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I’ve been surprised recently to discover that matrices are not now taught in English schools unless “extra” qualifications (GCSE further maths at 16, A level fu

I’ve been surprised recently to discover that matrices are not now taught in English schools unless “extra” qualifications (GCSE further maths at 16, A level further maths at 18) are taken, whereas when I did maths in the mid-80s they were included in the main syllabus. How are matrices taught at school (if at all) in other countries?

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vasco 2y ago
University level only in portugal. None in highschool. There's also no advanced programs.
7thaccount 2y ago
In US schools at least (a couple of decades ago for me), I think we did Kramer's rule or something like that. Not a lot of matrix math though until university. Edit: Cramer's Rule lol
notresidenter 2y ago
In France, matrices are taught in an optional mathematics class for students that want to go further.
roel_v 2y ago
In the Netherlands, it's not included in the 'standard' curriculum but it's optional if you take 'Wiskunde D', i.e. basically what elsewhere is called 'advanced placement math' or some such. ('Wiskunde D' / 'math D' is basically a 'capita selecta' of various math topics for those who want to prepare for math-heavy/STEM university studies, whereas math A, B and C have fixed curricula and each lay a different foundation for various follow on studies. Math A has the stuff useful for (amongst others) medical studies, such as statistics but less calculus, math B is the most 'rigorous' and math C is for those who can't tell a fraction from an asymptote but since math is a required subject still need a way to pass their high school final exams). When I was in highschool in Belgium 30 years ago, linear algebra (well, 'matrix calculations' is was called then) was part of math (depending on your electives) but I can understand why it's not taught today any more by default; there's just too much to teach, so you have to make choices. And I imagine that today they say 'we better do fewer things well than a lot with insufficient depth', which is what my experience is from how I took it 30 years ago. What's the point in doing linear algebra when it's only the purely numerical operations without teaching why or when you'd want to take a cross or dot product? And it's only a one semester course when you go to university anyway, so it's not like it's necessary to include early on or that any other high school subjects need it.
CoastalCoder 2y ago
I attended a decent high school on the U.S. in the late 1980s. IIRC, I took 5 math courses high school: algebra, geometry, precalc, calc 1, and calc 2. I don't think we ever covered matrices, except as a condensed format for solving systems of linear equations.
- trealira 2y ago
  I graduated in 2021, and my experience corroborates yours. I took that same sequence of math courses, up to calculus 2. If I had been on the more advanced path for math, there was exactly one more class; I don't remember what it was, but it wasn't linear algebra. I only took linear algebra in college.
- mhuffman 2y ago
  Mine was slightly different with geometry (middle school) > algebra (high school) > trig > calc 1 > calc 2, then in college they had calc 3 (which in hindsight was linear algebra with a heavy physics lean), then differential equations. That was all of my required math, I took two stats courses and a quantitative analysis and a game theory course as electives that all where under math but not required and didn't seem to be in any real order after prereqs.
froh 2y ago
In Germany simple basic matrix algebra is introduced in the last two or three years at school (grades 11/12 and 13 where that exists)
vmilner 2y ago
Thanks - sounds like Western Europe and the US arent that different from England. Anyone with experience from an Asian country or Eastern Europe (eg Poland Hungary)
sriram_malhar 2y ago
In India, matrix basics are in the standard high school curriculum (multiplication, associativity, adjoint, transpose, determinants , inverse etc). But the curriculum doesn't pay any heed to vectors or the notion of linearity, so we come away with no use or intuition for these curious objects.
crabbone 2y ago
To the best of my knowledge: * In Israeli high-school the system requires from students to take a number of credits in various disciplines. Some number of credits for certain disciplines is mandatory, while most are elective. Taking the maximum number of credits in math will include some matrix algebra. Taking maximum math credits isn't uncommon as the school graduation exams will have a major influence on college admission. * In Ukraine the equivalent of high-school is optional: a large fraction of students goes to an equivalent of a trade school instead. For those who stay, the program may vary greatly based on the teacher's own preferences, what they believe would be beneficial for the college entrance exams. So, it could include sometimes even somewhat advanced college-level math, but not necessarily uniformly so. I remember that our algebra teacher put a huge emphasis on solving problems from Skanavi's book (some scary-looking multiple layers of arithmetic expressions that need a lot of effort and creativity to simplify them), but there was very little attention paid to matrices (perhaps only mentioned in the context of linear equations systems).

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vasco 2y ago

University level only in portugal. None in highschool. There's also no advanced programs.

7thaccount 2y ago

In US schools at least (a couple of decades ago for me), I think we did Kramer's rule or something like that. Not a lot of matrix math though until university. Edit: Cramer's Rule lol

notresidenter 2y ago

In France, matrices are taught in an optional mathematics class for students that want to go further.

roel_v 2y ago

In the Netherlands, it's not included in the 'standard' curriculum but it's optional if you take 'Wiskunde D', i.e. basically what elsewhere is called 'advanced placement math' or some such. ('Wiskunde D' / 'math D' is basically a 'capita selecta' of various math topics for those who want to prepare for math-heavy/STEM university studies, whereas math A, B and C have fixed curricula and each lay a different foundation for various follow on studies. Math A has the stuff useful for (amongst others) medical studies, such as statistics but less calculus, math B is the most 'rigorous' and math C is for those who can't tell a fraction from an asymptote but since math is a required subject still need a way to pass their high school final exams). When I was in highschool in Belgium 30 years ago, linear algebra (well, 'matrix calculations' is was called then) was part of math (depending on your electives) but I can understand why it's not taught today any more by default; there's just too much to teach, so you have to make choices. And I imagine that today they say 'we better do fewer things well than a lot with insufficient depth', which is what my experience is from how I took it 30 years ago. What's the point in doing linear algebra when it's only the purely numerical operations without teaching why or when you'd want to take a cross or dot product? And it's only a one semester course when you go to university anyway, so it's not like it's necessary to include early on or that any other high school subjects need it.

CoastalCoder 2y ago

I attended a decent high school on the U.S. in the late 1980s. IIRC, I took 5 math courses high school: algebra, geometry, precalc, calc 1, and calc 2. I don't think we ever covered matrices, except as a condensed format for solving systems of linear equations.

trealira 2y ago
I graduated in 2021, and my experience corroborates yours. I took that same sequence of math courses, up to calculus 2. If I had been on the more advanced path for math, there was exactly one more class; I don't remember what it was, but it wasn't linear algebra. I only took linear algebra in college.
mhuffman 2y ago
Mine was slightly different with geometry (middle school) > algebra (high school) > trig > calc 1 > calc 2, then in college they had calc 3 (which in hindsight was linear algebra with a heavy physics lean), then differential equations. That was all of my required math, I took two stats courses and a quantitative analysis and a game theory course as electives that all where under math but not required and didn't seem to be in any real order after prereqs.

froh 2y ago

In Germany simple basic matrix algebra is introduced in the last two or three years at school (grades 11/12 and 13 where that exists)

vmilner 2y ago

Thanks - sounds like Western Europe and the US arent that different from England. Anyone with experience from an Asian country or Eastern Europe (eg Poland Hungary)

sriram_malhar 2y ago

In India, matrix basics are in the standard high school curriculum (multiplication, associativity, adjoint, transpose, determinants , inverse etc). But the curriculum doesn't pay any heed to vectors or the notion of linearity, so we come away with no use or intuition for these curious objects.

crabbone 2y ago

To the best of my knowledge: * In Israeli high-school the system requires from students to take a number of credits in various disciplines. Some number of credits for certain disciplines is mandatory, while most are elective. Taking the maximum number of credits in math will include some matrix algebra. Taking maximum math credits isn't uncommon as the school graduation exams will have a major influence on college admission. * In Ukraine the equivalent of high-school is optional: a large fraction of students goes to an equivalent of a trade school instead. For those who stay, the program may vary greatly based on the teacher's own preferences, what they believe would be beneficial for the college entrance exams. So, it could include sometimes even somewhat advanced college-level math, but not necessarily uniformly so. I remember that our algebra teacher put a huge emphasis on solving problems from Skanavi's book (some scary-looking multiple layers of arithmetic expressions that need a lot of effort and creativity to simplify them), but there was very little attention paid to matrices (perhaps only mentioned in the context of linear equations systems).