Setting for Maths in Year 7

[lucyanntrevelyan]

Can anyone tell me if their DC school does not set for any subjects even Maths at Year 7 ? This is a change the school have made for this year which I have just discovered at Open Morning. (Previous DC at school have all been set for Maths from this point in Year 7 and for other subjects in Year 9) I am not clear if there will be setting at all for the current cohort. My DC is very able at Maths and my research has suggested that not setting for Maths is a disadvantage for higher ability children. The Maths department told me 'research suggests mixed ability is better' but didn't give me any indication which research? Can anyone /teachers enlighten me with what research this was so I can be better informed and reassured this is the best thing for my child.

As I understand it, your argument is that every child can be taught, and can learn, at the same pace, in the same classroom.

Or perhaps that if a child DOES learn slower, then they should be given the extra support to 'close the gap' - so you are saying they do learn slower, but should be given the daily help that they need, to catch up.

However, particularly in secondary, where does that time come from? Either every child who needs the extra support must have two maths lessons per day (the Shanghai model, essentially) OR the curriculum is arranged so that such children spend more time on each concept so that they grasp it (essentially the English model).

Or there is an expensive other model - that every child has individual support in each lesson - but they can't be seated by ability to gain from that support, because that is setting.

Do you see that for someone who is trying to follow your points - because fundamentally I am not wedded to setting - the glaring inconsistencies are a real issue?

Does cakes think that teacher of bottom sets tediously go over the basic stuff at a slow pace, constantly revisiting while the class is getting it all correct and chomping at the bit to move on?

Because she seems to be of the opinion that the speed of learning is determined by the number of the set allocated, and not by the pupils contained within it.

They are not being artificially held back.

so equal percentage of Brits and of the French should be able to attain equivalent level of knowledge / qualifications
What evidence do you have that they don't?

I supplied you plenty, but of course you don't want to engage with the evidence that doesn't 'fit' your view.

You can't invalidate facts by declaring "you can't compare".

I'll reply in detail as you ask, but here for starters. This came up in search about Wechsler and I think it was mentioned earlier in the thread. However I dare anyone to actually read it. To actually take note of the facts and analysis and the words of the children.

^"Although there are substantial problems in interpreting the results of international comparisons (Brown, 1998, Wiliam, 1998), there is little doubt that, in a variety of respects, the performance of primary and secondary school students in the United Kingdom is modest by international standards (Beaton, Mullis, Martin, Gonzalez, Kelly & Smith, 1996; Mullis, Martin, Beaton, Gonzalez, Kelly & Smith, 1996). Kifer & Bursten’s (1992). Analysis of data from the Second International Mathematics Study (SIMS) suggests that the two factors that are most strongly associated with growth in student achievement in mathematics (indeed the only two factors that are consistently associated with successful national education systems) are opportunity to learn (ie the proportion of students who had been taught the material contained in the tests) and the degree of curricular homogeneity (ie the extent to which students are taught in mixed-ability, rather than setted, groups).

While Bennett, Desforges, Cockburn and Wilkinson (1984) found that teachers using within-class ability grouping tend to over-estimate the capabilities of weaker students, and set insufficiently challenging work to the most able, the evidence that we have found in the current study suggests very strongly that between-class ability grouping produces the opposite effect. Indeed, the strength of the curriculum polarisation, and the diminution of the opportunity to learn that we have found in the current study, if replicated across the country, could be the single most important cause of the unacceptably low levels of achievement in mathematics in Great Britain. The traditional British concern with ensuring that some of the ablest students reach the highest possible standards appears to have resulted in a situation in which the vast majority of students achieve well below their potential. As one student poignantly remarked:

Obviously we’re not the cleverest, we’re group 5, but still— it’s still maths, we’re still in year 9, we’ve still got to learn. (school R, set 5, girl)"^

Here

You cannot compare norm referenced and non norm referenced qualifications.

Incorrect. I am sorry, but you really might take a step back and appreciate the bigger picture.

Just think of all the scientists and doctors, nurses from other countries that work in UK. Most of them have non-norm referenced qualifications, (UK is unique I think) yet they are accepted as having equal level of knowledge and skill (and I hope you would agree they do have equivalent knowledge and skill). Likewise other countries accept UK qualifications, even though they don't match their local specs.

There is an old establishes and well functioning state mechanism of comparing and recognising qualifications. It is called NARIC. It has scientist and educational professionals working for it to analyses, compare and decide whether qualifications are equivalent, and to issue the certificate to this effect for those who ask.

Bac is equivalent to 3 A levels grade 4 or above. This is just a fact.

There is also Bologna process that compareds and alignes the curriculum and assessment methods of education system across participating countries, with the purpose to aid the international equivalence of qualifications. They look into curricula, assessment methods, everything. Basically they did look into and assertained that the absolute level of knowledge of those who pass Bac is equivalent to those who pass relevant A-levels.

So,
the fact that x percent of French students reach the standard that THEY call a pass and y % of British students reach the standard called 'Level 4' are two separate, .. but entirely comparable and found through NARIC and Bologna process to be entirely equivalent.

If you can show me that, given EXACTLY THE SAME TEST PAPER, after being taught EXACTLY THE SAME CURRICULUM, sat by CHILDREN AT EXACTLY THE SAME AGE French students achieve better, then that is worth talking about. That would be impractical, but the fact that it was not done does not invalidate other data that are available, like PISA and international equivalence of qualifications.

Until then, you are comparing apples with pears and pretending that you are comparing apples with apples.
I am comparing people with people under the premise that this is close enough.

i am not absolutely sure that fine-grained Maths sets from day 1 of Year 7 are necessary or desirable, especially since the vast majority of pupils will have been taught in mixed ability groupings in primary. But that qualified measure of support for non-setting has been completely eroded by cake's inability to engage ....
I am sorry, but indeed I failed to appreciate the great good of not setting on day 1, but of doing that on day 2, or after half term, or in year 8, or in year 9. I can appreciate that it might be necessary to separate into streams by ability and specialise for 6 form, post 16, what-ever. But I struggle how setting in year 8 is any better and is a "qualified measure of support for non-setting". That one is on me, I am a very imperfect being, I really did not understand this to be support.

And I don't believe there is no setting in primary. Where there are ability tables, there are sets.

Do you see that for someone who is trying to follow your points - because fundamentally I am not wedded to setting - the glaring inconsistencies are a real issue?
And there's the issue.The rest of us are quite open to the fact there are pros and cons of sets and mixed ability but the reality is much more complex than you make out.
The thing is you seem to dislike people exploring complexities because the same old regurgitated assertions don't work (And that's how we get claims of 90% needing a grade 4 with no reframing and then when people point out yet against doesn't work then it's 'use your imagination, you'd need to redraw the parameters and change the spec and change the assessment marking etc).

There's pros and cons to setting and mixed ability. I prefer loose ability groups for my subject so a half way house and enjoy teaching mixed ability and sets for my subject. Despite that, your claim sets ruin education make little sense.

Maths sets are different to any other subject. If you don't understand basic arithmetic you can't access any of the more complicated bits. If you can't recall 360 degrees in a circle, 180 degrees interior angles of a triangle, recognise right angles etc, trigonometry will be inaccessible.

Obviously someone with decent basic maths skills can have better and worse strands. I really sucked at vectors in abstract but was fine with them in Physics. Others might find stats harder than mechanics, but these are later strands all building on basic arithmetic, algebra and later calculus.

In subjects like English, history, geography and to an extent science the content isn't hierarchical. You don't have to study Midsummer Night's Dream before Macbeth and Merchant of Venice before Hamlet. They are all stand alone texts. Not getting the point of sonnets doesn't mean you can't get value out of modern poetic forms or limericks! You don't need to understand the minutiae of longshore drift to understand why takeaway shops tend to cluster on the edges of the city centre.

Language grammar is back to a more hierarchical learning structure. If you can't recognise a verb, or the subject you won't be able to get the agreement or conjunction right, but from recent playing around with Duolinguo repetition and memory can get you a long way into effective reading.

Maths always struck me as one of those subjects that some people just get, either instinctively or can be shown something once, do it a few times then get it enough to apply to similar scenarios from then on. One or two topics per lesson. This is what top set teachers deal with.

Other people really have to work at getting maths, may need to learn things like simultaneous equations in small pieces but once they get it, they get it thoroughly and can apply it to similar scenarios. Probably more middle set, at least 1, possibly 2 lessons per "topic".

Then people who believe they don't get it, don't retain the method until repeated many times, get completely thrown if the question looks different. Teacher will need to go through all possible ways a question could look with the class, and possibly again with individuals, reassuring at every step that it is right. The pupils should get it eventually but might still be thrown by an oddball question on this topic.

How can you teach all these types of lessons in one class. Much better to have a big top set or two with the limit being number of seats for bums to occupy, reducing numbers in other sets so teachers can give more time per pupil which is generally not required in the top set. With certain topics once the task is set the teacher could even blitz some marking for other classes - that little input was required in my GCSE class!

England's own maths expectations have dropped to even end up with all those still not passing.
I did gcse then additional maths which i think was a similar level as

In France children with average ability pass BAC, 90% in a school year, 80% in each year of birth
in a generation”, meaning by year of birth, 79% pass the Bac (page 222 of the pdf

Bac is equivalent to 3 A levels grade 4 or above. This is just a fact

But there are different types of French Bac.

From the 78.7% of students who passed the Bac in your pdf link:

41.1% passed the baccalauréat général - equivalent to A levels.

15.7% passed the baccalauréat technologique - technological baccalaureate.

21.9% passed the baccalauréat professionnel - a less academic, vocational baccalaureate.

Even within the baccalauréat général there are at least 3 different streams with greater/lesser weightings given to maths, e.g. the Bac S (scientific) gives a weighting of 7 or 9 points for maths and the Bac L (literature) only gives a weighting of 3 points for maths.

Where does it say that French Bac students all take the same maths exam?

This UK university, ranked 110th in the UK accepts French students with the baccalauréat technologique or the baccalauréat professionnel for an Art course but what else?
www.kingston.ac.uk/international/country-specific-information/europe/france/entry-requirements/

Southampton University will only consider a French Baccalaureat Technologique on a case by case basis - therefore it is not considered as good as the Baccalaureat General.

www.southampton.ac.uk/uni-life/international/your-country/europe/france.page#entryreqs

Concerning the processing speed and ability

Of course ability plays a role in outcomes, but not as an explanation for 35%. I'll come to this later. But processing speed is not the central issue of cognitive ability.

Noble, your photo of memo from JCQ about access arrangements talks about Cognitive processing, not processing speed. By "cognitive processing" they mean cognitive ability, which is analysed in finer detail for various components / factors of it. Processing speed is one of the factors, it is on the list, but not the central one by far. This is a question for EP and cognitive scientists, but generally, working memory tends to be the most limiting / most predictive factor of cognitive ability, not processing speed. Most cognitive assessment batteries do not even include processing speed, it is done on demand where there is a suspicion if could be a factor. This is why I said it is niche, but of course important for individuals concerned. Other factors in cognitive ability are verbal and non verbal reasoning. A child with spiky cognitive profile with strong reasoning, average working memory and weakness in processing speed may do very well, the processing speed will not necessarily be the defining factor, but of course they would be disadvantaged by tuition 'at speed'. With SEN every child is an individual this is why I don't want to focus on processing speed. There is a range of factors encapsulated in a broader term of cognitive ability, and then there are specific things like SpLd, Dyslexia, ASD, Dispraxia, Cerebral Palsy... I take the point from Alexander that her DC has 24%-tile processing speed in addition to a range of other factors including ASD. Of course it is a factor for her DC. My DCs also have ASD, spiky profiles with significant problems, but processing speed is not one of them. In itself it does not make my DC any less or more able than Alexander's. I don't know what role processing speed plays in Moderate Learning Difficulties, but still, I suppose it could be referred to as ability for the purpose of this discussion. MLD are diagnosed for 2%-tile.

To be clear JCQ extra time, according to this memo, is given following a difficult process by Senco, to children with presumed SEN, when at least two of their cognitive scores are 'low average', not sure whether they mean below 25%-tile, it would be specific to the test.

On a broader point that weakness in cognitive processing requires extra time during tuition. The answer requires to disambiguate the muddle. First, what you label as weakness, second what is the policy of dealing with the weakness if it is labelled, third, what happens with 35% and sets.

1. What is labeled as weakness? MLD is 2.2%-tile. Low ability is 10%-tile, IQ of 70-79,as I posted earlier. They are expected to struggle. Low average ability is 10 to 25%-tile. They are expected to keep up with some difficulty. 25 to 75%-tile are average. About 15% of children have some SEN, many among them would have high cognitive ability. SEN are not necessarily bottom ability.

So where do you draw the line, Noble? Roughly which ability is too low for GCSEs?
You can't just leave it open and elastic, to extend every time as it suits.

2. Policy. Are less able actually given extra time? No. They stay in education the same time as the most able, but they exit without good qualifications. Their curriculum is cut short because of slower progress (as I understand Nobles's point ). Only children with SEN, those with EHCPs are enabled to continue until the age of 25.

It is not acknowledged in policy that lower sets need extra time.
At least half of students in lower sets would not meet any definition of SEN and would not qualify for extra time. The policy does not provide for time. Perhaps this is the problem that needs to be acknowledged.

It is also not acknowledged transparently in the public discourse that lower sets are not expected to pass GCSEs due to system set-up, that they will never have the time to cover the curriculum, because the time is only just enough for the most able.

3. the 35% Since you talk of cognitive processing weaknesses, JCQ state that extra time is given if at least two measures are 'low average'. If you take 'low average' as a guidance threshold of GCSE pass ability, i am not sure all students in lower sets would have low-average scores. Definitely not all students missing on GCSEs are low average. 'Low average' percentiles are between 10 and 25%- tile. So actually 10% within the 35% who fail GCSE (35 take away 25 = 10) would not fit in this definition of those that need extra time... the JCQ definition of weakness.

There is no ability based reasonable explanation why those with ability between 25 and 35%-tile don't get good GCSEs.

And given that qualifications are equivalent internationally, you absolutely can compare with success rates in other countries.

The Finns, the French, northern Europe, but also Estonia, Poland etc have no trouble educating those with 25-35%-tile ability to the equivalent of A-level.

So the explanation purely based on low ability, on the premise that the children are not good enough does not stand really. That could only apply to bottom 10%.

The explanation is in how the system treats those students.

Others have pointed out that speed of cognitive processing affects pace of learning, and this is not caused by setting.

Speed of learning lays on a bell curve. 'Speed' of teaching is a policy choice. The policy of sets really means the pace of progress for good GCSE is set by top sets since Reception. It progressively amplifies and entrenches the gap between sets and limits curriculum. Thus it puts the lower sets beyond the threshold for GCSE .
Sets is a centrifuge, not a pipeline. Too many get ejected outside the threshold.

Unless you provide extra years of study to the mid and lower ability students, only a truly mixed ability comprehensive class would enable the low average student to just manage within the threshold for good GCSE. Bigger proportion of the cohort would stay within the threshold, go through the same curriculum, while the spread of exam results would reflect variation in ability. The most able will be on top, they have nothing to loose.

In most other countries the assumption is that difference between pace of learning is relatively minor, the whole bell curve of ability can fit within one classroom, and enables to educate the whole cohort with the exception of 5 or 10% in at the same mixed ability pace to the outcome which is equivalent in level to UK.

Yes, there is repeating of the year by about 10%

The notes in the pdf state that 12% of students taking the baccalauréat général were out of year but it's more than that for the
baccalauréat technologique and the baccalauréat professionnel.

The problem is that some people take more time to learn how to do maths problems. If this time is not given then it doesn't matter if they are taught the nexg thing because it is just another piece of useless information. Without knowing how to do long division, you will have no clue how to divide by a polynomial. Without knowing how fractions work, you will struggle to simplify equations using fractions. The foundations have to be in place or nothing makes sense. So there is no point moving on until the foundations are in place.

There are plenty of bright, "top set" kids who will be disruptive when bored - and might have special education needs of their own. Admittedly a bright kid might just mooch on through the text book beyond the work set by the teacher, and they will get ahead, get more bored disrupt the class and take teaching time away from those who need it. How does this help anyone?

The Finns, the French, northern Europe, but also Estonia, Poland etc have no trouble educating those with 25-35%-tile ability to the equivalent of A-level

But only 41.1% of French students in your pdf link passed the baccalauréat general. Are you suggesting that recently qualified hairdressers and car mechanics in France are educated to A-level standard?

Clavinova,

Yes, there are different types of Bac. But all types are compulsory mixes of subjects, all at reasonable level. They are all 'facilitating'.

Scientific Bac is quite tough on STEM. Literary Bac is tough on languages and literature. Here there is an English translation of of a 2011 Literary Bac paper in Maths. Not the same as A-level Maths, but quite robust.
gfbrandenburg.wordpress.com/2011/06/19/a-look-at-one-version-of-this-years-french-math-baccalaureat-exam/

Not all mixes of A-levels are equal either. Those with A-levels in Geography, Psychology and Media Studies are not going to be admitted on Southampton Electronics course.

The Bac technologique is more applied, but it is not hairdressing! It includes business studies option for example, but A-level and other Level 3 qualifications also can have less academic combinations, including dodgy ones.

The Bac professionnel is equivalent to BTecs. But the latter are also accepted by universities.

The big picture imo is that all Bacs taken together are equivalent to all Level 3 qualifications taken together.

On the pass rates, even if you exclude Btechs as I don't know the numbers, just comparing the General Bac with A-levels there is significant difference.

A-level pass rate for 3C+ is 34% and this is only the proportion of those who entered 6-form.

79% of the 'generation' pass all types of Bac.

If you compare GCSE, the Brevet exam taken by most at 15 has the pass rate of 90%.
Here is the Brevet maths paper in French. One can see it involves advanced algebra and some complex common sense questions, like total cost of a journey for a concert for 3 people. Not just basic arithmetics.
file:///C:/Users/mvanh/Downloads/BREVETMathematiques2018.pdf

USAS on equivalent qualifications.
Page 23 shows pass % for Finland. 5% Fail. 84% do Satisfactory.
www.ucas.com/sites/default/files/2015-international-qualifications.pdf

The other point is even if you consider for the sake of argument that Bac Professionnel are hairdressers, it shows that they passed a Maths paper that is more advanced that the Brevet they ought to have passed at 15.

It still shows that 80% of French population achieved a standard in Maths that is at least slightly superior to GCSE.
I only want to say that it is possible to teach maths to more people.

I said working memory is important. My sense is that something needs to be done very early, from Reception to help DC with low working memory to cope. This is what opens the gap and they don’t grasp the concepts, and don’t retain them. It is a working memory problem. You need highly visual, multisensory approach from the start. It is too late in year 5, the damage is done. Memorising also helps. I can’t see anything wrong with memorising time tables, or fragments of poetry. Memorising simple formula helps deeper understanding. You can come back to the idea and reflect on it in a different context without having to go through the whole concept from scratch. We all know E=mC**2, but we don’t know the maths that derived it. But we can reflect on it.

There is that discrepancy in verbal vs non verbal reasoning amongst reasonably clever children. Perhaps those with weakness in verbal and strength in non verbal have better visual working memory. They rely on visual learning, while the tuition model is based on verbal and auditory. Maybe they just sit through verbal explanations waiting to see what it is about and then grasp it all at once, not step by step. These children would do much better with more visual presentation of curriculum and free time allowed for them to visualise and retain the concepts, to ‘see’ it as a whole.

Just imagine that 90% of students actually cal solve quadratic equations... I don'tr know, like the Finns, the French

Severe shortcomings in Finnish mathematics skills

In 2005, over 200 university teachers - teaching maths at universities and polytechnics in Finland - were astonished at how poorly students could handle algebraic expressions and solve equations...it was not properly tested in the PISA study.

matematiikkalehtisolmu.fi/2005/erik/KivTarEng.html

Clavinova,

Ok, of course all systems have shortcomings. I am only making the broader point that higher proportion of population can be taught maths.

My pre-previou post went wrong. It should be this

As I understand it, your argument is that every child can be taught, and can learn, at the same pace, in the same classroom. In other systems, 90-95% can do, yes

Or perhaps that if a child DOES learn slower, then they should be given the extra support to 'close the gap' - so you are saying they do learn slower, but should be given the daily help that they need, to catch up. In the current system in this country, they should be given extra support, but not to keep them ‘working towards’, this crashes confidence and prevents from grasping concepts as per the next point. The intervention should bring them to ‘working at’. Intervention that stops at ‘working towards’ keeps children under an enforced ceiling.

However, particularly in secondary, where does that time come from? We need to openly acknowledge that time needs to be created somehow. By extending tuition to 18 for all, or just the lower stream. Reducing the curriculum to core subjects and having two maths lessons. Something got to give to bring the average children back within the threshold of GCSE success.

Either every child who needs the extra support must have two maths lessons per day (the Shanghai model, essentially) the main point of Shanghai is to remediate the problem immediately, not let the gap to open. This preserves confidence and motivation. OR the curriculum is arranged so that such children spend more time on each concept so that they grasp it (essentially the English model). I am sorry, this is perhaps the intention of the English model, but it is not the reality imo. The children who really struggle actually don’t grasp the concepts, precisely because of the way the tuition is arranged. They are left in a shaky state and lose confidence.

I was flamed in another thread to bring up learning styles. It means different things to different people. Let’s consider this.
Processing speed was discussed. OK, it’s a factor. Not all clever and talented people are quick, some start slow but jump far as it were. So a pedagogy based on speed will disadvantage many clever talented children.
The speed of passing CAT and the skills section is not necessarily a measure of processing speed. It is a measure of many things including coordination, executive functioning, attention and working memory.

I said working memory is important. My sense is that something needs to be done very early, from Reception to help DC with low working memory to cope. This is what opens the gap and they don’t grasp the concepts, and don’t retain them. It is a working memory problem. You need highly visual, multisensory approach from the start. It is too late in year 5, the damage is done. Memorising also helps. I can’t see anything wrong with memorising time tables, or fragments of poetry. Memorising simple formula helps deeper understanding. You can come back to the idea and reflect on it in a different context without having to go through the whole concept from scratch. We all know E=mC**2, but we don’t know the maths that derived it. But we can reflect on it.

There is that discrepancy in verbal vs non verbal reasoning amongst reasonably clever children. Perhaps those with weakness in verbal and strength in non verbal have better visual working memory. They rely on visual learning, while the tuition model is based on verbal and auditory. Maybe they just sit through verbal explanations waiting to see what it is about and then grasp it all at once, not step by step. These children would do much better with more visual presentation of curriculum and free time allowed for them to visualise and retain the concepts, to ‘see’ it as a whole.

The PISA maths paper (remember Finland's reputation rests mostly on its PISA performance) contains not a lot of actual hard-core maths (and it contained even less in the early 2000s). It is essentially a maths-y reading comprehension test, where you do things like read an article with an accompanying graph and then explain why the graph is misleading etc. etc. Very light on equations, calculating area and volume, things like that.

The PISA maths paper is a perfectly "good" test as a test of general statistical etc. literacy for the general population, but it is not a good test of college-readiness for STEM subjects. For that, you need to look at TIMSS scores. Finland scores below both the UK and the US on TIMSS.

theeconomyofmeaning.com/2016/11/29/timss-results-are-in-asia-still-reigns-finland-and-germany-see-lower-average-achievement/

Finland's education system has some good points and gets several things right but has been wildly overhyped by credulous journalists, and the Finnish cohorts who did really well (at PISA, that is) were those who went to school in the 1990s, so looking at what is going on in a modern Finnish classroom more than 2 decades later does not always tell you very much.

Just realised Bologna process is only for universities, although I've seen something Bologna on entry qualifications. A mistake.

The equivalence thing for secondary school is The European Qualifications Framework (EQF)