Is algebra necessary?

[LaCroix]

Again, I have to say: a master's degree in mathematics, one which ends in a thesis paper on some mathematical theory, is quite simply 'overtraining' for a high school position. All it does is use up two or three years of the teacher's working life, without really teaching them anything they are ever going to pass on to their students.

This is not to say that teachers should not have degrees in mathematics or math-related fields. But anyone who comes out of college with a bachelor's in (say) mechanical engineering will probably have as much mathematical proficiency as they will ever find time to use when teaching high school. Making it a requirement that they then go on to get that master's in mathematics just uses up time and money pointlessly.

*snip*

The point I'm trying to make is that "has an M.S. in mathematics" is not well correlated with "is a good teacher." The only real advantage is that the master's weeds out a few marginally less intelligent people who somehow managed to get their bachelor's in math without going insane... but it doesn't prove that they're competent to teach. That comes from the pedagogy training, which is a separate qualification.

So I wouldn't assume that Austrian or Finnish teachers are better because they have master's in mathematics. If they're good with it they'd be good without it; if they're bad without it they'll still be bad with it. However mathematics is a bit unusual in this respect; in history or literature the argument for requiring a master's is a bit stronger.

You're missing the point here. The ABSOLUTELY DO NEED a master's in EDUCATION to become teachers. Which means they have to become experts on teaching before they are allowed to teach.

Also, most of Europe does see a bachelor's degree (which was only introduced here a couple of years ago, and not even everywhere), as more or less useless. It's seen as a cheap 'I know a little something about something' diploma that isn't worth much. Much akin to a diploma mill. Most of these will not even get accredited at a real university if you want to get a master's degree later.

[Raesene]

In Austria, teachers need to have 3 Master degrees. One in education, and two 'subject' master degrees. (Usually, math is paired with physics) Only elementary school teachers can get away with only a degree in education and a certificate to prove qualification.

Similar here, a teacher must have a master's degree in education in addition to the subject he teaches (at the high school level, in higher academics the requirements can be even more stringent). I forgot to put that in my previous post.

LaCroix, has the system changed? When I started university (I hasve to admit that was nearly 20 years ago), there were special curriculae for future teachers that merged the educational and their chosen subject into one masters course. Because they were not considered full courses (except natural sciences, and even that has changed) for most subjects, they had to choose a secondary subject so they were able to teach two later on.
A friend of mine who first studied chemistry and after his PhD decided to try to become a teacher chose history as his second subject and had to attend the edicational theory classes considered those a joke, because there was hardly any time devoted to them.

[LaCroix]

In Austria, teachers need to have 3 Master degrees. One in education, and two 'subject' master degrees. (Usually, math is paired with physics) Only elementary school teachers can get away with only a degree in education and a certificate to prove qualification.

Similar here, a teacher must have a master's degree in education in addition to the subject he teaches (at the high school level, in higher academics the requirements can be even more stringent). I forgot to put that in my previous post.

LaCroix, has the system changed? When I started university (I hasve to admit that was nearly 20 years ago), there were special curriculae for future teachers that merged the educational and their chosen subject into one masters course. Because they were not considered full courses (except natural sciences, and even that has changed) for most subjects, they had to choose a secondary subject so they were able to teach two later on.
A friend of mine who first studied chemistry and after his PhD decided to try to become a teacher chose history as his second subject and had to attend the edicational theory classes considered those a joke, because there was hardly any time devoted to them.

There seems to be something off with the info I had from the teachers I knew. You do have a massively reduced curricula, it seems, for the subject master's, which funnily correlates with the requirements Simon_Jester proposed.

You still close with a master's degree, Mag. rer. nat., though.

Source for the
http://studentpoint.univie.ac.at/filead ... ematik.pdf (sorry, german only, since it's Austrian University...)

[phongn]

So, looks like the math education in the US is ridiculously slowed down and spread out.

Back when I was in elementary and high school, algebra started on 7th grade. After 9th grade you either go to grades 10-12 or to vocational school. If you take the high school (grades 10-12) route, you can choose between long math (11 courses) or short math (7 courses). In the long math, you get more algebra and trigonometry and such in the first few courses, with more advanced calculus stuff toward the end. By the time you are through, you should be able to do derivations and basic integrals without any problems. Don't know why, but of those two I always found the integral side much easier.

For an example of what an accelerated sequence in the US might look like:

6: Discrete Mathematics
7: Algebra I
8: Geometry (proof-based)
9: Algebra II
10: Trigonometry/Pre-Calculus
11: Calculus I-II (AP Calculus BC)
12: Calculus III, Differential Equations (via local community college), optionally Statistics (AP Statistics)

I took a slower, lazier version of the above (11: Calculus I (AP AB), 12: Calculus I-II (AP BC)).

[Block]

My class structure was something like:
6th:Algebra I
7th:Algebra II
8th: Geometry
9th: Functions and Statistics
10th: Precalc
11th: Calc 1
12th: Math was optional but you could take calc2/3 AP or a couple other things if I remember right.

[Simon_Jester]

You're missing the point here. The ABSOLUTELY DO NEED a master's in EDUCATION to become teachers. Which means they have to become experts on teaching before they are allowed to teach.

...Excuse me, I seem to have made you angry by talking about something you didn't intend for me to talk about.

The typical background education for teachers in the US is a bachelor's degree (four year university course of study) in education, with extra courses corresponding to whatever particular area they plan to teach. Most teachers are expected to go on and get a master's degree in education within the first... five to ten years of their teaching career. This requires additional years of part time graduate study, often undertaken while actively teaching at the same time.

Degrees in the content area (mathematics, literature, science, and so on) are optional, although it is normal for a school system to require some number of credit-hours (courses) in the content area in addition to the education degrees.

Also, most of Europe does see a bachelor's degree (which was only introduced here a couple of years ago, and not even everywhere), as more or less useless. It's seen as a cheap 'I know a little something about something' diploma that isn't worth much. Much akin to a diploma mill. Most of these will not even get accredited at a real university if you want to get a master's degree later.

Excuse me, this seems to be a translation error more than anything else.

Is a European "bachelor's" a four year university degree? Because a bachelor's in the US is. And it can in fact reflect serious, important knowledge, and fitness to begin work in a technical field.

A master's is a graduate degree requiring additional work: two or three more years of it.

There are areas where the bachelor's is not enough (teaching at a university, scientific research, becoming a medical doctor). Or where you can get a bachelor's without having to work very hard or show exceptional intelligence. But those are matters of detail; a bachelor's in the US is decidedly not a junk degree in general, and obtaining a master's generally requires at least six to seven years in the university system- undergraduate and graduate studies.


Of course, school systems that find themselves having trouble getting enough teachers into the buildings may try other things. I, for example, am being hired on the strength of a master's degree in physics, recommendations by people who I worked for as a teaching assistant in graduate school, and some accelerated summer and night courses in teaching technique. Because the district is short on math teachers and they can be damn sure I know math.

It might not work- in which case they fire me after a year or two and replace me with another teacher. But it lets them cover a gap in that would otherwise leave them with a hundred or so algebra students and no one to teach them.

However, that's not the normal mechanism teachers come into the district through; people in my program only make up about 10% of this year's inductees.

LaCroix, has the system changed? When I started university (I hasve to admit that was nearly 20 years ago), there were special curriculae for future teachers that merged the educational and their chosen subject into one masters course. Because they were not considered full courses (except natural sciences, and even that has changed) for most subjects, they had to choose a secondary subject so they were able to teach two later on.
A friend of mine who first studied chemistry and after his PhD decided to try to become a teacher chose history as his second subject and had to attend the edicational theory classes considered those a joke, because there was hardly any time devoted to them.

This may also be a translation error. Just to avoid any confusion, in American English when talking about universities, a "course" is a single specific class on a single subject, such as "History of post-Meiji Japan" or "Introduction to Electrodynamics."

The overall set of classes one must take to earn a degree might be called a "program" or something along those lines.

[Terralthra]

You're missing the point here. The ABSOLUTELY DO NEED a master's in EDUCATION to become teachers. Which means they have to become experts on teaching before they are allowed to teach.

...Excuse me, I seem to have made you angry by talking about something you didn't intend for me to talk about.

The typical background education for teachers in the US is a bachelor's degree (four year university course of study) in education, with extra courses corresponding to whatever particular area they plan to teach. Most teachers are expected to go on and get a master's degree in education within the first... five to ten years of their teaching career. This requires additional years of part time graduate study, often undertaken while actively teaching at the same time.

Degrees in the content area (mathematics, literature, science, and so on) are optional, although it is normal for a school system to require some number of credit-hours (courses) in the content area in addition to the education degrees.

I don't know where you're getting this information, but it's inaccurate. Teaching requirements across the states are mandated by NCLB, but were largely standardized before then; middle and high school teachers must have a college or graduate degree in the content area they wish to teach (or equivalent knowledge through examination by the state board of education), and a teaching credential (which is functionally a 1.5 year post-grad program in pedagogy, not rising to the level of an MEd). Primary school instructors can get by with a BA in Education or Liberal Arts, but that's all.

I have already posted this information upthread; I'm not sure why you're ignoring that in favor of posting inaccurate information.

[Simon_Jester]

I'm sorry, I got mixed up by having program requirements for one of those weird alternative things on my mind, and having people yelling in my ear about them for eight hours a day.

Pardon the idiosyncracy.

[Danny Bhoy]

Lang and Lit were separate mandatory GCSEs, but that was in a grammar school in Dorset back in the 80s. Guess things have taken a step backward since then, no doubt in order to improve schools rankings in the ever so important score tables.

Could be a regional variation. There's about six different exam boards coming up with the curriculums for each subject, and Local Education Authorities can pick aned choose as they see fit. At any rate, Lang and Lit were only separate subjects at A-Level ten years ago when I was in school.

Back in the day 20+ years ago, GCE O Levels in S'pore (more or less equivalent to the British GCSEs of the day) already had separate English Lang and English Lit.

I find it interesting that in the US, the general rule is to start Trig at Grade 10 which if I'm correct is approximate to the year in which GCE O/GCSE exams are taken. In S'pore it would be taken at Grade 9 equivalent(?) for the so call Additional Maths to be tested at GCE O / GCSE level the following year. You would need this in order to progress to the normal A level Maths which included calculus (which I think it's still the case given that LSE as far as I know still has fairly stringent and specific calc requirements for their BSc Econs programmes). I don't know what the more advanced "Further Maths" would have included.

I'm a pretty shitferbrains as far as maths goes, never even making it to Trig, tho I did pretty ok at Algebra. Odd thing was that 10 years later, I damn near killed myself doing a Corporate Finance course at SAIS Summer School which obviously includes calc while juggling a day job. Got a B-, a fucking miracle I passed to begin with.

[LaCroix]

Is a European "bachelor's" a four year university degree? Because a bachelor's in the US is. And it can in fact reflect serious, important knowledge, and fitness to begin work in a technical field.

A master's is a graduate degree requiring additional work: two or three more years of it.

There are areas where the bachelor's is not enough (teaching at a university, scientific research, becoming a medical doctor). Or where you can get a bachelor's without having to work very hard or show exceptional intelligence. But those are matters of detail; a bachelor's in the US is decidedly not a junk degree in general, and obtaining a master's generally requires at least six to seven years in the university system- undergraduate and graduate studies.

It is the same, but bachelor's degrees were introduced only in the last decade (+/- a handful years), and a master's was the minimum degree until then. So it is still regarded as the "easy" way out...

[Raesene]

The new Bologna system for harmonizing higher education in Europe has three steps:

the Bachelor (usually 3 years)
the Master (about 2 more years after the Bachelor)
and the Doctorate (at least three more years)


IIRC, european studies are more focussed on the study topic than US ones, a student of mathematics would't have to take a any literature classes to get his degree. although I have seen that gender studies-classes have crept into the curriculae.

[Darth Wong]

The problems I had with algebra was that I just couldn't see the use of it in life during school.

I learned maths much faster than I would have otherwise due to writing computer games from age 7 onwards. However I ran into the same issue with some of the more advanced stuff (e.g. memorising the rules for integrating and differentiating trig functions - didn't see the point until I went to university and did a module on electrical distribution systems).

That said this particular article seems to be a standard-issue humanities academic insisting that their field is of fundamental importance and everything else is just tiresome technical jargon, fit only for a few masochistic geeks.

Part of the problem with math education is that people don't seem to realize that math is basically like learning another language. It is very much like a language, designed to communicate a very specific class of ideas. Recent math education ideas often revolve around trying to find more "natural language" ways to express math, which to me is like making a French class where the ideas are expressed in English.

In any case, regarding the OP, the argument for teaching math is the same as the argument for teaching anything else: to produce an adult with a well-rounded base of education. Those who teach the "arts and humanities" courses have been using this "well-rounded" line to justify vocationally unnecessary subjects for decades; why should it not apply to mathematics? If we can argue that truck drivers need to study history or English literature in school, why can't we argue that novelists need to take math? Why should the maths and sciences be justified only by direct vocational application, while other subjects meet a much lower bar?

[Simon_Jester]

The new Bologna system for harmonizing higher education in Europe has three steps:

the Bachelor (usually 3 years)
the Master (about 2 more years after the Bachelor)
and the Doctorate (at least three more years)

Which places the EU Bachelor's somewhere noticeably below the American Bachelor's, and the Master's somewhere noticeably above it. See? That explains everything.

IIRC, european studies are more focussed on the study topic than US ones, a student of mathematics would't have to take a any literature classes to get his degree. although I have seen that gender studies-classes have crept into the curriculae.

Tight focus doesn't really make it practical to compress a difficult university degree much, in my opinion. Putting very intense pressure on the students can let you do that, but that's not the same thing.

I would have deep misgivings about, say, trying to turn an American four-year Bachelor's in a rigorous program into a three-year degree by cutting out all the electives (like literature for mathematics students, or mathematics for literature students)

[houser2112]

Degrees in the content area (mathematics, literature, science, and so on) are optional, although it is normal for a school system to require some number of credit-hours (courses) in the content area in addition to the education degrees.

During an employment crisis I was having about 8 or 9 years ago, I considered trying to become a math teacher. The relevant governing body required a teaching cert plus 30 hours of math courses to achieve this.

Of course, school systems that find themselves having trouble getting enough teachers into the buildings may try other things. I, for example, am being hired on the strength of a master's degree in physics, recommendations by people who I worked for as a teaching assistant in graduate school, and some accelerated summer and night courses in teaching technique. Because the district is short on math teachers and they can be damn sure I know math.

I was trying to do the same in a district that was supposedly having difficulty keeping math teachers, on the strength of a BSEE. I would have to get the cert, which I anticipated; however, they refused to let any of my engineering courses contribute to the math credit hours requirement. As anybody knows, engineering degrees require more than enough math knowledge to teach high school students trig, algebra, or calculus, but because those courses weren't taught by the actual math department, they don't count. I guess they didn't need math teachers all that badly after all.

[Raesene]

The new Bologna system for harmonizing higher education in Europe has three steps:

the Bachelor (usually 3 years)
the Master (about 2 more years after the Bachelor)
and the Doctorate (at least three more years)

Which places the EU Bachelor's somewhere noticeably below the American Bachelor's, and the Master's somewhere noticeably above it. See? That explains everything.

IIRC, european studies are more focussed on the study topic than US ones, a student of mathematics would't have to take a any literature classes to get his degree. although I have seen that gender studies-classes have crept into the curriculae.

Tight focus doesn't really make it practical to compress a difficult university degree much, in my opinion. Putting very intense pressure on the students can let you do that, but that's not the same thing.

I would have deep misgivings about, say, trying to turn an American four-year Bachelor's in a rigorous program into a three-year degree by cutting out all the electives (like literature for mathematics students, or mathematics for literature students)

Our secondary education (14yrs +) takes 4-5 years, depending on the school, leading to graduation at 18 or 19.
Austrian students probably learnt these things during their high school education. We can't deselect courses like maths, German and English or natural sciences like US pupils can, repeating them at university would be unnecessary and detract from the primary field of study.

[Losonti Tokash]

Forgive me if I'm wrong, but are you under the impression that American students aren't required to study math, science, and language in secondary school? My school district requirements for graduation included 3 years each of math and science, 4 years of English, and at least 2 years of a foreign language. This all in Omaha, Nebraska, not a place widely known for its scholarly achievements and strict standards.

[Raesene]

Forgive me if I'm wrong, but are you under the impression that American students aren't required to study math, science, and language in secondary school? My school district requirements for graduation included 3 years each of math and science, 4 years of English, and at least 2 years of a foreign language. This all in Omaha, Nebraska, not a place widely known for its scholarly achievements and strict standards.

Not not at all, just not to the extent maybe (the sum of hours studied during the school career vary, too; I have to admit I forgot how many hours exactly we had each subject). I checked the Curriculum, edition 2004 (they reduced the number of hours and eliminated saturday as a school day with this revision).

The values are total school hours (each 50 minutes) per subject for 10-14 and 15-18 year olds in those four years. They don't have that many hours every year .
I omitted PE, Music, Religion/Ethics, Arts, Informatics, Knitting or Engineering classes, they fill up the numbers to 120 for 10-14 year olds and 130 for 15-18 year olds.

In total, the usual Realgymnasium pupil aged 10 to 14 has to have 16 hrs of German class, 14 hours primary foreign language (usually English), 14 hours Mathematics and 16 hours of Physics, Chemistry and Biology. History 6 hrs, Geography/Economy 7.

From 15-18 he has 12 hrs German, 12 hrs primary foreign language, 14 hrs mathematics, 21 or 25hrs Biology, Chemistry and Physics (those with 21 hrs endure 4 hrs Descriptive Geometry). History/Politics is worth 7 hrs, Psychology/Philosophy 4, Geography/Economy 7. Total number of mandatory hours is 122, with 8 more mandatory-elective hours where pupils can focus on their subjects of interest.

Depending on the school type, these numbers vary. The type more focused on languages reduces the hours of natural sciences and mathematics and gains one more language. The number of mandatory and elective-mandatory hours can vary +/- 2.

Study time and hours spent on homework are not included, as are any voluntary subjects (typewriting, sports, maths olympiad, etc.)

Edit:
At the end of their 8th year, there's Matura (in Germany Abitur): a comprehensive exam on the whole subject matter taught the whole eight years (in theory, usually it's just years 5-8) of Mathematics, German and one foreign language (in writing) and 4 more subjects chosen by each individual, either all oral or 1 more written and 3 oral. There's also the option to write a small semi-scientific paper to replace the voluntary written exam.



I half-remember some comment on the PISA test (a comparison test of european pupils) that Austrian students spent nearly the most time at school, but have poor results nevertheless. Our system seems to be lacking efficiency, unfortunately.

[Simon_Jester]

Point of order: how do you define an "hour?" One hour of classroom time for one quarter of one school year? One half of one school year?

[Broomstick]

Part of the problem with math education is that people don't seem to realize that math is basically like learning another language. It is very much like a language, designed to communicate a very specific class of ideas. Recent math education ideas often revolve around trying to find more "natural language" ways to express math, which to me is like making a French class where the ideas are expressed in English.

In any case, regarding the OP, the argument for teaching math is the same as the argument for teaching anything else: to produce an adult with a well-rounded base of education. Those who teach the "arts and humanities" courses have been using this "well-rounded" line to justify vocationally unnecessary subjects for decades; why should it not apply to mathematics? If we can argue that truck drivers need to study history or English literature in school, why can't we argue that novelists need to take math? Why should the maths and sciences be justified only by direct vocational application, while other subjects meet a much lower bar?

What you're talking about, Mike, is math literacy.

Where to draw the line? In comparison with language literacy, I doubt any of us think all students should be able to function on the level of professional writers in hard subjects. Most people just aren't going to function at that level unless all else is sacrificed and perhaps not even then. On the other hand, the average person should be able to read and write to level "X", and everyone else to level "Y" for minimal competence, and anyone below that is officially handicapped.

So what is absolutely essential math for modern living? It's not calculus - you can exist just fine without it outside of technical fields. Your average store clerk or dental hygienist or barber doesn't need it. Figure out what is truly essential and that's your minimum competence level (I'm pretty sure we all agree that includes addition, subtraction, multiplication, division, fractions, and decimals).

The next level up is optimizing for the average person (which is not the same as the average member of SD.net, I'd like to remind people). That's probably through what my school district called Algebra I, geometry, and trig. While some individuals may struggle with it most will, eventually, get it. How much beyond is essential I'm not sure - some elementary knowledge of statistics is useful, for example, and knowing the difference between linear, geometric, and exponential progressions (which some might consider beginning algebra and others not). The distinction here is that while this is not essential math knowledge the average person will find it at least occasionally useful outside of technical/mathematical fields.

Then there's the stuff useful for those in math/science/engineering but will likely never be used by the people outside of those fields. Which is not to say some of them wouldn't be interested - I have a sister who took some very advanced math just because she found it interesting, not because it was required for her degree. Good for her.

[Blayne]

My only problem with the optimization line of thought is that I out of personal experience ended up wasting about two years of time because I wasn't taught properly or offered the Math courses I would eventually need to apply to University level Computer Science, a lot of young people decide "I don't need this, I'm going to do Y for a living" and how many ending up changing their minds and wasting a lot of time and money? From what I remember from recently taking Calculus I & II, Linear Algebra and College Algebra, I think all of these could in various forms be taught as early as high school with the right motivation if cleverly snuck into the curriculem.

Basic derivitives, completing the square, row reduction all of these are extremely formal and formula based you just have to be careful in how you teach it.

[Simon_Jester]

They could certainly be taught to some people, but remember the conditions. "You just have to be careful in how you teach it-" does this mean only the best 25% of math teachers can do it? Are they now assigned solely to teach those classes, at the expense of having these good teachers available for more routine subjects?

Manpower is a very serious issue in education.

At some point, you have to strike a balance between what must be taught to everyone (which takes a lot of manpower) versus what could profitably be taught to the 20% of the population who just happen to be the ones most likely to pick it up in college anyway.

If we're going to teach people more math, we have to come at the problem from the other end of the scale- first figure out how to routinely compress 3rd through 8th grade math into 3rd through 6th grade. Then figure out what you want to teach in the two years this frees up at the end of high school.

[Darth Wong]

What you're talking about, Mike, is math literacy.

Where to draw the line? In comparison with language literacy, I doubt any of us think all students should be able to function on the level of professional writers in hard subjects. Most people just aren't going to function at that level unless all else is sacrificed and perhaps not even then. On the other, the average person should be able to read and write to level "X", and everyone else to level "Y" for minimal competence, and anyone below that is officially handicapped.

And yet, we do not consider "barely functional English literacy" to be an acceptable standard for education. It has long been accepted that, in order to earn a high school diploma, one should exceed that low standard.

So what is absolutely essential math for modern living? It's not calculus - you can exist just fine without it outside of technical fields. Your average store clerk or dental hygienist or barber doesn't need it. Figure out what is truly essential and that's your minimum competence level (I'm pretty sure we all agree that includes addition, subtraction, multiplication, division, fractions, and decimals).

Again, taking this back to English, no one would seriously walk into a school board meeting and ask "what is absolutely essential English for modern living". It's universally assumed that you want to handily beat that standard, even for the (ahem) more challenged students.

The next level up is optimizing for the average person (which is not the same as the average member of SD.net, I'd like to remind people). That's probably through what my school district called Algebra I, geometry, and trig. While some individuals may struggle with it most will, eventually, get it. How much beyond is essential I'm not sure - some elementary knowledge of statistics is useful, for example, and knowing the difference between linear, geometric, and exponential progressions (which some might consider beginning algebra and others not). The distinction here is that while this is not essential math knowledge the average person will find it at least occasionally useful outside of technical/mathematical fields.

Then there's the stuff useful for those in math/science/engineering but will likely never be used by the people outside of those fields. Which is not to say some of them wouldn't be interested - I have a sister who took some very advanced math just because she found it interesting, not because it was required for her degree. Good for her.

Those categories are fair enough, but I still have to ask why the lower category would be acceptable for anything other than "you are learning-disabled". We would never accept such an incredibly low standard for English; why should we accept it for math? Can you imagine someone walking into a school board meeting and seriously arguing that if someone can read street signs and the instructions on a PFD, then that should be considered an adequate baseline?

[Simon_Jester]

What you're talking about, Mike, is math literacy.

Where to draw the line? In comparison with language literacy, I doubt any of us think all students should be able to function on the level of professional writers in hard subjects. Most people just aren't going to function at that level unless all else is sacrificed and perhaps not even then. On the other, the average person should be able to read and write to level "X", and everyone else to level "Y" for minimal competence, and anyone below that is officially handicapped.

And yet, we do not consider "barely functional English literacy" to be an acceptable standard for education. It has long been accepted that, in order to earn a high school diploma, one should exceed that low standard.

So what is absolutely essential math for modern living? It's not calculus - you can exist just fine without it outside of technical fields. Your average store clerk or dental hygienist or barber doesn't need it. Figure out what is truly essential and that's your minimum competence level (I'm pretty sure we all agree that includes addition, subtraction, multiplication, division, fractions, and decimals).

Again, taking this back to English, no one would seriously walk into a school board meeting and ask "what is absolutely essential English for modern living". It's universally assumed that you want to handily beat that standard, even for the (ahem) more challenged students.

And yet a lot of effort goes into making sure students stay at or near grade level in the grades where they get that.

I live in Maryland; here, the main test students must pass in math proficiency to graduate from high school stops at algebra. You have to take more courses than that, and pass them- but in my own county, scraping by with a C in geometry and leaving it at that would be considered 'enough.'

I don't particularly like that, and it certainly wouldn't get you anywhere near ready to graduate from college. But trying to push everyone up through trigonometry and complex numbers takes raw numbers that my county is having trouble finding. You can counter that by increasing class sizes, but that means the kids aren't getting the same quality of education at the low levels. Or, well. Hire more teachers? From where? For how much? The system is broke, and since it's being funded largely from local tax revenues, even fixing the federal tax system wouldn't help much.


No Child Left Behind is not helping, because of the way it demands ever-rising 'proficiency' on exams (up to 100% in 2014, theoretically) and punishes schools that don't make the curve. There's huge pressure to make all children adequate in mathematics. You can lose your job if your school doesn't cover algebra adequately. But no one gets fired if your school doesn't do a good job with precalculus.

Perverse incentive structure, in other words. Creating a tight link between the survival of a school and their test scores means that schools spend all their resources making as certain as possible that they can meet the quotas for test scores. This is good for education at the low end, but bad at the high end which gets starved of resources.

You may find this counterintuitive, depending on how you feel about the high-stakes testing movement in the US.

Those categories are fair enough, but I still have to ask why the lower category would be acceptable for anything other than "you are learning-disabled". We would never accept such an incredibly low standard for English; why should we accept it for math? Can you imagine someone walking into a school board meeting and seriously arguing that if someone can read street signs and the instructions on a PFD, then that should be considered an adequate baseline?

Looking at demographics, something like 10% of the population is learning-disabled, probably more.

Another slice, and I'd bet on them being well over 10%, are badly alienated from education- by bad teachers, bad parenting, or grinding poverty. And that guess might even be optimistic. Getting those kids up to par is extremely difficult. How much money are you willing to throw at that? What opportunity costs are you willing to accept?

[Terralthra]

Those categories are fair enough, but I still have to ask why the lower category would be acceptable for anything other than "you are learning-disabled". We would never accept such an incredibly low standard for English; why should we accept it for math? Can you imagine someone walking into a school board meeting and seriously arguing that if someone can read street signs and the instructions on a PFD, then that should be considered an adequate baseline?

Looking at demographics, something like 10% of the population is learning-disabled, probably more.

Another slice, and I'd bet on them being well over 10%, are badly alienated from education- by bad teachers, bad parenting, or grinding poverty. And that guess might even be optimistic. Getting those kids up to par is extremely difficult. How much money are you willing to throw at that? What opportunity costs are you willing to accept?

I don't think he's saying all kids need to be brought up to par, regardless of developmental disability, alienation from school, etc. He's saying that if they can't, they shouldn't be given a high school diploma.

[Darth Wong]

Precisely. I don't know where the hell Simon got the idea that I was thinking it should be possible to take the shittiest 10% of students and make them proficient in trigonometry. I certainly never said anything of the sort. I was just saying that we shouldn't grant a high school diploma to students who cannot demonstrate a well-rounded base of comprehension. What the hell does a diploma even mean, if we make it possible for even the worst students to get one?

I know, I know, it might not be their "fault". Maybe it's their socioeconomic class. Well that's very sad and we need better social programs to solve those problems, but you can't solve the problems of class or race or wealth in this society by pretending that everything is fine, and that's what these watered-down high school diplomas do.

When you downgrade the requirements of a high school diploma in order to make sure everyone gets one, then you make a high school diploma nothing more than a worthless piece of paper. This is precisely what we've been doing to ourselves, and it doesn't help anyone. It devalues the diploma for those who deserve one, and it grants a worthless diploma to those who don't deserve one. How does that help anyone?