What to do about Maths?!

[Hiddeninplainsight]

Right, I have been reading the very interesting thread on maths. So many interesting experiences. I am hoping you all can advise. My DD is in Y4. She is a bright girl, not exceptionally ‘gifted’ but is still a substantial outlier in her school. The main problem is Maths. She isn’t so exceptionally mathematical as some of your DC, but with that she doesn’t have an innate thirst for maths. However in Y1, and possibly still y2 it was her favourite subject and she has been bored in school since the beginning of y2 (with a brief respite when she was first introduced to fractions).

School are useless and have taught her maths is easy and dull. They want her to write out her workings but it is all so easy for her she can’t bring herself to explain (I think half the time she just knows).

It makes me really sad that they have turned her off Maths, but more than that I want her to know that Maths is hard, that it is about problem solving and the fun is in solving the problems. She loves a challenge so I think she would love it.

So, my main question is what do we do? I think she needs to have a focus and she needs to have something hard which she has to write out her workings for. We did an online maths thing which explored her knowledge and it said she was working roughly at the level of a y8 child (this was not based on what she has been taught, but what she worked out). My husband and I were wondering if we should get a tutor to teach her GCSE maths. I am worried she would then be bored in secondary school, although she is bored out her mind now (literally, she zones out for 40 minutes a day during the maths mastery whole class explanations). My thought is that it would challenge her, I think she would enjoy the challenge, I think it would provide a focus and I think she would enjoy it. But is it a mistake? Any other ideas?

We were looking for alternative to IXL once, to follow the NC so he won't have any gaps in knowledge. We declined maths wizz for same reason as your dd. It only goes up to yr8. Still can't find any site other than IXL that follows NC but also allows free access to higher year group.
But it's not the end of the world, there are so many site out there. One might encourage her to pursue at her level.

I don't think there is a single person on this thread that disagrees with the premise that the current education system fails the outliers. I feel that there may be some disagreement with the best way to support them.

OYBBK you are right. Although I think part of the issue also who is called outliers and what is suitable for them. For some kids acceleration is absolutely right because they are simply not working at the same level as the vast majority. How that acceleration is done is another matter, but I don’t get the blanket idea that acceleration is just wrong. IF it is accepted for some kids, then surely the question becomes for which degree of outlier is it need, and then (the really problematic question), how is it implemented. I hasten to add I am not talking about my DD necessarily. For her, I don’t know if the greater depth system alone would work because even that isn’t implemented in schools. But there are kids who will need greater depth AND acceleration.

Hidden Maths education is being ground down in England by a serious lack of qualified maths teachers, an obsession with data, tracking and league tables which results in kids being trained to pass exams.

But if we’re talking about ‘the system’ as the curriculum offering from primary through to sixth form, then I think that bright kids are actually the best served out of all the groups. Weak kids are totally failed by the system, and the GCSE syllabus is crap for middle ability kids.
In primary schools where they are misunderstanding what mastery means for the top end, there are definite issues - this is a new development. However, the new KS2 SATs are difficult (too difficult, it could be argued - worth getting your DD to sit some papers to see how she copes against end of Y6 expectations www.gov.uk/government/publications/key-stage-2-tests-2017-mathematics-test-materials ).
Once in secondary, most schools set students and top sets race ahead. The old maths GCSE was pants for the brightest, but add in Further or Additional Maths GCSE and it was pretty good. The new GCSE is so challenging that to be in the top 3% of the country last year you only needed to get 79%. In sixth form there’s maths and further maths A-level and STEP papers which are really challenging.
Obviously that assumes that the school has the teachers required to offer these, but the options are there.

In over a decade of teaching, and I’ve taught plenty of top sets, I’ve only taught one kid who needed special provision, for whom the age-appropriate curriculum, even for top set, was beyond trivial. I’ve taught kids who found maths pretty easy, but they still needed teaching and I could still make them think with extension work. The top 1% were kept occupied. This student was much rarer.

If you want talented students to be trained into the world’s top mathematicians with hours and hours of maths every day like they train dancers or musicians, then mainstream schooling doesn’t offer that, but I don’t think it should, tbh.

Noble, now I understand I think. You are so right about the teachers. And you were right about primary school teachers (and the whole failure for mastery to be properly explained and resourced for primary schools).

I also now see your point about GCSE maths in relation to the top grade and the scope for understanding beyond that. I think DD will be fine in secondary (if she hasn’t gotten so turned off Maths first - I think we as parents can help that). And I do understand what you are saying about the middle group. What an utterly rediculous system.

It is rediculous it can fail two groups so appalling in primary school (the two tails of ability) and almost everyone so badly in secondary. I am grateful to you and other teachers who try to do their job in spite of the rediculous mess.

This article written by a teacher makes some interest points:
why I will accelerate my daughter but won't tell you what do with yours

How many need substantially different/accelerated provision is a key question. It depends in part on what you mean by "need". If you mean "will manage not to go stir crazy and set fire to the classroom" then the number is low. If instead you mean "would derive a significant net benefit from" then the number is much higher. Internationally, "gifted" tends to be defined as top 2% and research shows acceleration to be extremely beneficial for that population. The previous government (DCSF - 2008) produced some remarkably sensible guidance on the exceptionally able (which they defined as top 2%). So also is the guidance from some of the main US institutions.
For the top ~0.1% (highly gifted) acceleration becomes a fundamental need, not a nice to have. With a UK school population of a little over 8 million, there are over 8000 kids in the top 0.1%. They deserve to have their existence acknowledged in an evidence-based policy designed to ensure their right to an appropriate education is met.

I agree with NobleGiraffe that additional/further maths at KS4 and further maths/STEP provide a good route for the bright and moderately gifted. But I think there are still two problems. Firstly, these provisions only kick in at age 14. That is too late. Many highly able kids in the top 1-2% won't survive the wilderness years of KS2 and KS3 without becoming completely disengaged and developing an antipathy to the subject and to school in general. Secondly it's still not enough for the extreme outliers in the 0.1%.
These kids do not need to spend hours per day to develop high level expertise. the whole point is they learn far faster and are already at a far higher level. All that is needed is to ensure their regular classroom time is not wasted. Computer instruction / virtual classrooms would go a long way if the expertise is not in their local school.

I do think one of the biggest problems with maths in particular is that the very organisations that should be providing research-based guidance (ACME, NCETM, UKMT, and the government itself) are all engaged in misdirection.

Shameless place marking

Self motivated students can thrive extremely well under the UKMT framework if they are the sort of student who can work through material themselves.

OP, I have not read all the thread, but I thought you might like to hear from someone who did let their dd do GCSE in year 6.
The reason we did so was because dd was bored in maths lessons as she was doing things she had done 2 or 3 years earlier. We did try speaking to the school many times, but they insisted she was being taught at the right level and was not as advanced as we were making out. The only enrichment offered was that if she sat through the lesson she would be given a more difficult work sheet. This stopped when she went up a year,
We decided to home educate and dd got A* at the end of year 6 and went into a secondary school in year 7. She sits quietly at the side of the class doing A level maths and is much happier.
I would say, do not let her take the GCSE unless she stands a good chance of getting top grade as she will just spend the next few years ring to improve and it will count as a retake.
I have no regrets in dd taking GCSE early as she finds the challenges of A level very enriching.

I was wondering how your dd has been getting on :)

Which year group is she in now? Is she just doing A level maths or other stuff too? What happens after she completes it?

I was going to say as well, do not worry too much about the not writing out all the steps. When dd got to doing practice papers. We would go through the mark scheme together. After dd seeing she was getting one mark instead of two for questions, she suddenly found she was able to write down steps.

If your dd had had a tutor richmal and still had to sit through normal school lessons, and take part in them would that have worked for your dd?

Kitten, dd will go on to do further maths A level. She is now in year 10. I think you have to do what is right for your child and for dd this was the best option when dd realised she would never be taught any maths in primary school.

She now is at an excellent secondary, with very good teachers.

Kitten, sorry x posted. I do not know, because I was in a position to teach her maths and the main problem for dd was the enforced hour of boredom every day in what was her favourite subject. If I had not home educated I do not think dd would have had the time to work on GCSE.

I'm glad she's happy. My dd took a different path as you probably know - she didn't take any exams early and while primary was utterly awful, enrichment in secondary school worked very well, bar a couple of hiccups at the start of a new school year.

I've talked to dd about whether we should have home schooled in primary, I think we've concluded that perhaps we should have done, but I don't know. It's hard to know though, we did what we thought was best and threw a lot of different activities her way. Some primary teachers were better than others. By keeping her in primary, it did for her probably mean that going into Secondary was easier friendships wise.

Kitten, every child is different and I do not think there is a right or a wrong choice, you just go with what you think is right at the time. If things were just slightly different, I would probably have made a different choice. Doing what you think is best for your child at the time, generally works out best.

It's an eye-opener to trace where ACME's and UKMT's opposition to acceleration actually stems from.

ACME's document containing their patently false statement on acceleration contains "Particular thanks are due to to Tony Gardiner for his advice and support in the drafting of this paper" and he led/chaired the discussion groups that fed into it. The only reference to an academic journal is to a paper in the De Morgan Journal with sole author ... Tony Gardiner. The paper itself contains no empirical research or evidence and is essentially a peeved rant of the appeal to authority type.

Similarly, UKMT was set up in the 90's largely by ... Tony Gardiner. Its policy statement which we an assume was either written or heavily influenced by him says it " supports a policy of mathematical enrichment rather than acceleration through the examination system ". Let's ignore for the moment that acceleration is characterised by the use of appropriate pace and high level material and need have nothing to do with the exam system, and instead look at the actual evidence they provide. It gives only three supporting references:

1. the ACME statement already mentioned above.
2. a link to the NRICH website which states : "There are different ways in which teachers can meet the needs of their most able mathematicians. The most prevalent in UK schools is through acceleration - pupils move through the school curriculum faster than others, often taking assessments or examinations early. For some highly able students this is fine".
3. The Mathematical Association's policy which states "The Mathematical Association believes that mathematics teaching should focus on the needs of the individual. Every student should have an enriched mathematical experience, with that enrichment pervading curricula rather than being bolted on. Accelerating students should occur sparingly and judiciously." So, a majority (2 out of 3) of the references "supporting" UKMT's statement against acceleration actually acknowledge it is appropriate in some circumstances. The other derives from the same source (Gardiner) as UKMT's own policy and is thus not independent corroboration.

So, what does history tell us about the accuracy of Tony Gardiner's pronouncements on acceleration. Well in 2001 he was on record as say, of a small group of children who has been accelerated that " none of these children will ever come to anything. They are not really gifted kids or child prodigies, just children who have taken their exams early " (nice, eh?).
You can see here here and here exactly how accurate Gardiner's statement has proved - which is as neat a case of disproof by counterexample as one could wish for. If he wasn't correct about the specific children of whom he was so dismissive, why should we take his view on what is appropriate for all children (and indeed for our children, of whom he knows nothing) seriously?

Lastly a comment about UKMT's "activities" - these are all geared to entering the British team for the international mathematical olympiad. So they cherry-pick a handful of bright kids - some as young as 14, and overwhelmingly from grammar and private schools - and give them fast paced instruction on topics not generally covered till after A level: combinatorics, advanced algebra, projective geometry, number theory. i.e. they accelerate them. So look how quickly they will break their own rules when there's the chance of reflected glory in a pissing contest with their international counterparts. And who was the chief coach of the British IMO team for many years? Tony Gardiner.

In short - one person has exerted disproportionate influence in poisoning the UK mathematics community against acceleration.

gfrnn - it would be helpful for us to know a little bit about you, why this is of interest. I'm interested in your actual experience with acme and ukmt.

When you say UKMT 'cherry pick' a handful of bright kids, that's not actually very accurate - students take multiple level of competitions, most of which don't need anything beyond GCSE knowledge and an ability to manipulate it deeply - before they end up on the squad. To compete internationally of course they then need to have similar knowledge to other teams.

There are mentoring schemes available, all students can access the lower mentoring schemes - if they know about them and are self motivated - that's the achilles heel. But they still require nothing more that a deepening of knowledge. What they really learn from the mentoring schemes are an ability to think for a sustained period of time deeply and to then show their thought process accurately.

The one area I would say they are accelerated on is the general principle of being able to solve problems by proof.

Let's ignore for the moment that acceleration is characterised by the use of appropriate pace and high level material and need have nothing to do with the exam system

But ignoring that means you are constantly talking at cross-purposes with most people on this thread. Acceleration here (especially when the OP talked about a tutor for GCSE) is used to mean kids sitting exams early. Kids doing UKMT stuff is seen as enrichment. Talking to kids about stuff not on the school curriculum (e.g. university masterclasses) is also seen as enrichment.

The ACME statement against acceleration makes it clear what they mean. “Potential heavy users of mathematics should experience a deep, rich, rigorous and challenging mathematics education, rather than being accelerated through the school curriculum.”

They say later “At Key Stage 4, ACME has argued in the past against schools’ propensity to enter students early to GCSE Mathematics, whether in an attempt to accelerate high achieving students or for other reasons. This early entry to standard assessments is often not in the best interests of the student – a position that is now acknowledged and supported by Ofsted.”

They are absolutely correct. Schools were entering whole classes of students early for GCSE maths and kids were being denied the chance of a better grade because of this. There were posts on MN about kids who had been entered early, got a B, did no maths in Y11 as they were now concentrating on other subjects and weren’t allowed to take A-level. The practice was widespread. It is in that context that you need to read their statement, where they are clear that they are identifying able students as those with the capability to study maths at A-level which is a far lower standard than people on the G&T threads usually expect.

They also say that “At the same time it is damaging for young people who have progressed to a notional target to be allowed to coast, repeat work, mark time or otherwise to be under challenged. All young people regardless of their prior attainment should be entitled to a challenging and rewarding classroom mathematics experience.”

“Although appropriate in-class provision is the most urgent need for able young mathematicians, extra-curricular provision as outlined in footnote 6 is also important for nurturing robust mathematical inclinations.“

Hard to disagree with that, surely?

I haven’t read the thread, and assume it has moved on, but you could have a look at how America is teaching maths at the moment as it is quite interesting. They look at teaching addition, subtraction, multiplication and division in a different way to how we do it here. Many parents are up in arms about it as initially it looks very different to how they would have been taught, but mathsy sorts respond to it by saying that this is how they logically work out maths in their heads anyway. I’m not describing it very well, but here is an example as to how they approach subtractionwww.dummies.com/education/common-core-standards/a-common-core-homework-headache-subtracting-by-adding/

It might be something you could look into together.

In America, you can also whizz through the high school curriculum and take college courses ahead of time, if you are lucky in your access to a good school. They have a totally different system, which I think can be far better for talented kids at a good school, but can also be terrible for kids who struggle or who don't have access to the right school.

@OhYouBadBadKitten I have no connection with acme and ukmt and no "history" or grudge concerning them. I think the actual materials they produce are good - it's their opposition to acceleration that I take issue with because it contributes to an anti-acceleration mindset in schools. I've tried to avoid personal anecdotes and give links to reliable sources of information. Would my personal circumstances affect their validity?

Re: "students take multiple level of competitions, most of which don't need anything beyond GCSE knowledge and an ability to manipulate it deeply"
I think this was covered pretty well here, where when you made essentially the same claim: "It is perfectly possible though to do very well in bmo 1 without having done your gcse."
GHGN responded with two very informative posts explaining that even BMO1 requires topics beyond A level understanding and that pupils without specialist coaching (which tends to be localised to elite schools) don't tend to make it beyond BMO1.
The few dozen kids they take to their training camp(s) from which team will be selected have thus already had specialist input and receive more, whereas there are hundreds of kids of equal natural ability who don't get a look-in because their schools can't provide an equal level of facilitation.

UKMT can provide undergraduate mentors to exceptionally able kids who have proved themselves in the earlier rounds if asked so the school don’t need to do any coaching themselves.

It’s the ‘if asked’ bit that’s problematic. Schools don’t know to ask. The UKMT should be more on top of it IMO.

@NobleGiraffe "ignoring that means you are constantly talking at cross-purposes with most people on this thread. Acceleration here (especially when the OP talked about a tutor for GCSE) is used to mean kids sitting exams early. Kids doing UKMT stuff is seen as enrichment. Talking to kids about stuff not on the school curriculum (e.g. university masterclasses) is also seen as enrichment."

Actually, it just means that you and I are talking at cross-purposes with each other - only two others on the thread have even mentioned acceleration, one of them favourably. In my first post (which was the first on the thread to raise the subject of acceleration), I linked an encyclopaedia article which discussed exactly what acceleration meant in the sense it is used internationally in gifted education, so I don't think I could have been much clearer.
On the other hand you seem to be confused about what acceleration is, so let me clarify with two examples:

1. you wrote "It depends on what you mean by acceleration. A student who gets a 9 at GCSE and an A^ in Further maths aged 16 has been accelerated compared to the student who gets a 4 at GCSE" This is not acceleration. They've followed curricula and sat exams intended for age 16 at the age of 16. Extension - yes. Enrichment - quite possibly. Acceleration : no. Good practice? yes, in most cases.
2. you wrote here that a year 7 child " could get into studying shapes and symmetry, which would get into group theory (Further Maths A-level/uni level maths) without having needed to study A-level. "
   This is acceleration because group theory is generally not encountered until further maths A level at the earliest, and often not until 2nd year of a degree, and thus corresponds to higher-level, more abstract material generally given to much older students. I have no problem with either of these - they are both appropriate for different ability levels.

What I do have a problem with is that ACME, UKMT and NCETM have adopted positions opposing all forms of acceleration for all children all of the time. They are statements of belief, which ignore all the research on gifted education done internationally. A carefully worded statement opposing a trend toward early entry to GCSE / other exams for too many students could have been justified, but they have thrown the baby out with the bathwater.

The result is that many teachers are opposed to giving students access to higher level material (either standard curriculum/UKMT/other) originally targeted at older children and instead try to divert them sideways into more material of a level intended for their chronological peers. For the highly gifted this is not just a waste of time as they are not working within their zone of proximal development, but can also completely destroy their motivation to learn and contribute to school refusal/ dropout/depression. Hence the advice: first accelerate, then enrich

That's the crux of the issue Noble, outside mentoring is available if people know to trawl through the ukmt website. It doesn't need to be the school that asks either.

The summer camps following intermediate olympiads are accessible to students who haven't had access to any training at all. Those camps are part of the path towards specialist training but it isn't necessary to have attended one of those to go further in ukmt training or competitions.

Students do make it into BMO2 from comprehensive schools. If a school enters students into ukmt competitions then well motivated students can make it to the top no matter their background without training from their school. What is lacking is the understanding from schools or parents of the opportunities available from ukmt.