Teaching maths to more able children in East Asian countries – collecting evidence.

I’m going to put bits and pieces here when I find them, just for reference: much of this stuff is in subscription-only publications.

Firstly, snippets from The Proceedings of the 12th International Congress on Mathematical Education (2015)

Sun-Hwa Park, in the ‘National Presentation of Korea’, says that they will discuss

Three types of institutions for the gifted: schools, education
centers, and classes. Additionally we introduce several gifted education programs
that are implemented at the elementary and secondary level schools.
In Singapore, according to Berinderjeet Kaur, Cheow Kian Soh et al., ‘Mathematics Education in Singapore’pp312-3 , the maths curriculum is structured as follows:
The content in each strand is revisited and taught with increasing depth across levels. There is differentiation in the content, pace and focus among syllabuses within the same levels to cater to different student profiles. Primary 1–4 students follow a common mathematics syllabus, covering the use of numbers in measurements, understanding of shapes and simple data analysis. At Primary 5–6, there are two syllabuses: the Standard Mathematics syllabus builds on the concepts and skills studied in Primary 1–4, whereas the Foundation Mathematics

syllabus revisits some of the important concepts and skills taught earlier. At the secondary level, there are 5 different syllabuses for students in the Express, Normal (Academic) and Normal (Technical) courses.
…There are also programmes to support the slow progress students and stretch those talented in mathematics. Primary 1 students (about 5 %) who lack age- appropriate numeracy skills are given support through the Learning Support Programme for Mathematics where they are taught in small groups by specially-trained teachers. For gifted learners, there is an enriched mathematics curriculum that emphasizes problem solving, investigations, making conjectures, proofs and connections among concepts. The NUS High School of Mathematics and Science also offers mathematically talented students a broad-based 6-year programme that includes undergraduate level topics and a mathematics research component.
Clearly, neither of these systems teaches the same curriculum to all children, or expects children to ‘all move together’ as the NCETM advises schools to do here.

A voice in your head?

Filling the pail

When I read, I hear a voice in my head. The voice is usually a pretty flat version of my own voice and it’s the same as the voice I hear when I think. Occasionally, when I receive an email from someone with a distinctive voice then I might hear their voice instead. And I sometimes hear characters’ voices when I am reading fiction.

In the past, it would never have occurred to me to mention this because I would have assumed that everyone has the same experience. But we do not. Recently a respected researcher commented in an email forum I follow that he hears no voice when he reads. I couldn’t imagine that but I did believe him so I looked into the issue and found two things; people do seem to have diverse experiences of reading ‘voices’ and yet there is little research on this phenomenon.

Let us…

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Maths mastery and high attaining / high potential children – the beginning of a journey!

Update I’ve had a very disappointing interaction with the NCETM on twitter, who have now twice refused to answer publicly on the role of selection in China (or other Asian systems) and the implications for (apparently) taking a method that’s used for the broad middle of ability only, and imposing it on the full ability range.

The reason they gave (in a longish private message) is that they do not have time to answer these things on Twitter but would do so by email. This is not really logical – I have already suggested that they could write a response up and link to it. The important thing would be for it to be a public explanation of their views, since so far I can’t seem to find discussion of the curriculum of ‘supernormal’ schools (or similar selection in other systems) in the public explanations they give for their approach.

They pointed me to this blog post; but it does not answer any of the questions that I asked.

The NCETM sound very confident in their approach, so it should not be complicated to answer these questions:

  1. What contact has the NCETM had with Chinese teachers from ‘supernormal’ schools?
  2. Where in the NCETM materials do they explain their decision to ignore the selective aspect of Asian education systems (if they made this decision)?
  3. Why do they think it is beneficial to the most able children in England to do the standard curriculum when in the systems on which mastery is based, this does not seem to happen?

I’m out of my depth here! It needs maths specialists to look at the issues and ask more detailed questions about content, depth, selection, etc.

I know the NCETM has the best of motives. I just wish they would explain themselves rather than repeating the same material and not mentioning selection in the source countries.

NB I’m not suggesting we should be adopting similar selection here. Simply that in those countries the standard curriculum seems not to encompass all abilities as the NCETM says, so if that’s their intention here I think they should be able to justify it.

The maths mastery approach has spread quickly through English primary schools, in large part because of the support of the NCETM and the Maths Hubs.

The NCETM suggests that all children, even the most able, will benefit from an approach which contains ‘increased depth’ rather than acceleration of content. They say that they base their view on knowledge of the East Asian countries where mastery approaches have been successful.

I’m slightly confused, though, by what they actually mean. Many schools seem to have taken it to mean that children should be given no content outside that specified for the year they are in; but the NCETM is clear (as is the NC) that schools can take content from other NC years if they think this is appropriate. The NCETM materials quote the NC on this point, and then say:

Schools should identify when they will teach the programmes of study and set out their school curriculum for mathematics on a year-by-year basis. (Oxford Owl/OUP/NCETM/MAths Hubs ‘Teaching for Mastery – Questions, tasks and activities to support assessment’)

In principle this would mean that you could include Year 6 content in a Year 1 class if you thought it would be beneficial. You could, in fact, structure your year-by-year curriculum to include all levels of work in all years, to be accessed at need.

So there’s a contradiction somewhere – either in the logic of what the NCETM is saying, or in how schools are implementing it.

I’m unsure as to how greater ‘depth’ can be achieved without adding extra content, past a certain level, and would value comments below giving examples of depth without new content which would be more challenging than the NCETM’s greater depth examples.

A useful example might be: How do you give a very mathematically able Y3 child conceptual challenge at the level of the Y5 content (which is the level at which said child begins to need to think about the answer) while remaining within Y3 material? Is that what is meant (because remaining within eg Y3 material seems to be what many schools are doing)?

But the main thing that I think needs sorting out is that I have found no mention in NCETM materials of the selective aspects of the various Asian systems. In particular, though there is much talk of China and the really interesting and important project of bringing Chinese teachers here so we can learn from them, there is no discussion (that I have found) of the role of ‘supernormal’ as a category in Chinese education.

It’s a bit of a startling word, but it’s basically what we’d know as ‘giftedness’. So it seems you can have ‘supernormal’ children; but there are also ‘supernormal’ schools which cater for the most able/high attaining children. I think there are also additional evening schools, but I’m only just learning about it all, so I’m not sure.

Anyway, it’s clear that ‘supernormal’ is an important category, and it would seem to be the case that these children are not taught the same curriculum in the same way as the majority (why would you select them, if you were to do that?!). This is from an article comparing Chinese and Honk Kong teachers of gifted children:

Education for the Gifted in Beijing
There are several schools for the gifted in Beijing that are
known as supernormal schools. These schools identify highly
intellectual students at an early age and educate them in self-
contained classes or schools. In supernormal schools, four
components are deemed essential to bring forth the talent
and potential of gifted students: the integration of excep-
tional intelligence (which refers to the interconnectedness of
different abilities and behavior), the provision of accelerated
learning experiences, the application of appropriate learning

styles, and the encouragement of a positive attitude. (‘Competencies and Characteristics for Teaching Gifted Students: A Comparative Study of Beijing and Hong Kong Teachers’, Hoi Yan Cheung & Sammy King Fai Hui, Gifted Child Quarterly

55(2) pp 140-1)
It is clear from this that ‘gifted’ is a recognized category, and that children identified as belonging to this category are educated differently. Most importantly, this difference includes acceleration of content.
I have asked the NCETM, via Twitter, to give their view on the role of the ‘supernormal’ category in mastery teaching for the most able (in this country as well as in China). They have, I think, spent a long time researching the Chinese system prior to their work driving the mastery approach in England, so I hope that they will be able to give an overview of how it fits within the approach as they have structured it.
Update: Tim Dracup sent me a link to his writings about gifted ed in Asia and looking at those it seems even odder that this aspect of the Asian systems is not discussed in English mastery approaches. I hope the NCETM will be able to clarify!

The forest for the trees – or, what is the point of phonemes?

I have recently started re-reading Alan Watts’ The Way of Zen, and (as ever) a conversation on Twitter has prompted this little ramble. I’m going to quote a lot of Watts, I’m afraid. Early in Chapter 1, he says this:

The task of education is to make children fit to live in a society by persuading them to learn and accept its codes – the rules and conventions of communication whereby the society holds itself together. There is first the spoken language. The child is taught to accept ‘tree’ and not ‘boojum’ as the agreed sign for that (pointing to the object). We have no difficulty in understanding that the word ‘tree’ is a matter of convention. What is less obvious is that convention also governs the delineation of the thing to which the word is assigned. For the child has to be taught not only what words are to stand for what things, but also the way in which his culture has tacitly agreed to divide things from each other, to mark out the boundaries within our daily experience.

(NB as a Zen Buddhist, he doesn’t really think this is what education should be; he is commenting on how it appears to him to work in practice)

Rather than seeing ‘tree’ as your unit of definition, it’s possible (actually, maybe, more accurate) to imagine conceptualizing a whole forest as the complete organism, which then consists of parts: soil, roots, mycelium, understorey, canopy, fauna. In fact the view that a tree is a separate ‘thing’ is, ecologically speaking, rather problematic.

As with trees, so with words. This lovely study, by Amanda Seidl at Purdue University, looked at how babies learn to separate the sounds of words as discrete units of meaning:

“Parents may pause before saying an infant’s name, but they almost never do so for other words. This research explored whether touches could help infants to find where words begin and end in the continuous stream of speech. They need to find words before they can attach real meaning to their words,” Seidl said. “Because names of body parts are often the first words that babies learn and touching is often involved when caregivers talk about body parts, we speculated that touch could act as a cue to word edges.”

That is, babies may learn to distinguish words from the actual flow of sounds via the tickling of their toes.

Watts’ paragraph above continues:

Scientific convention decides whether an eel shall be a fish or a snake,and grammatical convention determines what experiences shall be called objects and what shall be called events or actions. How arbitrary such conventions may be can be seen from the questions, ‘What happens to my fist [noun-object] when I open my hand?’ The object miraculously vanishes because an action was disguised by a part of speech usually assigned to a thing! In English the differences between things and actions are clearly, if not always logically, distinguished, but a great number of Chinese words do duty for both nouns and verbs – so that one who thinks in Chinese has little difficulty in seeing that objects are also events, that our world is a collection of processes rather than entities.

So… my point is that yes, as many have said, the concept of the phoneme is an abstract one, an imposition upon the flow of sound which really makes up human speech. But then so too, in its way, is the concept of the word.

The separation of words in text is something that we take for granted – but many cultures in the past did not do this, and a few still do not do so today. To what extent are the unseparated words less conceptually separate, I wonder? (Or possibly more so, if no visual divider is needed?)

Just as babies need help separating words from the flow of speech, so new readers need help separating the chunks of sound that make up words. Current phonics practice is only one way of doing this, but in order to understand the mechanics of our language, it’s a pretty good starting point (as long as the words worked on are real ones, of course). The phoneme is an artificial distinction – but then, according to Alan Watts, so is everything else we think we can see.

ITT and synthetic phonics – collecting experiences

Questions relating to the efficacy of SSP in schools often return to the issue of how teachers were trained, and how they are trained now – as well as to the quality of CPD.

Many people who are in favour of the current approach to using SSP in schools seem to feel that it is not taught properly/enough/at all in ITT – or at least, their experiences suggest to them that this has been the case so far.

Yet apparently ITT programmes will fail Ofsted if they do not teach SSP, so presumably all are now doing so.

Is this discrepancy the result of a slight lag in the effect of all ITT programmes teaching how to use SSP? Or is it more complex (for instance, there could be different approaches to teaching the subject within different ITT courses, some of which prove more useful in the classroom than others). There are so many potential ways to teach SSP to ITT students, with potentially hugely varying results in how they might engage with it once they are teaching.

A deeply important question is – what about the TAs? Are they confident and knowledgeable in their support of children’s literacy?

NB I have no idea at all of the truth (if there is one – there could be many); this post is basically a call for information, from teachers, trainers, ITT students, and anyone else with an interest in/knowledge of past and current situations.

Please comment – this seems to me to be an area in which greater clarity might prove to be extremely helpful in removing some urban myths.

Edited to add: Andrew Davies sent me this, which does seem to allow for great variability:

ofsted SSPAnd to add: there ‘s a thread in the RRF forum on the issue here.

And: I spoke to Keith Turvey (of the University of Brighton) on Twitter, who pointed out that ‘most ITT time is in school now’ and also said: ‘Most [ITT courses] set out expectations for SSP like we do but the execution on the job is down to schools and trainee, and the quality of trainee experience and opportunity varies significantly IMO. Thus partnership key.’

These seem some of the most important practical points, to me.

Look, Cover, Write, Check

Imagine if maths were taught the same way that the Look, Cover, Write, Check method ‘teaches’ spelling.

Each week, children would be given a list of 5-10 calculations, perhaps 10×45=450, 5×60=300, 4×39=156, 76×89=6764, etc, depending on how far up the school they are.

They have not been taught times tables, nor have they been taught how to do those calculations. They simply learn them by rote, so that in the test at the end of the week they can write out the whole of each calculation from memory.

How many children would be able to deduce, over time, the underlying patterns and rules and simple maths facts which are common to these calculations?

A few would, of course, and would be able to apply this knowledge to other similar calculations. Some would work out a bit of it, and so might make a decent stab at calculations which are close enough to the learned ones for some inferences to be made.

Many would have no clue.

If the specific calculations did not happen to turn up in other class work, I think most children would forget the list within weeks.

Yet this is what we expect from children in the Look, Cover, Write, Check method.

Without work on phonics and morphemes, rote-learning the spelling of ‘whether’, or ‘stupidly’, or ‘procrastination’ is no more useful than rote-learning 35×16=560 but never looking at 3×1, 30×10, 5×6, etc..

Memorization is crucial for some things, but pretty useless for others. When ‘rote’ learning is discussed, whether positively or negatively, it’s absolutely essential for this aspect to be clear.

See Improving Literacy by Teaching Morphemes for more on better methods.