Is it reasonable to expect ds to have some challenging material in maths?

[Parsimon]

I have a ds in Y8 at a grammar school. His school don’t set for maths at this stage. He is pretty good at maths and is feeling dejected about maths lessons: he came home today saying he was being untaught.

(For maths teachers: he was being taught about gcd and lcm. He didn’t understand why he couldn’t just use Euclid’s algorithm for the first and the product divided by the gcd for the second - he knows the proof for the Euclidean approach as well as how to use it. Instead the class had to factorise everything and find the overlapping factors for the first, and write down lists of multiples for the second, and see where the two lists overlap. I can sympathise with his maths teacher that this is a perfectly sensible way to introduce the topics to kids who are unfamiliar with it.)

I’ve told ds that it’s tough, and he has to sit through the maths lessons and use the method the teacher is telling him, as it’s for the benefit of the class, not him. I also feel bad telling him that.

Ds did really well in the UKMT junior maths challenge and Olympiad last summer and over the holidays he spent his time doing past papers from the intermediate and senior challenges, kangaroos and olympiads. He was consistently getting near full marks on the intermediate papers, and scoring high enough for a gold on the senior challenge papers, and about half the time getting a score which would mean he would have qualified for the senior Olympiad. For a boy just turned 12, I understand that this is quite unusual. I emailed ds’s maths teacher at the start of the academic year to tell him this and ask if ds would be able to participate in the UKMT Intermediate and senior challenges this year, as well as the junior one, and he hasn’t replied. This teacher didn’t teach ds in Y7.

Is it reasonable for me to ask again? Ds is clearly talented at maths and at the same time is becoming demotivated by the school maths lessons. I can imagine that the maths teacher isn’t going to want to get an email from a parent explaining that their son is super special and finding maths lessons utterly pointless, and I know that there are 30 kids in the class not just 1. In primary school Ds used to do a weekly online challenge called parallel, but that’s a bit easy now, so he sticks to Olympiad papers in his spare time. I think he is teaching himself quite a bit so perhaps I should just let it lie. At the same time, it’s a lot of hours for ds to be bored and I don’t want him to lose his love for the subject.

Is it reasonable for me to approach the teacher again about the maths challenges and shall I mention that ds isn't finding the lessons challenging?

[JustRichmal]

If it is a grammar, I should think they do the IMC and SMC, so I would politely ask again in an email.

Does the school have a maths club or do they send teams for the UKMT team maths challenges? Team work is always a good skill to build.

What would you like to happen in lessons?
Does he know enough maths to get 9 at GCSE? If so, could he do the GCSE this year then study A level by himself in year 9, 10 and 11?
Would you be happier for him to sit quietly in the lessons, but just get on with his own maths for the parts he finds easy?
Would you like the teacher to provide much more challenging questions on a subject? eg, "Explain why Euclid's algorithm finds the greatest common denominator."
I think you need to get an idea of what you would like before you speak to them, but be open to alternatives they may put forward.

I do not think he will become demotivated if he enjoys maths; he will just see school as somewhere he does not learn it. This happened to dd in primary.

In the mean time at home he could try on YouTube:
Numberphile
Mathsologer
or
Brilliant.org

As he gets more advanced there is 3blue1brown and of course, MIT

[noblegiraffe]

If he is already acing the senior maths challenge in Y8 then Y8 maths lessons are never going to be challenging for him. That’s not the fault of the teacher, and really, it isn’t a problem that should be put on them as a class teacher to fix every lesson.

What happened in Y7?

You need a meeting with the head of maths to discuss a plan of action about what he will be doing in his lessons when everyone else is finding the factors of 24. UKMT put out a lot of materials preparing for the challenges so perhaps he could work through these - they can also assign him an undergraduate mentor.

@ohyoubadbadkitten might have some advice.

[OhYouBadBadKitten]

Thanks for tag Noble Your advice is very good :)

I wouldn't be just emailing school, I would request a meeting with the Head of Maths and the Head of Year if you are feeling any resistance.
From a UKMT point of view, your ds should definitely be taking the IMC and there is no harm at all in him taking the SMC if he is enjoying it.

UKMT mentoring has changed quite a lot recently, so my advice is probably going to be out of date but, it used to be that initially they are mentored in school, then they move on to an external mentor - not necessarily an undergrad.
ukmt.org.uk/enrichment/mentoring-scheme

Which books does your ds have?
Has he looked at the Art of Problem solving website for further olympiad enrichment outside of UKMT?

In terms of school work, dd came off the school curriculum mostly from the middle of Year 7 and did either set work, (some teachers were better than others and there were some frustrations along the way) or eventually her own work. She went to a comprehensive school.

I do not advocate Richmals approach, though it has worked well for her dd - for my dd just ignoring the existence of GCSE worked extremely well. There's no need to limit them to boring curriculum work at all.

Feel free to pm me if you want to chat about things.

[MrTinky]

Hi, My lad is similar. Last year (year 8) I asked the school to put him in for the IMC/IMO and he got the best in school in the challenge and just missed out on a medal in the olympiad. Did the junior as well and got a medal.
I'm not putting him in for the SMC/... He'd do ok in the challenge (has done a few) but the BMOs would be beyond him, but that is a personal decision.
My gut feeling is that if you're in the medal region for junior, you're not going to be far off in the intermediate/senior challenges. The geometry/algebra/number theory is a bit more advanced, but not so much that an interested young kid can't pick it up relatively quickly. The development of the olympiad material is more challenging though, and some of the algebra/geometry in the Maclaurin / BMO is head scratching at times. So maybe focus him more on this material?

As you say, school lessons are fairly boring. There seems to be little that can be done there, but if you can sign up for the ukmt mentoring, get the aops books, ... as mentioned above, they are good ways to motivate him outside the classroom. Our local university runs a maths club which he goes to. Also, if hes into computing, the brebas challenges have a strong algorithm - problem solving element, and there are various cypher challenges (southampton, manchester, ...) which are run over several weeks.

[MrTinky]

Argh ... forgot to say, he might like
www.openbookpublishers.com/product/979
Tony Gardiner's newish book which is a bit beyond his Extension Maths books. Free to download

[OnceFreshFish]

As a maths tutor unfortunately your DS will probably be bored in maths for the forseeable future. I would follow other people's advice about interesting material to keep him enthusiastic. I'd also advise that he definitely avoids going further ahead with the syllabus - there's plenty of maths challenge type material which requires no new material to be learned. Secondly he should definitely learn some programming as it employs similar skills and is just a great skill to have - he could learn a simple language like python. If he already knows python or similar he can go straight to Euclid problems (online - they start easy and get very tough). I definitely second the suggestion of ensuring he's signed up to UKMT with his school.

[FanSpamTastic]

If you wanted to give him some challenges that he could work on at school instead of getting bored then take a look at the weekly challenges set by Kings Maths school here.

Also ask the school what they "gifted and talented" policy is. Schools have an obligation to challenge and stretch their high performers as well as trying to get the lower achievers up to expected levels.

Also encourage your son to help others in the class who might be struggling. It is one thing for him to know how to do something himself but quite a challenge to be able to explain it to someone else and to teach them to understand it too.

[GHGN]

I taught in quite a few grammar and none of my colleagues knew what Euclid’s algorithm was so don’t be surprised by that. Olympiad Maths is quite a niche area of school Maths that many teachers will find it beyond their comfort zone. For kids like your son, there are two options:

1. aim to do well in the challenges and then be one of the top scorers in the country in any Olympiads. If he can do so out of his age group then it is even better. He will then be noticed by the UKMT and will be trained by them. School will have very little to do with him after that.
   
   
2. convince your son’s school to register him with the UKMT for one of their mentoring scheme. If he can do the highest level, sometimes they can assign him a mentor and at least it will be more interesting.
   
   There is one extra option, if he knows enough about Geometry for senior olympiads, ie all the circle theorems, similarity, congruency and things like that, pm me and I might be able to point you to something else.

[Parsimon]

Thank you for all this advice. To the pp who recommended Numberphile: it’s great and we all love it. Through Numberphile we came across mathsgear.co.uk where most of ds’s birthday presents came from (along with some UKMT books: “ten years of mathematical challenges” entertained him for the last fortnight of the holidays!)

I will have a look at the kings challenges, and get in touch with the maths teacher again to suggest the mentoring.

GHGN I think he will do very well at the Junior Olympiad this summer as he got 49 last year, with no practice, and has since immersed himself in solving these sorts of problems. He can do the intermediate challenge papers (consistently 120-130) and the same with the pink/grey kangaroos, tending to get all but one question right. On the senior challenges he’ll just attempt the 19-20 questions he can answer and then get them all right. He wouldn’t do well on the BMO yet, though, as that does seem to be a notch of difficulty above the rest.

I will check how he’s doing with circle theorems. He certainly does the trig questions but as he’s been taught by himself he probably doesn’t have the identities ingrained, and I think the geometry questions are probably where he is weaker. I have seen him use power of a point, and the thing about the angle from the centre being twice the angle from a point on the edge, but I expect he’s not particularly ninja about geometry as they do so little at school. I can help him with geometry as I got through to the BMO back in the day, and I like a good triangle

[Pythonesque]

Good sounding advice here already. I'd strongly encourage him with geometry - specifically learning how to right out good proofs in a systematic way. That will help him develop the skills to do well in BMO type problems in the future. I've been surprised to realise how little geometry is covered in GCSE and A level maths - I thought the education system I went through was weak on geometry but we certainly did more. "We were weak on geometry" means, amongst other things, our IMO team was weak on geometry.

Getting a child like this access to maths at the level they need in order to challenge them is essential, in my opinion. I spent most of year 9 and 10 getting bored and indeed behind in my class maths because my teacher wouldn't let me work ahead in the text book. End of year 10 I was picked up for olympiad training and to be honest I don't know how I would have survived school if I hadn't. Ended up getting a bronze medal at the IMO in year 12 (less than 2 years after I'd first heard of the IMO). Sometimes wish I'd taken a gap year as I could have done even better at a 2nd IMO...

All the things suggested above - eg numberphile, coding, the cipher challenges - are things that have appealed to my youngest who's a couple of years older than your son and I think may have the same kind of maths potential I had.

Good luck, hope you can find the right activities and mentoring and balance what he should do when in school.

[Tvstar]

If he/you choose to push himself so far ahead then you can't then Complain that the lessons are unsuitable because it's a problem of his/your own making
Why don't you enter him for a level maths and further maths yourself then once he holds these, he can go off to the library and do something else in maths lessons

[Parsimon]

@Tvstar there isn’t a lot of benefit in racing through the GCSE and A Level curriculum, and the depth and reasoning skills demanded by maths Olympiad questions are much more challenging and enjoyable than churning out a page of sine rule questions. I don’t want ds to plough through the curriculum fast, I want him to get the depth. There’s a lot of accessible material not on the curriculum, like fractals - I found ds on the computer this afternoon writing a programme to draw the Sierpinski triangle, which is probably the start of him exploring fractals for a week or so, which is a great area of maths and not on any school curriculum.

In any case, I got in touch with the school and had a positive response about the UKMT challenges, so it looks as though we have some cause for optimism.

[Tvstar]

That's not going to help him in his day to day lessons though isit?

[Mugglingstrum]

Parsimon it looks like you will be able to give a good level of support given your knowledge of the subject. Looks like he is a good self-starter given that he is absorbing high level material independently.

[crikeylam]

Has he looked at the King's Maths School weekly challenges? www.kingsmathsschool.com/weekly-maths-challenge

If you live close enough they also have a fortnightly Mathematics Circle which I think may be on Saturdays: www.kingsmathsschool.com/activity/outreach-for-students

[MrTinky]

As well as the gardner book mentioned above, there is a series of maths books for high school(+) from the 60s and 70s. Still readable and while out of print, some are pdfs,djvu, ... online.

NEW MATHEMATICAL LIBRARY (MAA)
1 Numbers: Ration$ and Irrational by Ivan Niven
2 What is Calculus About? by W. W. Sawyer
3 An Introduction to Inequalities by E. F. Beckenbach and R. Bellman
4 Geometric Inequalities by N. D. Kamrinoff
5 The Contest Problem Book I Annual High School Mathematics Examinations
1950-1960. Compiled and with solutions by Charles T. Salkind
6 The Lore of Large Numbers, by P. I. Daois
7 Uses of Infinity by Leo Zippin
8 Geometric Transformations I by I. M. Yaglom, translated by A. Shields
9 Continued Fractions by Carl D. Olds
10 Graphs and Their Uses by Oystein Ore
11 Hungarian Problem Books I and 11, Based on the Eotvos
12 Competitions 1894-1905 and 1906-1928, translated by E. Rapaport
13 Episodes from the Early History of Mathematics by A. Aaboe
14 Groups and Their Graphs by I. Crossman and W. Magnus
15 The Mathematics of Choice or How to Count Without Counting by Ivan
Niven
16 From Pythagoras to Einstein by K. 0. Friedrichs
17 The Contest Problem Book I1 Annual High School Mathematics Examinations
1961-1965. Compiled and with solutions by Charles T. Salkind
18 First Concepts of Topology by W. C. Chinn and N. E. Steenrod
19 Geometry Revisited by H. S. M. Coxeter and S. L. Greitzer
20 Invitation to Number Theory by Oystein Ore
21 Geometric Transformations I1 by I. M. Yaglom, translated by A. Shields
22 Elementary Cryptanalysis-A Mathematical Approach by A. Sinkoo
23 Ingenuity in Mathematics by Ross Honsberger
24 Geometric Transformations 111 by I. M. Yaglom, translated by A. Shenitzer
25 The Contest Problem Book 111 Annual High School Mathematics Examinations
26 1966-1972. Compiled and with solutions by C. T. Salkind and I. M. Earl
27 Mathematical Methods in Science by George Pblya
28 International Mathematical Olympiads-1959- 1977. Compiled and with soh - tions by S. L. Greitzer
29 The Mathematics of Games and Gambling by Edward W. Packel
30 The Contest Problem Book IV Annual High School Mathematics Examinations
1973-1982. Compiled and with solutions by R. A. Artino, A. M. Gaglione and
N. Shell
31 The Role of Mathematics in Science by M. M. Schiffer and L. Bowden
32 International Mathematical Olympiads 1978- 1985 and forty supplementary
problems. Compiled and with solutions by Murray S. Klamkin
33 Riddles of the Sphinx (and Other Mathematical Puzzle Tales)
by Martin Cardner

[Parsimon]

Crikeylam those challenges are brilliant and he’ll really enjoy them! He did do the parallel.org challenges when they first came out (I think he must have been Y5 or Y6 at the time) and they were described as “really hard” but the difficulty seems to have been watered down a bit, even though they go up to Y10 now.

Thank you MrTinky for the book recommendations. Ds is working his way through a UKMT book called “crossing the bridge” at the moment, which is quite fun and I think he could get into geometry.

I know that the entry deadline for the senior maths challenge has come and gone this week and he hasn’t heard from school that he’s been entered, irritatingly, but I think that even though he’d probably qualify for the first round of BMO this year he wouldn’t progress further, so there’s no harm in doing challenging stuff at home and talking to the school again before the intermediate challenge.

We haven’t changed the situation with class maths lessons, but this gives me lots of good maths fuel for ds outside school, and I think he’s mature enough to understand that he’s just got to sit through the school maths lessons and save the fun stuff for out of school.

[Monsterandmonkey]

Art of Problem Solving. UKMT sell the books.

[Pineapplemintandstrawberrysage]

brilliant.org/
mathigon.org/
parallel.org.uk/

[milienhaus]

I have nothing real to add to this but to say that I did Maths at Cambridge and your DS sounds way way way smarter than me - in particular he sounds incredibly motivated which can’t really be taught so congratulations and I’m sure he has a bright future ahead of him!

[parsimon]

Happy update. Ds wasn’t allowed to do SMC (but did it at home when the paper was published and got gold score) but did IMC and got 135. He’s been getting more and more fed up with class maths but is cheered up by this (even though he found IMC quite easy!) the Caley Olympiad will be more fun though.

[Surreyhillsbutnobike]

Nrich ,an online site, has good problems.

[GHGN]

That’s an outstanding result. However, the Cayley is quite a straight forward paper in terms of mathematical content. Students often lose marks because they don’t know how to write their solutions, not because they can’t solve the problems. Ime, they mark this paper more harshly compares to the JMO. Q5 & 6 of the JMO can be much harder than Q4,5 of the Cayley paper actually.

[avocadoze]

Thank you for the tip: ds has decided to work through a couple of past questions a day so I will advise him to work on ensuring he is setting out his answers clearly. He got a bronze medal in the JMO but I think he will have his sights set higher for the Cayley!