I live in another country, so the school curricula for maths in our two countries may differ, but maths concepts are universal and my son used a variety of online resources.
We supported his enthusiasm to explore mathematics and his school achievements were largely a by-product, rather than his main focus. He is now in his second year at Uni, so I’m posting about his journey as it has had a relatively successful outcome.
From an early age, he watched YouTube videos, particularly Numberphile videos which cover a broad range of interesting ‘big’ ideas (eg. infinite sets). Khan Academy videos are great free online resources which explain maths concepts in easily digestible bite sizes, which may be useful if concepts are covered too lightly in videos that aren’t specifically intended to be educational.
At the beginning of high school, the maths HoD assessed him with a grade 7 test and confirmed he had mastered all of the content so she agreed that acceleration would be appropriate. The school bought subscriptions to Maths Pathways (which only covered grades 1-10 content back in 2017 but now covers grades 11 & 12 as well) and Maths Online, so that he could be radically accelerated whilst physically attending class with same aged peers (which was ideal for both his academic and social development). He covered grades 8-10 in six months with Maths Pathways and switched to Maths Online to cover grades 11 & 12 in less than a year for each grade, which enabled him to sit his first HSC (grade 12 exit) exam in grade 9 and the HSC extension exams the following year. Private subscriptions, which are a bit more expensive than school based subscriptions, are available to either of these programs. Both companies offer free trials.
DS received invitations to the Australian Maths Olympiad event (the US has its own USAMO), but we live outside of the major cities and our local school has no experience preparing anyone for these comps. Whilst he also received invitations to the AMT Olympiad training camps/schools, after attending one week-long training school, the rest were suspended due to COVID, so he was essentially isolated. We searched online for a suitable mentor and found an honours maths student at Cambridge Uni who had been on the British Olympiad team and engaged him as our son’s mentor (at a rate of $300/hr due to the exchange rate between stirling pounds and the Aus dollar, so this was the one extravagant expense for us, but since my son attended a public school, we saved a six figure sum on his education compared to many relatives and friends). After a few months, our son found past IMO papers tedious and not the best value for learning, so whilst he has been on the AMO merit list a couple of times, he abandoned his original aim of getting to the IMO. Instead, his mentor showed him some of the postgrad maths he was studying at Cambridge Uni and my son found the material much more interesting. These sessions prepared him well for his own time at Uni, where as a freshman last year, he was able to achieved HDs in first and second year advanced maths courses and is currently enjoying deep dives in various advanced courses relevant to his R & D Engineering degree. He now tutors/mentors high school students.
PS: DS competed at state level in several track and field events and during his time at high school, was generally recognised as his school’s star athlete, so that came with a lot of social currency and he was popular with his peers even as a maths & science scholar.
