Virginia DOE proposes math change up, stops advanced math in lower grades.

[Benjamin Frank]

This is why I support public and non profit charter schools rather than a 'one size fits all' model (at least for grades 8 and up), but most of my fellow Democrats (if I lived in the United States) don't agree with me.

[Sestak]

I think the unique challenge with maths curricula in secondary education (in general; I’m not that familiar with the US*, but this applies everywhere) is the wide variety of uses pupils go onto have for maths. For most, it will just be being functionally numerate. But for the more able, they will actually go onto use it in their university studies - and within this group, you further have a spectrum from those who need it for maths itself or physics, to somewhat less mathematical natural sciences like biology and chemistry, to the social sciences. For this reason, I do think it really makes sense to stream maths curricula from the age of 13 or 14.

*Could someone clarify for me what students in their final two years of high school typically learn in the US in maths? In the UK, for those who choose maths (students at this age in generally have a free choice of any three or four subjects - you can also choose further maths, in addition to normal maths (as I did), the only subject for which this is possible, so that maths takes up half your timetable), it’s a range of pure maths (functions, trig, calculus, logarithms, proof, vectors, series, binomial expansion) and statistics (hypothesis testing, conditional probability) and mechanics (constant and variable acceleration, forces on an object, moments, projectiles). Further maths extends these topics and introduces ones such as complex numbers, matrices and differential equations.

Generally the most base standard track would develop all the principles till 7th grade and starts Pre-Algebra in 8th. Algebra in 9. Geometry in 10 . Algebra 2 in 11 and Pre Calc in 12. The Algebra > Geometry> Algebra 2 gap is a pretty big deal IMO and really should not be done. Accelerated paths also exist and for example one would start Pre Algebra in 7th or 8th and then be doing Calc in 11th or 12th.

What (briefly) is the contents of these courses? So do you spend the whole of 10th grade doing geometry and not touching other (more relevant, IMO, or maybe that’s just because I never particularly liked geometry compared to algebra ) areas of maths?

The way I experienced it (trying to remember as I haven't taken these courses in over half a decade) was that Alg I covered everything up until and including solving quadratics. Alg II then covers polynomials more generally, exponentials, logarithms, rational functions. The way I experienced it was with Alg II being shunted together with trig, though I think in various different curriculums the exact placement of trig varies.

[Benjamin Frank]

The geometry split of algebra is a tough nut to crack. On the one hand, geometry, if taught properly, is extremely useful for teaching rigorous proof and reasoning skills as opposed to simply rote computation; thus it or an adequate replacement should be part of any reasonable path.

On the other hand, splitting algebra in two like that is very awkward indeed and puts a lot of people in a strange place before heading into Alg II.

I know you mentioned geometry and not trigonometry, but trigonometry is also very useful to show ratios and the like if it's taught using fractions, but in most if not all cases, it's taught with formulas with students using calculators.  An entirely pointless rote exercise.

I appreciate that students will think 'why should I learn this when a calculator/computer can do it for me anyway.  But, to go against what I said about the 'once sized fits all' approach, if it were up to me, calculators would be banned in math class.

I realize that I shouldn't use my own personal experience to apply to everybody, but I 'failed' my grade 12 math exams (60% combined) before the finals, but had to still take the final.  While studying for the final, I noticed that trigonometry (at least in high school) was nothing but ratios, so I ditched the calculator and did all the math using fractions with pen and paper (or in my head) and I got an solid A on the final.

[Former President tack50]

Classes are split this way for the benefit of all of the students and it has nothing to do with leaving anyone behind or privileging certain students. In fact, placing struggling students in classes that require them to learn faster than they're capable of will probably hurt them even more than it hurts the advanced students to be placed in the more basic classes. It isn't even a question of intelligence so much as aptitude with a certain subject since I imagine it's not too uncommon for a student to be in a standard math class while being in an advanced English class or vice versa.

Isn't that what grades are for? Assuming the difficulty is tailored towards the median student you should have the gifted students getting A or A+ results while less gifted students will get just bare passes with a C or C-; so no need to split students based on ability.

Also, for the people who are completely inept at math, they should be able to drop math alltogether after like year 10 or so.

Plus, for what is worth, in my anecdotal experience, separating the good students from the bad students just creates more inequality. Sure, perhaps the good students might end up performing better, but the class with all the bad students will end up underperforming and those students learning even less than with a "mixed" class

How does it benefit anyone to withhold advanced mathematics from students capable of learning it successfully and forcing them to share in the same lessons as children who struggle at math? Terrible idea.

I was in advanced classes, then they said there wasn’t enough space available in 4th and 5th grade for me; I was part of the unlucky who lost that lottery at my elementary school. I became bored of school, my grades declined, and they never truly recovered until my senior year. I’d hate to see other advanced students face that same fate. Fortunately for me, I was still invested in learning for learning’s sale and chose to educate myself on a variety of subjects that were never addressed in school; however, I do believe I would’ve benefitted more from advanced classroom education - and so would most students.

     Advanced tracks for gifted students are critical, and we hurt them a lot by denying them those opportunities. Otherwise the concept of tracking has merit, but is at odds with the nature of university education which focuses in many departments on training students for academia and expecting them to manage the transition to industry if they choose to go that route.

Thing is, separating kids into "advanced classes" and "¿Standard? classes" has a very negative effect for those who get placed in the lower performance groups, both psychologically and in terms of those less gifted students learning even less than they would have if students from all performance levels were together in the same classroom.

In a way that most left of centre people will understand separating kids in such a way might make the gifted kids even more gifted, but it makes the less gifted kids perform even worse; raising inequalities. You can add to that for #woke points if you want that the people in less gifted groups will come from less advantaged socioeconomic groups and what not.


For people more interested on the broad concept of having students from all performances be together in the same classroom, that is what is called "Comprehensive schooling". I am not going to claim it is perfect (indeed for gifted students, which are probably overrepresented in Atlas, it is actually a downgrade). But it is a model that in theory does reduce inequalities and i am surprised at so many people left of centre being against it (indeed, repealing or watering down those models is a routine right wing education reform here!).

https://en.wikipedia.org/wiki/Comprehensive_school

[Benjamin Frank]

Classes are split this way for the benefit of all of the students and it has nothing to do with leaving anyone behind or privileging certain students. In fact, placing struggling students in classes that require them to learn faster than they're capable of will probably hurt them even more than it hurts the advanced students to be placed in the more basic classes. It isn't even a question of intelligence so much as aptitude with a certain subject since I imagine it's not too uncommon for a student to be in a standard math class while being in an advanced English class or vice versa.

Isn't that what grades are for? Assuming the difficulty is tailored towards the median student you should have the gifted students getting A or A+ results while less gifted students will get just bare passes with a C or C-; so no need to split students based on ability.

Also, for the people who are completely inept at math, they should be able to drop math alltogether after like year 10 or so.

Plus, for what is worth, in my anecdotal experience, separating the good students from the bad students just creates more inequality. Sure, perhaps the good students might end up performing better, but the class with all the bad students will end up underperforming and those students learning even less than with a "mixed" class

How does it benefit anyone to withhold advanced mathematics from students capable of learning it successfully and forcing them to share in the same lessons as children who struggle at math? Terrible idea.

I was in advanced classes, then they said there wasn’t enough space available in 4th and 5th grade for me; I was part of the unlucky who lost that lottery at my elementary school. I became bored of school, my grades declined, and they never truly recovered until my senior year. I’d hate to see other advanced students face that same fate. Fortunately for me, I was still invested in learning for learning’s sale and chose to educate myself on a variety of subjects that were never addressed in school; however, I do believe I would’ve benefitted more from advanced classroom education - and so would most students.

    Advanced tracks for gifted students are critical, and we hurt them a lot by denying them those opportunities. Otherwise the concept of tracking has merit, but is at odds with the nature of university education which focuses in many departments on training students for academia and expecting them to manage the transition to industry if they choose to go that route.

Thing is, separating kids into "advanced classes" and "¿Standard? classes" has a very negative effect for those who get placed in the lower performance groups, both psychologically and in terms of those less gifted students learning even less than they would have if students from all performance levels were together in the same classroom.

In a way that most left of centre people will understand separating kids in such a way might make the gifted kids even more gifted, but it makes the less gifted kids perform even worse; raising inequalities. You can add to that for #woke points if you want that the people in less gifted groups will come from less advantaged socioeconomic groups and what not.


For people more interested on the broad concept of having students from all performances be together in the same classroom, that is what is called "Comprehensive schooling". I am not going to claim it is perfect (indeed for gifted students, which are probably overrepresented in Atlas, it is actually a downgrade). But it is a model that in theory does reduce inequalities and i am surprised at so many people left of centre being against it (indeed, repealing or watering down those models is a routine right wing education reform here!).

https://en.wikipedia.org/wiki/Comprehensive_school

1.Part of the issue with mathematics I think comes from the snobbery of those in charge of the curriculum, that 'academic math' (Algebra II/Precalculus) is 'better' than applied or practical math (probability and statistics.)  If they believed and explained to teachers and students that they are different (at the high school level) but that neither is 'better' I think that would go a long way to ending any stigma at that level.

I think practical math is very important for the development of critical thinking skills and I strongly disagree with the notion that outside of the handful of people who have a mental condition that makes it impossible for them to do math, that there are any people who can not do basic mathematics.

How many people accept it if somebody says "I no can do no sentences.'

In a broader context, separating kids need not be a problem.  Just as the 'snobby educational elites' look down upon practical math, so do they look down upon other practical skills, so cooking or other trades in schools are looked down on in schools compared to algebra or history.  It is the rare student who is better at every subject, so the students who do not excel in the primarily academic subjects might likely do better in cooking or 'shop' (if that's still available, and it should be.)  Learning we are all individuals with our own unique abilities that are neither better or worse than other people's abilities is an important life lesson but that what's important is applying your abilities.

Edit to add: I admit that 'shop' is looked down on by more than just the education elites (or at least it was in my day) but I've never understood why.  if 'shop' isn't applied mathematics (and physics) I don't know what is.  Of course this is the same thing with skills training and apprenticeships being looked down on compared to academia.  I've never understood that.  Carpenters, plumbers, ironworkers... are highly skilled people requiring a practical understanding of many academic subjects.


2.In the old British T.V show Yes, Minister though this was from the sequel Yes, Prime Minister, Prime Minister Hacker is arguing in favor of reinstating the draft with basic training and argues "we can give them a comprehensive education...to make up for their comprehensive education."


Those who are unable to do math at all have a condition called dyscalculia.

https://www.mentalfloss.com/article/62436/11-facts-about-math-disorder-dyscalculia

I looked it up after writing the above, and a quote from a professor there argued the same as I just did:

A big part of the general population's unfamiliarity with dyscalculia has to do with our culture’s general discomfort with numbers, and our ingrained belief that math—compared to reading—is just supposed to be hard. Dr. Gavin Price, an assistant professor at Vanderbilt University who has researched dyscalculia in several countries, says, "When I teach classes, I’ll ask at the beginning, 'How many people think they’re not good at math, they’re bad at math?' And half of them put their hands up. Then I ask, 'Are any of you bad at reading?' And nobody puts their hand up."

[Sestak]

I mean tack, the counterpoint is that you are essentially taking certain levels of mathematics (as well as access to rigorous math education overall) and just declaring them to be forbidden for no reason. Forbidding people from learning stuff like that is quite frankly ridiculous (and I especially take offense at it in my own field).

Admittedly, what I'm not so sure about is the whole idea of 'testing' or 'placement' into laning - arguably, in an ideal world it would be entirely up to choice as to what track or level of rigor you wanted. Sure, there would be choices that are inadvisable - but again, I don't think anyone should be deprived the choice of taking a more rigorous math course.

Also, a note on math specifically - building a very robust knowledge of a set of mathematical concepts is essential to being able to learn future concepts on top of it. For instance, it is entirely possible to muddle and/or bash your way through a standard Algebra (I or II) course. But doing this will leave you lost if you try to learn anything that builds on top of it. Thus, for anyone who seeks to do anything math-related in higher education etc., taking courses that ensure this level of knowledge (and cannot just be muddled through for a grade) are pretty much essential unless they are to waste substantial amounts of time later "relearning" the same thing with more rigor. And this is what - at least in principle - the advanced or honors lane provides which a unified lane could not.

[Former President tack50]

I mean tack, the counterpoint is that you are essentially taking certain levels of mathematics (as well as access to rigorous math education overall) and just declaring them to be forbidden for no reason. Forbidding people from learning stuff like that is quite frankly ridiculous (and I especially take offense at it in my own field).

Admittedly, what I'm not so sure about is the whole idea of 'testing' or 'placement' into laning - arguably, in an ideal world it would be entirely up to choice as to what track or level of rigor you wanted. Sure, there would be choices that are inadvisable - but again, I don't think anyone should be deprived the choice of taking a more rigorous math course.

Also, a note on math specifically - building a very robust knowledge of a set of mathematical concepts is essential to being able to learn future concepts on top of it. For instance, it is entirely possible to muddle and/or bash your way through a standard Algebra (I or II) course. But doing this will leave you lost if you try to learn anything that builds on top of it. Thus, for anyone who seeks to do anything math-related in higher education etc., taking courses that ensure this level of knowledge (and cannot just be muddled through for a grade) are pretty much essential unless they are to waste substantial amounts of time later "relearning" the same thing with more rigor. And this is what - at least in principle - the advanced or honors lane provides which a unified lane could not.

It is not really "forbidding" things though? A model like the one I studied with definitely doesn't forbid kids from taking "pure math"; which included stuff like basic integrals, derivatives, geometry, matrices and a couple other stuff in year 12 (I can remember less well the contents of other years and I'd have to look them up).

For a student that is so brilliant and so excellent at math that they are so good, you can argue they are being held back by not being presented with even harder stuff and they are! (I guess this is what you mean by "forbidding") But it is not for "no reason". It is best for the whole of society is precisely that model, where  the most brilliant students get held back so that the less brilliant ones don't fall even further behind than they should.

This of course gets into a whole philosophical argument where whether individual liberty or the greater good of society should matter most; and an argument where there is no right or wrong answer. I am not saying the "comprehensive education" model is superior; but is is a model that does reduce inequalities. (which is indeed why I was so surprised at so many left of centre people in Atlas being against it. Just watch the UK example, with the reform being implemented by the Labour governments of Wilson and Blair; and being watered down by a certain Margaret Thatcher, first as secretary of education and then as Prime Minister)

A student that is bad at math and would be placed in those "standard" classes; let's face it, is unlikely to later pursue a mathematics heavy path in college (like say, Engineering or indeed a mathematics degree). That student would be better served from taking an applied maths class centered around statistics and what not; or possibly dropping math alltogether and in its place pursuing other classes like world history or art, instead of being forced to learn math against their will all the way until they graduate HS. Math beyond a certain level which gets achieved approximately in year 9 or 10, is not really for everyone.

This basically means your 3rd paragraph, while true, isn't really all that relevant? Someone who wants to be say, a lawyer, or a historian, or a translator, or something like that; will not need many mathematics other than super basic stuff in college (or in their professional life for that matter)

I do agree with your 2nd paragraph that if laning happens, people should not be stopped based on academic results; and that any reports they get should be exclusively non-binding. I just don't think laning based purely on academic performance is a good thing

For what is worth you could argue a model like I grew up with is de facto laning and I would even agree with it; humanities students (the ones that don't get math; or physics and chemistry and other sciences for that reason); are generally stereotyped as "dumber". But that is a stereotype and the humanities path isn't intended to be easier in any way. I would have been just as miserable learning about "History of Art" (or even "Biology", which I dropped after year 9) as a humanities student would have learning calculus or physics

[Benjamin Frank]

I mean tack, the counterpoint is that you are essentially taking certain levels of mathematics (as well as access to rigorous math education overall) and just declaring them to be forbidden for no reason. Forbidding people from learning stuff like that is quite frankly ridiculous (and I especially take offense at it in my own field).

Admittedly, what I'm not so sure about is the whole idea of 'testing' or 'placement' into laning - arguably, in an ideal world it would be entirely up to choice as to what track or level of rigor you wanted. Sure, there would be choices that are inadvisable - but again, I don't think anyone should be deprived the choice of taking a more rigorous math course.

Also, a note on math specifically - building a very robust knowledge of a set of mathematical concepts is essential to being able to learn future concepts on top of it. For instance, it is entirely possible to muddle and/or bash your way through a standard Algebra (I or II) course. But doing this will leave you lost if you try to learn anything that builds on top of it. Thus, for anyone who seeks to do anything math-related in higher education etc., taking courses that ensure this level of knowledge (and cannot just be muddled through for a grade) are pretty much essential unless they are to waste substantial amounts of time later "relearning" the same thing with more rigor. And this is what - at least in principle - the advanced or honors lane provides which a unified lane could not.

It is not really "forbidding" things though? A model like the one I studied with definitely doesn't forbid kids from taking "pure math"; which included stuff like basic integrals, derivatives, geometry, matrices and a couple other stuff in year 12 (I can remember less well the contents of other years and I'd have to look them up).

For a student that is so brilliant and so excellent at math that they are so good, you can argue they are being held back by not being presented with even harder stuff and they are! (I guess this is what you mean by "forbidding") But it is not for "no reason". It is best for the whole of society is precisely that model, where  the most brilliant students get held back so that the less brilliant ones don't fall even further behind than they should.

This of course gets into a whole philosophical argument where whether individual liberty or the greater good of society should matter most; and an argument where there is no right or wrong answer. I am not saying the "comprehensive education" model is superior; but is is a model that does reduce inequalities. (which is indeed why I was so surprised at so many left of centre people in Atlas being against it. Just watch the UK example, with the reform being implemented by the Labour governments of Wilson and Blair; and being watered down by a certain Margaret Thatcher, first as secretary of education and then as Prime Minister)

A student that is bad at math and would be placed in those "standard" classes; let's face it, is unlikely to later pursue a mathematics heavy path in college (like say, Engineering or indeed a mathematics degree). That student would be better served from taking an applied maths class centered around statistics and what not; or possibly dropping math alltogether and in its place pursuing other classes like world history or art, instead of being forced to learn math against their will all the way until they graduate HS. Math beyond a certain level which gets achieved approximately in year 9 or 10, is not really for everyone.

This basically means your 3rd paragraph, while true, isn't really all that relevant? Someone who wants to be say, a lawyer, or a historian, or a translator, or something like that; will not need many mathematics other than super basic stuff in college (or in their professional life for that matter)

I do agree with your 2nd paragraph that if laning happens, people should not be stopped based on academic results; and that any reports they get should be exclusively non-binding. I just don't think laning based purely on academic performance is a good thing

For what is worth you could argue a model like I grew up with is de facto laning and I would even agree with it; humanities students (the ones that don't get math; or physics and chemistry and other sciences for that reason); are generally stereotyped as "dumber". But that is a stereotype and the humanities path isn't intended to be easier in any way. I would have been just as miserable learning about "History of Art" (or even "Biology", which I dropped after year 9) as a humanities student would have learning calculus or physics

I was thinking this is also a philosophical argument on liberalism.  Younger liberals (progressive?) like you are clearly arguing here on the basis of 'self esteem.'  Older liberals like me argue that real self esteem is derived from real accomplishment and that accomplishment need not be academic but can be from sport, art or a trade skill.  And that, we need to emphasize that we are all unique individuals with individual skills that are neither better or worse than anybody else's (except for the 1% or so who are truly superior at everything) but that what matters is making use of your abilities, but also that we all (with noted exceptions) have enough minimum skills to be able to do most everything at a basic level (sports like dancing of course can require physical abilities that some people don't have.)  In my case, I have no sense of timing, so, as much as I'd like to, I can't even play a musical instrument at a basic level.

[Former President tack50]

I was thinking this is also a philosophical argument on liberalism.  Younger liberals (progressive?) like you are clearly arguing here on the basis of 'self esteem.'  Older liberals like me argue that real self esteem is derived from real accomplishment and that accomplishment need not be academic but can be from sport, art or a trade skill.  And that, we need to emphasize that we are all unique individuals with individual skills that are neither better or worse than anybody else's (except for the 1% or so who are truly superior at everything) but that what matters is making use of your abilities, but also that we all (with noted exceptions) have enough minimum skills to be able to do most everything at a basic level (sports like dancing of course can require physical abilities that some people don't have.)  In my case, I have no sense of timing, so, as much as I'd like to, I can't even play a musical instrument at a basic level.

I agree in this (and indeed, with the critique you made previously); although I think instead this is just one of those topics where as a foreign poster who grew up in a very different education system I just plain can't relate and get shocked. I've routinely clashed with US posters of all ideologies on the issue of education.

Something I've noticed in my time in Atlas is that US education, (even as late as college!!!!) tends to put a big focus into the concept of "liberal education" and similar concepts; seemingly wanting to make everyone a "jack of all trades"; while my own education put a much bigger focus into specialization, with various "paths" in HS depending on what you plan on studying in college (or what trade you planned to get into if you weren't planning on going to college). That is not to say there weren't "liberal education minimums" (philosophy/ethics, history and Literature classes were mandatory throughout); but there seems to be less of a focus on teaching everyone "a bit of everything" (though I have more of an issue with that philosophy for college than for HS).

Self esteem is one of the main factors why people in the "standard" groupings fail more yes (they think lesser of themselves; wondering "am I stupid? am I unfit for education?") though it is not the only one.

And indeed you can also look at it from a philosophical perspective of "greater good" vs "individual liberalism". I am not arguing one model is inherently superior to the other; I am just defending the opposing position since it is the one I think is better.

Ironically in most other issues I tend to side with the "older liberals" and the less #woke position; education is a very big exception, though I am against other "new progressive" measures that in my view would dumb down education.

[GeneralMacArthur]

I think the unique challenge with maths curricula in secondary education (in general; I’m not that familiar with the US*, but this applies everywhere) is the wide variety of uses pupils go onto have for maths. For most, it will just be being functionally numerate. But for the more able, they will actually go onto use it in their university studies - and within this group, you further have a spectrum from those who need it for maths itself or physics, to somewhat less mathematical natural sciences like biology and chemistry, to the social sciences. For this reason, I do think it really makes sense to stream maths curricula from the age of 13 or 14.

*Could someone clarify for me what students in their final two years of high school typically learn in the US in maths? In the UK, for those who choose maths (students at this age in generally have a free choice of any three or four subjects - you can also choose further maths, in addition to normal maths (as I did), the only subject for which this is possible, so that maths takes up half your timetable), it’s a range of pure maths (functions, trig, calculus, logarithms, proof, vectors, series, binomial expansion) and statistics (hypothesis testing, conditional probability) and mechanics (constant and variable acceleration, forces on an object, moments, projectiles). Further maths extends these topics and introduces ones such as complex numbers, matrices and differential equations.

Generally the most base standard track would develop all the principles till 7th grade and starts Pre-Algebra in 8th. Algebra in 9. Geometry in 10 . Algebra 2 in 11 and Pre Calc in 12. The Algebra > Geometry> Algebra 2 gap is a pretty big deal IMO and really should not be done. Accelerated paths also exist and for example one would start Pre Algebra in 7th or 8th and then be doing Calc in 11th or 12th.

What (briefly) is the contents of these courses? So do you spend the whole of 10th grade doing geometry and not touching other (more relevant, IMO, or maybe that’s just because I never particularly liked geometry compared to algebra ) areas of maths?

YMMV but what I remember it was:

Algebra I
Standard inequalities and linear equations, things like that.  I remember algebra being really difficult for me to grasp the first time I encountered it because I was like "I know that if x + 2 = 3 then x = 1, why do I need to do this (x+2)-2 = (3-2) crap?"

Geometry
This was all the basic details of circles, triangles, 3D objects, and other shapes.  Most of it was memorizing equations for area/perimeter and how to calculate things based on angles.

Algebra II
Exponents, logarithms, wave functions, polynomials (including the quadratic formula), various algorithms to solve equations, different types of numbers like rational/irrational, complex, imaginary numbers (kill me), etc.

Pre-calc/Trigonometry
In my experience these were the same thing.  There were a few new concepts introduced such as binomial equations, but most of the class involved doing algebra with the previously-learned concepts.  There were a bunch of rules to memorize and then apply to simplify.  Most tests were just "Simplify" at the top, and then a whole bunch of complicated-looking equations.

Calculus I
Derivatives and limits.  IMO there is a pretty large jump in difficulty from "pre-calc" to calc.

Calculus II
Integrals

Calculus III
Multiariable functions, partial derivatives, integrals of 3D objects

My high school offered all the way up to Calc III, but I only made it to Calc II and ended up taking III in college.

IMO everything up to Algebra II should be mandatory for all American high school graduates as Algebra II is basically a survey course of different advanced mathematical topics and important to understanding anything math-related you read for the rest of your life.  Even if you never use "imaginary numbers" ever again, you still need to understand logarithms and exponents for day-to-day life.  But if you want to be college-ready you absolutely have to take through Calculus II.  Integration is a fundamental concept to all the hard sciences and engineering.  You can take Calc I and Calc II in college, but then if you want to do hard science or engineering, you'll be a year behind everyone else and taking the weed-out courses for your major your sophomore year.  That's how you end up with kids changing majors halfway through college.

Calculus III was only really useful in graduate-level courses.  Unless you plan on reading a lot of research papers for math/engineering/hard science, I wouldn't take it.

Linear algebra, though, is extremely useful and applicable to all science/engineering disciplines as well as a lot of "soft science" disciplines, and IMO should be offered at high school level and treated with the same respect that probability and statistics courses get.  You can take linear algebra after Calculus I.  Linear algebra is basically anything involving vectors and matrices, basically reasoning about the relationships between collections of numbers.

[lfromnj]

I think the unique challenge with maths curricula in secondary education (in general; I’m not that familiar with the US*, but this applies everywhere) is the wide variety of uses pupils go onto have for maths. For most, it will just be being functionally numerate. But for the more able, they will actually go onto use it in their university studies - and within this group, you further have a spectrum from those who need it for maths itself or physics, to somewhat less mathematical natural sciences like biology and chemistry, to the social sciences. For this reason, I do think it really makes sense to stream maths curricula from the age of 13 or 14.

*Could someone clarify for me what students in their final two years of high school typically learn in the US in maths? In the UK, for those who choose maths (students at this age in generally have a free choice of any three or four subjects - you can also choose further maths, in addition to normal maths (as I did), the only subject for which this is possible, so that maths takes up half your timetable), it’s a range of pure maths (functions, trig, calculus, logarithms, proof, vectors, series, binomial expansion) and statistics (hypothesis testing, conditional probability) and mechanics (constant and variable acceleration, forces on an object, moments, projectiles). Further maths extends these topics and introduces ones such as complex numbers, matrices and differential equations.

Generally the most base standard track would develop all the principles till 7th grade and starts Pre-Algebra in 8th. Algebra in 9. Geometry in 10 . Algebra 2 in 11 and Pre Calc in 12. The Algebra > Geometry> Algebra 2 gap is a pretty big deal IMO and really should not be done. Accelerated paths also exist and for example one would start Pre Algebra in 7th or 8th and then be doing Calc in 11th or 12th.

What (briefly) is the contents of these courses? So do you spend the whole of 10th grade doing geometry and not touching other (more relevant, IMO, or maybe that’s just because I never particularly liked geometry compared to algebra ) areas of maths?

YMMV but what I remember it was:

Algebra I
Standard inequalities and linear equations, things like that.  I remember algebra being really difficult for me to grasp the first time I encountered it because I was like "I know that if x + 2 = 3 then x = 1, why do I need to do this (x+2)-2 = (3-2) crap?"

Geometry
This was all the basic details of circles, triangles, 3D objects, and other shapes.  Most of it was memorizing equations for area/perimeter and how to calculate things based on angles.

Algebra II
Exponents, logarithms, wave functions, polynomials (including the po, various algorithms to solve equations, different types of numbers like rational/irrational, complex, imaginary numbers (kill me), etc.

Pre-calc/Trigonometry
In my experience these were the same thing.  There were a few new concepts introduced such as binomial equations, but most of the class involved doing algebra with the previously-learned concepts.  There were a bunch of rules to memorize and then apply to simplify.  Most tests were just "Simplify" at the top, and then a whole bunch of complicated-looking equations.

Calculus I
Derivatives and limits.  IMO there is a pretty large jump in difficulty from "pre-calc" to calc.

Calculus II
Integrals

Calculus III
Multiariable functions, partial derivatives, integrals of 3D objects

My high school offered all the way up to Calc III, but I only made it to Calc II and ended up taking III in college.

IMO everything up to Algebra II should be mandatory for all American high school graduates as Algebra II is basically a survey course of different advanced mathematical topics and important to understanding anything math-related you read for the rest of your life.  Even if you never use "imaginary numbers" ever again, you still need to understand logarithms and exponents for day-to-day life.  But if you want to be college-ready you absolutely have to take through Calculus II.  Integration is a fundamental concept to all the hard sciences and engineering.  You can take Calc I and Calc II in college, but then if you want to do hard science or engineering, you'll be a year behind everyone else and taking the weed-out courses for your major your sophomore year.  That's how you end up with kids changing majors halfway through college.

Calculus III was only really useful in graduate-level courses.  Unless you plan on reading a lot of research papers for math/engineering/hard science, I wouldn't take it.

Linear algebra, though, is extremely useful and applicable to all science/engineering disciplines as well as a lot of "soft science" disciplines, and IMO should be offered at high school level and treated with the same respect that probability and statistics courses get.  You can take linear algebra after Calculus I.

I took Linear in HS FWIW. Definitely good move and moves like what VA is doing should include it. I guess I would defer to PIT's point. I think the focus on Calculus is too much for most people and most people actually don't take calculus in college.  You don't need Calculus for Linear really lol.

[Benjamin Frank]

I think the unique challenge with maths curricula in secondary education (in general; I’m not that familiar with the US*, but this applies everywhere) is the wide variety of uses pupils go onto have for maths. For most, it will just be being functionally numerate. But for the more able, they will actually go onto use it in their university studies - and within this group, you further have a spectrum from those who need it for maths itself or physics, to somewhat less mathematical natural sciences like biology and chemistry, to the social sciences. For this reason, I do think it really makes sense to stream maths curricula from the age of 13 or 14.

*Could someone clarify for me what students in their final two years of high school typically learn in the US in maths? In the UK, for those who choose maths (students at this age in generally have a free choice of any three or four subjects - you can also choose further maths, in addition to normal maths (as I did), the only subject for which this is possible, so that maths takes up half your timetable), it’s a range of pure maths (functions, trig, calculus, logarithms, proof, vectors, series, binomial expansion) and statistics (hypothesis testing, conditional probability) and mechanics (constant and variable acceleration, forces on an object, moments, projectiles). Further maths extends these topics and introduces ones such as complex numbers, matrices and differential equations.

Generally the most base standard track would develop all the principles till 7th grade and starts Pre-Algebra in 8th. Algebra in 9. Geometry in 10 . Algebra 2 in 11 and Pre Calc in 12. The Algebra > Geometry> Algebra 2 gap is a pretty big deal IMO and really should not be done. Accelerated paths also exist and for example one would start Pre Algebra in 7th or 8th and then be doing Calc in 11th or 12th.

What (briefly) is the contents of these courses? So do you spend the whole of 10th grade doing geometry and not touching other (more relevant, IMO, or maybe that’s just because I never particularly liked geometry compared to algebra ) areas of maths?

YMMV but what I remember it was:

Algebra I
Standard inequalities and linear equations, things like that.  I remember algebra being really difficult for me to grasp the first time I encountered it because I was like "I know that if x + 2 = 3 then x = 1, why do I need to do this (x+2)-2 = (3-2) crap?"

Geometry
This was all the basic details of circles, triangles, 3D objects, and other shapes.  Most of it was memorizing equations for area/perimeter and how to calculate things based on angles.

Algebra II
Exponents, logarithms, wave functions, polynomials (including the quadratic formula), various algorithms to solve equations, different types of numbers like rational/irrational, complex, imaginary numbers (kill me), etc.

Pre-calc/Trigonometry
In my experience these were the same thing.  There were a few new concepts introduced such as binomial equations, but most of the class involved doing algebra with the previously-learned concepts.  There were a bunch of rules to memorize and then apply to simplify.  Most tests were just "Simplify" at the top, and then a whole bunch of complicated-looking equations.

Calculus I
Derivatives and limits.  IMO there is a pretty large jump in difficulty from "pre-calc" to calc.

Calculus II
Integrals

Calculus III
Multiariable functions, partial derivatives, integrals of 3D objects

My high school offered all the way up to Calc III, but I only made it to Calc II and ended up taking III in college.

IMO everything up to Algebra II should be mandatory for all American high school graduates as Algebra II is basically a survey course of different advanced mathematical topics and important to understanding anything math-related you read for the rest of your life.  Even if you never use "imaginary numbers" ever again, you still need to understand logarithms and exponents for day-to-day life.  But if you want to be college-ready you absolutely have to take through Calculus II.  Integration is a fundamental concept to all the hard sciences and engineering.  You can take Calc I and Calc II in college, but then if you want to do hard science or engineering, you'll be a year behind everyone else and taking the weed-out courses for your major your sophomore year.  That's how you end up with kids changing majors halfway through college.

Calculus III was only really useful in graduate-level courses.  Unless you plan on reading a lot of research papers for math/engineering/hard science, I wouldn't take it.

Linear algebra, though, is extremely useful and applicable to all science/engineering disciplines as well as a lot of "soft science" disciplines, and IMO should be offered at high school level and treated with the same respect that probability and statistics courses get.  You can take linear algebra after Calculus I.  Linear algebra is basically anything involving vectors and matrices, basically reasoning about the relationships between collections of numbers.

Calculus I.  Derivatives, yes, but also differential!  (How could you mention the integral without mentioning the differential?)  Differential and integral calculus, the reverse processes.  

From my experience, differential calculus was no more difficult than Algebra II leading up to the Fundamental Theorem of Calculus, but integral calculus was far more difficult.  However, once understood, differential and integral calculus make calculations in physics much, much easier (and also highlight relationships between concepts in physics.)

There is a reason why the circumference of a circle is taught as 2*Pi*r and not as Pi*D (at least it was in my day) obviously because it's easier to show the relationship with the area calculated as Pi*r^2.

I agree that Algebra I should be mandatory (which is where imaginary numbers are taught) but Algebra II should be an elective for those planning to take STEM subjects in college.  I argue probability and statistics should be mandatory at the high school level as it is far easier to integrate into other classroom subjects.  

Edit to add: looking closer, a whole bunch of the things that you list as part of Algebra II, are part of Algebra I.  I learned quadratic equations, for instance, in grade 8.  Quadratic equations are nothing more than an application of basic arithmetic and mathematical concepts.  It shouldn't be hard to teach people to grasp a fuller meaning of 2 + 3 = 3 + 2 (The Commutative Property of Addition.)

As I argued previously, there is no point for a student to leave off high school having only taken Algebra II.  If Algebra II is going to be mandatory then so should at least differential calculus.  If the 'meaningless' abstractions of Algebra II are going to be taught, then the students should at least leave with some understanding of what all those abstractions mean.

[Sestak]

This basically means your 3rd paragraph, while true, isn't really all that relevant? Someone who wants to be say, a lawyer, or a historian, or a translator, or something like that; will not need many mathematics other than super basic stuff in college (or in their professional life for that matter)

You are missing the point of the paragraph. My point is if everyone only has the option to take less than rigorous courses in secondary school, then anyone - even relatively talented students - who seek to specialize in any math-related field (be it math itself, physics, anything that uses modeling [which is a ton of stuff in both the sciences and social sciences], statistics, etc.) - is going to struggle if they haven't seen it rigorously before. An entire pretty substantial body of students are going to be severely handicapped and delayed in their education and are going to find it very hard to catch up. This could have very major negative implications on all sorts of fields of research.

You have noted, yes, that there are many people for whom the foundations of many parts of mathematics will go unused. But you are proposing to "remedy" this by making everyone go through a class which will build an incomplete, unstable facsimile of a foundation which will collapse if you do try to build anything on top of it. And that, to me, is an unacceptable system.

[Former President tack50]

This basically means your 3rd paragraph, while true, isn't really all that relevant? Someone who wants to be say, a lawyer, or a historian, or a translator, or something like that; will not need many mathematics other than super basic stuff in college (or in their professional life for that matter)

You are missing the point of the paragraph. My point is if everyone only has the option to take less than rigorous courses in secondary school, then anyone - even relatively talented students - who seek to specialize in any math-related field (be it math itself, physics, anything that uses modeling [which is a ton of stuff in both the sciences and social sciences], statistics, etc.) - is going to struggle if they haven't seen it rigorously before. An entire pretty substantial body of students are going to be severely handicapped and delayed in their education and are going to find it very hard to catch up. This could have very major negative implications on all sorts of fields of research.

You have noted, yes, that there are many people for whom the foundations of many parts of mathematics will go unused. But you are proposing to "remedy" this by making everyone go through a class which will build an incomplete, unstable facsimile of a foundation which will collapse if you do try to build anything on top of it. And that, to me, is an unacceptable system.

This is not the "solution" I am proposing though? I don't think the math classes I have depicted are any less rigurous* than the ones you are imagining. Indeed looking at the list of contents MacArthur posted, by the time you'd finish HS under the classes I am thinking of, you would have covered everything up to Calculus II; with the only thing out of reach in HS being Calculus III which from my understanding most people take in college anyways.

I guess the main difference on a system I am proposing is that if you aren't good enough at math and are unable to take that class; instead of taking "Math for dummies" or taking Year 10 or 11 "Pre-Calc" while being older than all your classmates, you would be taking something like "World History" or "Economics" or "Latin" in its place. Which if you are going to be a historian or lawyer in the future; will be more useful to you than having to learn derivatives and integrals.

<sup>*: On this note I actually took a look at the differences between "Applied Math" and "Pure Math" classes and there are surprisingly few; biggest one being that "applied math" lacked geometry and of course a bigger focus on statistics for "Applied Math" (though pure math still sees some statistics thrown in).

Though this might be a very recent reform (dating to 2015) and things weren't that way back when I was in HS, when there were more different. Back in my day "Applied math" was mostly statistics, with some analysis of functions and perhaps derivatives thrown in; while "Pure Math" lacked any statistics whatsoever.</sup>

[Mercenary]

Incredibly stupid. As someone who took advantage of higher level math as a kid I am thabkful this lunacy wasnt so common back then. If anything, I wish more opportunity for acceleration were in place.

[VBM]

Why are Democrats so oddly anti-math in schools? I swear it’s always the Democrats, surprisingly, who are trying to limit the amount of math taught in schools. Is the reason some woke nonsense like black and latino kids do worse than white and asian kids on average in math, so we gotta make math much easier to make the races get closer grades?

[RFayette 🇻🇦]

Given that American mathematics education is already significantly behind many of our competitors (just Google gaokao math questions, and you'll see that even most advanced math students here would struggle with it), this is a really bad move.  

[Sestak]

This basically means your 3rd paragraph, while true, isn't really all that relevant? Someone who wants to be say, a lawyer, or a historian, or a translator, or something like that; will not need many mathematics other than super basic stuff in college (or in their professional life for that matter)

You are missing the point of the paragraph. My point is if everyone only has the option to take less than rigorous courses in secondary school, then anyone - even relatively talented students - who seek to specialize in any math-related field (be it math itself, physics, anything that uses modeling [which is a ton of stuff in both the sciences and social sciences], statistics, etc.) - is going to struggle if they haven't seen it rigorously before. An entire pretty substantial body of students are going to be severely handicapped and delayed in their education and are going to find it very hard to catch up. This could have very major negative implications on all sorts of fields of research.

You have noted, yes, that there are many people for whom the foundations of many parts of mathematics will go unused. But you are proposing to "remedy" this by making everyone go through a class which will build an incomplete, unstable facsimile of a foundation which will collapse if you do try to build anything on top of it. And that, to me, is an unacceptable system.

This is not the "solution" I am proposing though? I don't think the math classes I have depicted are any less rigurous* than the ones you are imagining. Indeed looking at the list of contents MacArthur posted, by the time you'd finish HS under the classes I am thinking of, you would have covered everything up to Calculus II; with the only thing out of reach in HS being Calculus III which from my understanding most people take in college anyways.

I guess the main difference on a system I am proposing is that if you aren't good enough at math and are unable to take that class; instead of taking "Math for dummies" or taking Year 10 or 11 "Pre-Calc" while being older than all your classmates, you would be taking something like "World History" or "Economics" or "Latin" in its place. Which if you are going to be a historian or lawyer in the future; will be more useful to you than having to learn derivatives and integrals.

<sup>*: On this note I actually took a look at the differences between "Applied Math" and "Pure Math" classes and there are surprisingly few; biggest one being that "applied math" lacked geometry and of course a bigger focus on statistics for "Applied Math" (though pure math still sees some statistics thrown in).

Though this might be a very recent reform (dating to 2015) and things weren't that way back when I was in HS, when there were more different. Back in my day "Applied math" was mostly statistics, with some analysis of functions and perhaps derivatives thrown in; while "Pure Math" lacked any statistics whatsoever.</sup>

You are misunderstanding what I mean; when I speak of rigorous education I'm not talking about the overall list of concepts covered. If that were the only issue, then single laning would be fine as long as students could skip ahead to a later grade's class if they were at a high enough level.

No, I'm talking about the rigor with which each concept is taught within this classes. At the moment, standard level classes mostly just check if you are good at solving a certain repertoire of problem types within the area. Advanced classes, on the other hand, will often have exams that throw more challenging types of problems which require a more advanced understanding of the subject and lateral thinking - problems which will, at least to some level, require you not just to understand the concepts but for them to be intuitive to you.

Now, when you first learn algebra, if you "know" arithmetic but it doesn't come instinctively or intuitively to you, then learning algebra will be a struggle. The same, in turn, is true of learning calculus - if you can solve algebra problems but haven't developed an intuition for algebra, then you will struggle with calculus. And this continues onwards as one continues to learn. Thus, if you don't plan on learning much more math beyond a certain subject, taking the "normal" standard for that subject might be acceptable; if all you really need to know is how to solve the canonical problem types, then the intuition is not really needed. If one plans to continue onwards, however, then you need a stronger intuitive knowledge of the material in order to avoid struggling badly later.

[President Punxsutawney Phil]

Given that American mathematics education is already significantly behind many of our competitors (just Google gaokao math questions, and you'll see that even most advanced math students here would struggle with it), this is a really bad move. 

https://www.reddit.com/r/math/comments/88b6cw/translated_version_of_gaokao/
to those curious - I found this on reddit, this might give y'all a sense of what RFayette is talking about.

[Sestak]

Given that American mathematics education is already significantly behind many of our competitors (just Google gaokao math questions, and you'll see that even most advanced math students here would struggle with it), this is a really bad move. 

I will note that this is not entirely a fair comparison since there is a curriculum difference in prioritization between the curriculum for the gaokao and ours; they generally do a lot more geometry etc. Usually the problems I've seen cited as "the hardest" are analytic geometry problems, which are generally not learned by many people - in high school here this is never really covered (even though it could be; there's no prerequisite students here don't have) and the only people who spend time on it are specifically people who prepare for contests.

The broader point about them being rather difficult compared to exams here stands, though.

[Bootes Void]

This validates the right's talking point that they treat minorities like a bunch of children unfortunately 

[junior chįmp]

Huh....so damn...all this time, I did so bad in math cuz math was racist. Mother fu**king polynomials were just racists

[SInNYC]

Wow the state of Virginia is mega based. Virginia may be for lovers, but I sure do love the Virginia DOE

That seems like a great reform to me. To be honest it reminds me of the very own way I got taught math; where every student got the same curriculum up to year 9. Year 10 math got divided into Math "A" (mostly statistics, intended for future humanities students) and Math "B" (functions, equations and what not, intended for future STEM, sciences and medical students)

Year 11 and 12 also had math packaged in the same way ("Applied Math" vs "(pure) Math"), except you could drop math alltogether if you chose the "arts" path (very rare since very few schools offer it) or the "pure humanities" path (more common). If you chose the social sciences path you got "applied math" and if you chose one of the STEM paths you had plain old "Mathematics".

No laning or splitting math into Calculus/Algebra/Geometry/Trigonometry/etc, which feels very unnecessary to me

Also I am suprised that most of the red avatars and left leaning people so far have come out against the proposal claiming it harms gifted kids and what not while the only one I've seen in favour is noted libertarian lfromnj

I would be fine with everybody getting the same math through 9th grade if it were rigorous. But even if you teach a course with the same title, there are clearly different levels of rigor - algebra I could range anywhere from MAA competition problems to 'how to use mathematica'. The unfortunate reality in the US is that the math courses for most students are ridiculous rote procedure memorization, and nowdays are trending towards 'how to run program X to output the solution to this problem' (though this is more at the CC and college level than the high school level so far). When I was in high school, the lowest students took "calculator math" as their highest math course, while the top students took calc AB, and programs such as pathways almost always end up catering to the lowest common denominator.

Also keep in mind that the first two years of US undergrad education is really more like high school math-wise in countries like England or France (I dont know Spain). I fear that this VA pathways thing lowers it even more so that college is the new high school for math.

[🦀🎂🦀🎂]

Great news.  Math is a pointless subject in the age of gadgetry and iPhones.    

...

[Former President tack50]

Great news.  Math is a pointless subject in the age of gadgetry and iPhones.    

I graduated from a public university in Virginia, and they had the right idea years ago.   For any non-STEM degree, the highest mathematics requirement is some BS-course like "Math for the Liberal Arts".  (read:  the "history" of numbers.  lol)

And I turned out pretty damn fantastic.  

Ironically, while I fully agree with your 2nd paragraph (in fact I'd get rid of math requirements at all if you studied something from the humanities!); calling math useless in the modern world is stupid, almost as saying that literature is useless in the era of Microsof Word.