an Indian Publisher; E3 EduSolutions. This is an extremely comprehensive text book series with course books, work books and teacher manuals. Originally published in 2013 and now in a second edition, this is intended to embed the Singapore Approach for Indian schools up to roughly the equivalent of an English GCSE. It is interesting to see how in England we are only now reaching this stage. An central feature not seen in England is the availability of proper board games and other games and indeed the physical manipulatives that are embodied in the enactive and iconic phases: Dienes blocks, Mulitlink cubes and Cuisenaire blocks; these are all embedded in the scheme. The principle iconic mechanism taken from the Singapore approach is the so called ‘bar’ method. This essentially amounts to using blocks formatted in one or two dimensions for comparisons. A fraction wall is a classic example of this approach, however, here it is used as a jotting – a thinking tool. This practice is used throughout the series, so would be become second nature to users of the books. Also, Polya‘s general approach to problem solving is given a page and a photo at the start of each book, so problem solving is foregrounded.

It would be impossible to do justice to the details of such a large scale work in a blog post. However, this is a comprehensive and valuable work and it is fascinating to see the embedding of such a range of approaches very familiar to older UK maths teachers, which have largely disappeared from our text books. Everything starts from a diagrammatic or recognisable object, which is translated into an iconic form, which carries the mathematical content and thus to the symbolic form. There is an enormous amount of practice, which develops each idea in a coherent way. The whole is interspersed with open projects and ‘Lab Activities’. These are recognisable as ‘investigations’ the former with less structure and guidance the latter directed to the teacher, with more. Side bars provide additional thinking and discussion points ‘in daily life’, ‘discuss’ remember’ etc. Also, to the UK reader, the details of Indian life and indeed counting system differences are fascinating. It is very clear that these are directed at an Indian audience and are not generic.

Text books have a profound influence on how maths is taught. The influence of Shanghai and Singapore on English maths education is now very significant. The WOW maths series is a very serious effort to engage with these influences and is well established in India and therefore of significant interest to educators in England.