Maths mastery: the Asian picture

In a recent blog post, I talked about the way in which the much-praised Asian education systems are rethinking their ‘grades are everything’ approach to education. It is encouraging to see that they are beginning to realise the importance of a more holistic, child-friendly approach, though I worry that for some years we in the UK have been heading the other way a little too rapidly, under what I refer to as the ‘Red Dress Fallacy’.

In this piece, which has a slightly different focus, I want to clarify the specific role that mastery has played in the teaching of mathematics in Singapore and Shanghai, as my own travels in Asia suggest that this has not been as accurately portrayed here at home as it might have been.

The first well-propagated myth is that mathematics lessons are very dry, even in primary. My experience is that while they are more formal than many UK children are used to at the moment, they are far from dry. Thorough yes, but always pacey, detailed, and painstakingly constructed. There is more than a nod to the findings of Benjamin Bloom (1976) and Thomas Guskey (2009), which are excellent, yet slightly at odds with some of the current received wisdom about mastery in this country. They have high expectations of all pupils, and carry out thorough diagnostic pre-assessments in order to find out exactly where to pitch their content. This pre-teaching has been slow to enter mainstream consciousness in the UK, yet it is the very beginning of the mastery approach, though I have visited some schools doing this to great effect.

The second thing that stands out is a reluctance to split classes into ability groups. Despite what we sometimes hear, this DOES happen sometimes, but nowhere near as much as we are doing in the UK. This again is a reference to the work of Bloom, and even during this phase the teacher is constantly assessing progress through carefully targeted questioning.

One of the things that needs to be defined more carefully is the use of the word ‘assessment’. We frequently use the word to mean ‘end of unit, formal, silent test’ or ‘Standardised test designed to give benchmarked scores’. In the best classrooms at home and abroad assessment is more of a habit than a formal test. This is true in Asian classrooms – teachers constantly ask questions to assess students’ understanding of something before moving ahead. This inevitably takes time, but it is noticeable that by the age of seven children have already made up this time.

A simple analogy might be redecorating a room. The first stage is to remove any barriers, such as old wallpaper, nails or bumps, cracks, etc. This might equate to pre-teaching, in recognition of the fact that preparation is key to success. It could equally well apply to key stage 1: take time to prepare the ground!

Then the wall is assessed for smoothness; different areas might need a bit more smoothing, etc. Only when everything is ready, is the wall finally painted.

However – we are in danger of taking the opposite approach. It is almost as though we have looked at a neighbour’s bedroom and thought how much more painted it is, and rushed ahead with the painting before the walls are ready. Red Dress Fallacy again. Before long we will need to redo our walls due to cracks appearing. Or ‘revisit fractions’ as is the constant complaint.

In Singapore, for instance, they don’t worry about Roman Numerals, analogue time, etc. early on. Instead they spend a lot of time in Years 1 and 2 mastering how numbers are able to be broken down and combined in different ways; it doesn’t sound very exciting but it is delivered by teachers who have a life-long commitment to professional development; continuing professional development or CPD in its true sense.

Another myth is that Asian teachers are entirely focussed on textbooks. This view has arisen due to the unfortunately named yet very successful ‘textbook project’ in the UK. I say ‘unfortunately named; as it wrongly puts the focus on the tool rather than the users – the teachers and pupils.

Being DfE sponsored, the project achieved widespread awareness and definite success, yet entirely missed the point of a mastery approach. Giving someone a Ferrari does not make them a good driver. In the same way, giving people high-quality textbooks – and they are certainly that – means nothing without the ‘driving lessons’, or first-rate training in the thinking and pedagogy behind the books, rather than the books themselves. Those schools who performed best in the ‘textbook project’ had teachers who were thoroughly trained in the underpinning pedagogy. This leads us to my final point:

During tough economic times such as those we currently face, it is a very understandable mistake to think that you can get away without investing in CPD.

This is like not visiting the dentist, or avoiding having your car serviced, in that nothing appears to be lost in the short term. But a mistake it most certainly is. In the long term, you find that your best assets (your teachers) become worn-out, de-skilled, un-inspired and more importantly of all, lacking in opportunity for professional reflection.

Perhaps the biggest thing about the Asian teachers is the heavy emphasis they place on professional development that is both regular and focused. The difference in planning time here and abroad is also often talked about, though the evidence seems less clear as to whether they get hugely more than we do.

Until we up the ante on the value we put on our teachers by giving them up-to-date training and resources (both are almost useless without the other) we can never hope to compete with those places that do. Again, the ‘Red Dress Fallacy’. Behind the textbooks are rigour, CPA, scaffolding, constructivism, precision language and more. These things are unlikely to be intuited by all teachers who pick up the book.

So yes, do buy the textbooks – there is a vast amount of theory underpinning both the Shanghai and the Singapore series of books – but my greatest fear is that schools will increasingly decide that CPD is the easiest thing to do without in the short term.

Without the training, you will have bought a very expensive car with no knowledge of how to drive it. And ultimately, that’s not safe for anyone.

Having taught for twenty years, Andrew is now the director of Magic Message Ltd delivering primary maths training. He works domestically and internationally, as well as being an independent primary maths consultant and keynote conference speaker. Andrew is also known for his alter-ego, the ‘Maths Magician’ and is the original creator of the ‘Magic of Maths’ show, seen in over a dozen countries on three continents.

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