I would agree that it is one of the hardest A levels in the sense that you can't bluff your way through but the reason why quite a lot of people who are reasonably good at maths take the A level a year or more early (and if you don't have a mental block about maths, it really is relatively straightforward) is that there is a Further Maths A level that they can then go on to do and that is probably one of the harder A levels to do well at.

I think the idea is that A level Maths is meant to be fairly accessible for those who want to go on to degrees or careers that require some basic mathematical ability above GCSE level, whereas A level Further Maths aims to be a bridge between school and university level maths for those who intend to study highly mathematical subjects like maths itself, physics, etc.

I think having two A level stages for maths is a good idea, even though Further Maths still didn't give me the slightest inkling of how tough a maths degree was going to be at the university I went to.

According to my wife, maths in British schools is all completely trivial and easy compared to maths in Chinese schools, so make of that what you will.

In any case, doing Maths A level two years early is unusual and hence quite impressive, and doing it while also becoming one of the best junior tennis players in the country and (I think I've read this, but apologies if I'm wrong) an accomplished musician makes it even more so, so very well done to Mimi!

It was a bit different in my day. You could do a Pure & Applied Maths A level and then do separate Pure Maths and Applied maths papers. The Chinese seem to do arithmetic in a different way to us. I saw a comparison side by side and the Chinese girl got the answer quicker and with less working than the English girl. Emma is also a mathematician and a musician and she also paints. Maths seems to go with tennis for some reason.

There's probably a higher correlation between being good at maths and having Chinese parents (yes, it's a stereotype, but in my experience pretty accurate and, obviously, a positive thing too) than between maths and tennis - the Chinese definitely have all kinds of clever tricks for doing arithmetic quickly but my theory is that another reason they tend to take to maths more easily than the average European child is that numbers in Chinese are exceptionally simple - e.g. 99 is nine tens nine, unlike English with it's messing about between 11-20, French with it's quatre-vingt dix-neuf (80 19) for 99, etc, and worst of all German/Dutch with their units before tens when written longhand or spoken. I'm convinced this makes the Chinese far less likely to have mental block with basic arithmetic, which in turn can make a huge long-term difference to confidence and progress.

__________________

GB on a shirt, Davis Cup still gleaming, 79 years of hurt, never stopped us dreaming ... 29/11/2015 that dream came true!

There's probably a higher correlation between being good at maths and having Chinese parents (yes, it's a stereotype, but in my experience pretty accurate and, obviously, a positive thing too) than between maths and tennis - the Chinese definitely have all kinds of clever tricks for doing arithmetic quickly but my theory is that another reason they tend to take to maths more easily than the average European child is that numbers in Chinese are exceptionally simple - e.g. 99 is nine tens nine, unlike English with it's messing about between 11-20, French with it's quatre-vingt dix-neuf (80 19) for 99, etc, and worst of all German/Dutch with their units before tens when written longhand or spoken. I'm convinced this makes the Chinese far less likely to have mental block with basic arithmetic, which in turn can make a huge long-term difference to confidence and progress.

Really interesting

Slight aside, sorry Mimi, but language can make a huge difference

I'm convinced that French kids basically have a problem with the need to work hard to earn a living because their word for earning a salary is 'gagner', which is also their word for 'winning' - and the winning translation is the most obvious/natural so basically they think that you 'win' your salary and your tax return is how much you 'won' last year - as you say, if that's your language, from the day you're born, it makes a big difference

There's probably a higher correlation between being good at maths and having Chinese parents (yes, it's a stereotype, but in my experience pretty accurate and, obviously, a positive thing too) than between maths and tennis - the Chinese definitely have all kinds of clever tricks for doing arithmetic quickly but my theory is that another reason they tend to take to maths more easily than the average European child is that numbers in Chinese are exceptionally simple - e.g. 99 is nine tens nine, unlike English with it's messing about between 11-20, French with it's quatre-vingt dix-neuf (80 19) for 99, etc, and worst of all German/Dutch with their units before tens when written longhand or spoken. I'm convinced this makes the Chinese far less likely to have mental block with basic arithmetic, which in turn can make a huge long-term difference to confidence and progress.

Really interesting

Slight aside, sorry Mimi, but language can make a huge difference

I'm convinced that French kids basically have a problem with the need to work hard to earn a living because their word for earning a salary is 'gagner', which is also their word for 'winning' - and the winning translation is the most obvious/natural so basically they think that you 'win' your salary and your tax return is how much you 'won' last year - as you say, if that's your language, from the day you're born, it makes a big difference

Further aside, but language does indeed make a difference. I really struggled with numbers when I lived in Denmark for a year. 90, for example, works out as (roughly translated) "half way (from 80) to 5x20". Phew! I found learning numbers in Cantonese really easy for the reason stated above - it was just so logical.

Am I the only one to be surprised that the whole world seems to be Base 10?

The whole world has 10 fingers?

In fact Welsh still has a vigesimal system alongside the decimal system. I believe other Celtic languages may.

I do not speak Welsh but I occasionally watch sport (where numbers are frequent and important) on S4C and I can confirm I have heard commentators using the vigesimal system.

When I was younger, and the world was less aware, it was rumoured (presumably apocryphally) that some aboriginals somewhere (probably antipodean) counted "one, two, many", as they had no use for larger numbers.

I know we all have ten fingers, but we also have eight fingers and two thumbs, or five fingers (or four fingers and a thumb) on one hand - it surprises me that no nation/ tribe/ whatever adopted five as the base, or eight, or any other number really.

... but maybe they did, and were all bullied into conformity by the Base 10 users before counting began to be recorded.

The Mesopotamians used base 60, that's why we use hours and minutes subdivided into 60 parts.
The Aztecs counted in twenties.
"The Aztecs: their numbers, their days, and their gods" www.mexicolore.co.uk/aztecs/kids/aztec-numbers

Some very obscure ones from WP: Positional numeral systems, and in general these are ethnic peoples, not [former] countries, except Mayans:

The Ndom language of Papua New Guinea, which employs senary counting, includes a basic word for 18 and another for 36.
The Mayan Long Count calendar employs a "modified vigesimal" counting system that sets apart 360 as the number of days in a year, i.e. 18 months with 20 days.
Base 12/ Duodecimal: [various peoples using Duodecimal]
Base 15/ Pentadecimal: The Huli language of Papua New Guinea is reported to have base-15 numerals. Ngui means 15, ngui ki means 15×2 = 30, and ngui nguimeans 15×15 = 225.
Base 27/ Septemvigesimal numeral system. Several Papua New Guinean languages use such a base.
Many languages of Papua New Guinea use a system of counting in which numbers are associated with a body-part tally-system, typically starting at the little finger of one hand continuing across the body and face, and ending at the little finger of the other hand. Unlike the 10 fingers of the decimal system, these systems can use up to 72 names of parts, but eight languages, including Oksapmin and Telefol use a base of 27 names of parts expressing larger numbers with a phrase like "one man and" - adding the extra 'digit' name.
Base 32/ Duotrigesimal: Ngiti [Congo] is reported to have a base 32 numeral system with base-4 cycles.

By the way, the commentator said yesterday that Mimi sat her A level maths this year - two years early

That's impressive. Maths is one of the hardest A levels! Two years early, gosh.

Rubbish. It is almost certainly one of the easiest.

... as long as you know the answers. It is one of the very few subjects with objectively right answers. It is without doubt one of the hardest of A levels to waffle and bluff, but that is as it should be.

This has to be the worst comment I have ever read

I think this is quite an interesting question (and don't agree really with Blue Belle that it's only teenagers' or Mimi's view that counts)

Like you, twentytoone, christ's post rankled slightly

It can't be right that Maths A level is the 'easiest' because maths has 'right' answers - otherwise a Maths degree has to be easier than other degrees, for the same reason. And a Maths Masters is easy too. (And a Maths PhD is a doddle)

But it is certainly true that more students take Maths A level early than other A levels - there are figures for that. And there are more maths young prodigies than, say, political science young prodigies. Which obviously has something to do (or all to do) with the nature/clarity of the subject (after all, even our politicians haven't sorted out political science). But this doesn't mean maths is 'easier'.

I respectfully disagree - post A Levels Maths gets quite hard quite quickly, but up until A Levels it is about gathering and applying tools.

Possibly I should have been more nuanced in my response - I probably should have said "due to the nature/clarity of the subject, more students take Maths A level early than other A levels" rather than the (shorter) "one of the easiest".

... but I find it interesting that my response drew ire where the original "Maths is one of the hardest A levels" was awarded a pass.

I love this debate cos I can really see it both ways! I think I've always been more inclined to agree with Christ overall though - or at least really see what he means in the sense that there will be a lot of people for whom maths just comes easily enough to them that they can take it early more easily than they could another subject. I was not one for these people. For me maths came pretty easily up until A level - I was the only one in my class to get A* at GCSE - but I was shocked how much more I struggled with it at A Level! I did modular A levels so was able to see the problem early and I got an F in the first pure maths module after a couple of terms of the A level. For me the issue was just that I needed to worth through all the calculus at my own pace and wasn't quite absorbing it just from copying it down as the teacher went through it. When I finally did this it clicked and I did much better. Interestingly though two guys joined my highschool six form college who from other highschools who were the types it just clicked for and they clearly could have taken things early easily. You needed 6 modules for an A level and a further 3 for AS further maths. One of the two new guys who maths just clicked for did 12 modules to get two full maths a levels along with doing all three sciences so got 5 a levels. The other found it so easy that he looked set to get I think 3.5 maths a levels by doing all the 21 available modules as well as chemistry and physics (sadly he went of the rails big time and was kicked out of his home and lost all focus). I definitely see Christs point and agree with it whilst personally having found it hard most of the way through and only got a C (pretty sure I'd have got a higher grade if id been more focused on working through at my own pace til I understood rather than struggling to keep up with following along in class whilst taking notes - I worked when I retook that F and I got 98% on the retake!)

The Mesopotamians used base 60, that's why we use hours and minutes subdivided into 60 parts. The Aztecs counted in twenties. "The Aztecs: their numbers, their days, and their gods" www.mexicolore.co.uk/aztecs/kids/aztec-numbers

Some very obscure ones from WP: Positional numeral systems, and in general these are ethnic peoples, not [former] countries, except Mayans:

The Ndom language of Papua New Guinea, which employs senary counting, includes a basic word for 18 and another for 36. The Mayan Long Count calendar employs a "modified vigesimal" counting system that sets apart 360 as the number of days in a year, i.e. 18 months with 20 days. Base 12/ Duodecimal: [various peoples using Duodecimal] Base 15/ Pentadecimal: The Huli language of Papua New Guinea is reported to have base-15 numerals. Ngui means 15, ngui ki means 15×2 = 30, and ngui nguimeans 15×15 = 225. Base 27/ Septemvigesimal numeral system. Several Papua New Guinean languages use such a base. Many languages of Papua New Guinea use a system of counting in which numbers are associated with a body-part tally-system, typically starting at the little finger of one hand continuing across the body and face, and ending at the little finger of the other hand. Unlike the 10 fingers of the decimal system, these systems can use up to 72 names of parts, but eight languages, including Oksapmin and Telefol use a base of 27 names of parts expressing larger numbers with a phrase like "one man and" - adding the extra 'digit' name. Base 32/ Duotrigesimal: Ngiti [Congo] is reported to have a base 32 numeral system with base-4 cycles.

Fascinating! Thanks for sharing! I have always wondered about this and never got to looking it up!

The Mesopotamians used base 60, that's why we use hours and minutes subdivided into 60 parts. The Aztecs counted in twenties. "The Aztecs: their numbers, their days, and their gods" www.mexicolore.co.uk/aztecs/kids/aztec-numbers

Some very obscure ones from WP: Positional numeral systems, and in general these are ethnic peoples, not [former] countries, except Mayans:

The Ndom language of Papua New Guinea, which employs senary counting, includes a basic word for 18 and another for 36. The Mayan Long Count calendar employs a "modified vigesimal" counting system that sets apart 360 as the number of days in a year, i.e. 18 months with 20 days. Base 12/ Duodecimal: [various peoples using Duodecimal] Base 15/ Pentadecimal: The Huli language of Papua New Guinea is reported to have base-15 numerals. Ngui means 15, ngui ki means 15×2 = 30, and ngui nguimeans 15×15 = 225. Base 27/ Septemvigesimal numeral system. Several Papua New Guinean languages use such a base. Many languages of Papua New Guinea use a system of counting in which numbers are associated with a body-part tally-system, typically starting at the little finger of one hand continuing across the body and face, and ending at the little finger of the other hand. Unlike the 10 fingers of the decimal system, these systems can use up to 72 names of parts, but eight languages, including Oksapmin and Telefol use a base of 27 names of parts expressing larger numbers with a phrase like "one man and" - adding the extra 'digit' name. Base 32/ Duotrigesimal: Ngiti [Congo] is reported to have a base 32 numeral system with base-4 cycles.

Fascinating stuff, and thanks for that.

I am not sure that A Level Maths would be that easy in a Septemvigesimal system.

I see what you mean. Can't split threads though, unfortunately. I'm sure this thread will be back to pure Mimi soon though and a few pages down the line, this little (or not-so-little) diversion will be forgotten about.

__________________

GB on a shirt, Davis Cup still gleaming, 79 years of hurt, never stopped us dreaming ... 29/11/2015 that dream came true!