UKMT maths challenges - how to?

[justanotherdaduser]

Would like to understand how children who do well in the UKMT maths challenges (junior, intermediate etc) prepare, whether they prepare at all etc

DD (year 8) is okayish in maths - in top set and get usually 85% and over in class exams, but not innately brilliant (in my opinion)

I used to teach her maths in primary, specifically for 11plus preparation, but have stopped since end of year 6.

The teaching in class is focused on breadth first, quickly moving from one topic to another, not spending enough time on any one topic to develop deeper understanding. I think the school aims to iterate over these same topics repeatedly for the next few years before GCSE.

For example, I think most of the class can solve simultaneous equation of two variables, but will probably struggle with a third variable and likely to struggle with a complexly worded problem where sentences may not easily be translated into simultaneous equations.

So DD struggles with the UKMT challenges - about the first 50% of the questions are doable, she finds the later half harder.

I feel there is benefit in doing these papers - encourages out of box thinking, helps in developing much deeper understanding of the topic, builds resiliency etc. I am encouraging her to do them seriously (school makes all top set students take the UKMT challenges), but also conflicted that maybe I shouldn't push too hard because unsure whether these problem solving skills are meant to come naturally.

Question is - if your DC does (or did) well in these challenges, did they prepare specifically for such types of questions? Or was school work enough for them to do well?

I had never heard of this until today when my son came home and told me he’d been told he had to take part in a ‘secret maths test’ but the teacher wouldn’t tell them what it was. He said he didn’t want to write his name on the paper because he ‘didn’t want to give his data to the government bruh’ if they wouldn’t tell him what the test was for. He then managed to sneak a look at what was written on the teacher’s paper, and found half a used rubber on the floor that he could write down the name on so he could come home and ask me about it.

FFS I don’t think his future lies in maths but it may lie in some kind of police work 🤣

We didn’t even know about it they just did it at school yesterday. School didn’t mention it was happening.

Thank you all for a very helpful and informative thread.

Just summarising here the responses, in case anyone else is looking for similar information later

Summary :

1. Nine posters said their DC never practiced or prepared for the tests (and most of these DC had done well).
2. Nine posters said their DC practiced (including one poster who herself practiced). Two of these DC went on to BMO and one of them awarded gold in Maclaurin Olympiad.
3. Two posters had seen others practice.

Also several good suggestions on practice resources

1. Most popular resource are past papers and solutions in UKMT website : https://ukmt.org.uk/competition-papers. One poster also mentioned UKMT books - https://ukmt.org.uk/textbooks
2. The second most frequently mentioned resource was Dr Frost https://www.drfrost.org/worksheets.php?wdid=44

Few other resources mentioned, in no particular order -

Maths circle : mesme.org/online-maths-circles/ and also Moscow Maths circle book [I had a look at this and think it is superb idea (and also the book), not just for UKMT tests but in general to improve mathematics skills]

https://mathsaurus.com/

https://artofproblemsolving.com/store

Parallel https://parallel.org.uk/

Mathletics

I want to add, about 50% of the participants did JMC will get bronze award or above. Gold vs Silver vs Bronze is about 1:2:3, I assume that is what is considered "done well".

Top 5% will go to Kangaroo round and less than 0.5%-1% go to JMO (BMO is equivalent top% for SMC)

and that’s why they stopped there. Some kids want to go much further so they need to train and do a lot more than just turning up.

To triumph in mathematics competitions like the IMO, you may need to undergo rigorous training. However, such training isn't a prerequisite for becoming a proficient mathematician. Simply repeating exercises mechanically isn't conducive to mathematical excellence. Despite the outstanding performance of East Asian countries and the Asian descendants in Western nations at the IMO, it's noteworthy that none have received the Fields Medal for quite some time. It's more beneficial to engage in mathematics with enthusiasm and interest rather than engaging in excessive repetition that could diminish one's passion for the subject.

IMO and Fields medal award are very different thing. IMO is a competition of solving known mathematical problems for high school students where a lot of winner student won't continue doing mathematian research as career, many will end up doing problem solving and apply mathematics knowledge to various industry and become successful.

FIelds medal is award to under 40 mathematician for their research contribution to the field, not problem solving skillset. Also, It’s not accurate to say that no individuals of Asian descent have won the Fields Medal in recent years. In fact, in 2022, June Huh, a mathematician of Korean descent, was awarded the Fields Medal. Before that Terence Tao a Chinese descent mathematician who won multiple IMO medals was warded Fields too.

To be top at either field it is prerequisite to have rigorous training, however just repeating exercises mechanically will probably never get any chance.

June Huh was not an IMOer. Terence Tao left the IMO circle very early (13 years old?) before he was worn out by the rigorous training.

That just shows IMO and Fields are very different thing. T Tao has start his maths rigorous training as early as 5 years old when his parents his parents discovered his prodigious talent in maths. He started attending university-level mathematics courses at the age of 9 before he participate in IMO.

That's my point. IMO only need GCSE-level knowledge. I wonder if it's worth spending so much time training for that. It may be beneficial for children who enjoy competition, but not for all young mathematicians.

I agree that not all young mathematicians are interested in competitions like the IMO, just as not all athletes/sports participants aim for the Olympics. However those who do dream of such achievements need to train hard to succeed. Challenges like the JMC, IMC, and SMC are there to get more students into math, not just to prepare for the IMO. Being good at the IMO isn’t necessary to be a great mathematician, since it focuses on quick problem-solving. But many who do well in the IMO succeed in careers where they use math and logic. And many also successfully in mathematics research career too.

Certainly, those who excel in the IMO are likely to thrive in their careers, as typically only around two or three newcomers are able to join the national IMO team each year. They represent the pinnacle of mathematical talent, after all.

Not sure what your point was or if you were following the conversation. I have done enough IMO training and maths to a reasonable level to know the difference between the two.

and that’s why they stopped there Don't agree this. A kid has different way to progress to a good mathematician.

IMO only need GCSE-level knowledge.

IMO aka International Maths Olympiad only needs GCSE-level knowledge? You must be joking. Have a look at past problems and guess what percentage of those who get 9 at GCSE Maths can understand the problems, let alone solve them.

The International Mathematical Olympiad (IMO) covers four main fields: number theory, combinatorics, geometry, and algebra. IMO primarily assesses problem-solving techniques rather than mere knowledge, unlike GCSE and A-level maths. Even university maths graduates may not necessarily be able to solve a single one of the six IMO questions. While these topics are included in GCSE maths, it's doubtful that many who got 9 could tackle a BMO2 question, let alone an IMO question.

DS is older now, and a Maths grad just finishing his Masters. He was a gifted Mathematician and used to love UKMT challenges - he was naturally drawn to the problem solving style. For him, practicing questions after he finished classwork was what kept him interested but there is a definite 'style' once you reach Kangaroo or Olympiad which I think are probably inaccessible other than to dc with a strong interest in Maths.
DS's view is that they are a great challenge that everyone should be encouraged to participate in as generally they can support greater depth in mathematical learning. And that learning can be applied to dc who want to go on and take the MAT or STEP papers. His proudest moment was reaching Senior BMO 02 and having a solution published.

Following

to add to your excellent data gathering process: Ds (who is now studying maths and comp sci) did these - gold, got through to Olympiad, although silver ‘only’ at sixth form iirc, although he did well in step. He practiced a few past papers in class I think, and did a lot of programming/comp sci type maths for fun, but nothing else.

For BMO2, you must love it, my daughter could try to work out one single problem the whole week. It is NOT repetitive training. The BMO2 was very challenging this year, she attempted 3 and didnt get any full mark. In fact, it is not possible to train for BMO2 or IMO if the kids dont love them. It requires many hours deep thinking about ONE problem. That is what she loves the most.

Hello ChatGPT!

Your DD sounds fantastic! Would be nice to know how she got on with JMC this year, participating in a challenge with children who are years older than her. Her school is very supportive!

Terence Tao stopped doing the IMO because he lost eligibility when he enrolled in university. Before that, he'd participated for three years, which is more than the vast majority of kids who make it that far, plenty of time to burn out if IMO participation really causes that. Also, while he is of Chinese descent, he was educated in the Australian system, although I suspect he learned very little math in it.

A different way of phrasing it might be that the material you cover in A Levels isn't particularly useful for the IMO. The facts you learn for GCSE are sufficient - if you really know how to apply them.

That said, a deep corpus of knowledge in the relevant areas of math really helps but you don't cover that in A Levels.

Terence Tao on math competitions.

"I greatly enjoyed my experiences with high school mathematics competitions (all the way back in the 1980s!). Like any other school sporting event, there is a certain level of excitement in participating with peers with similar interests and talents in a competitive activity. At the Olympiad levels, there is also the opportunity to travel nationally and internationally, which is an experience I strongly recommend for all high-school students.

"Mathematics competitions also demonstrate that mathematics is not just about grades and exams. But mathematical competitions are very different activities from mathematical learning or mathematical research; don’t expect the problems you get in, say, graduate study, to have the same cut-and-dried, neat flavour that an Olympiad problem does. (While individual steps in the solution might be able to be finished off quickly by someone with Olympiad training, the majority of the solution is likely to require instead the much more patient and lengthy process of reading the literature, applying known techniques, trying model problems or special cases, looking for counterexamples, and so forth.)

"Also, the “classical” type of mathematics you learn while doing Olympiad problems (e.g. Euclidean geometry, elementary number theory, etc.) can seem dramatically different from the “modern” mathematics you learn in undergraduate and graduate school, though if you dig a little deeper you will see that the classical is still hidden within the foundation of the modern. For instance, classical theorems in Euclidean geometry provide excellent examples to inform modern algebraic or differential geometry, while classical number theory similarly informs modern algebra and number theory, and so forth. So be prepared for a significant change in mathematical perspective when one studies the modern aspects of the subject. (One exception to this is perhaps the field of combinatorics, which still has large areas which closely resemble its classical roots, though this is changing also.)

"In summary: enjoy these competitions, but don’t neglect the more “boring” aspects of your mathematical education, as those turn out to be ultimately more useful."