The fact is this is just totally false. There are a million teachers in the U.S. trying a thousand different teaching techniques and no one has any better than about a half success rate. Yes homework, no homework, personal drills, group work, project-oriented, detailed writing exercises, exploratory work, no one can make a dent in the success rate. (My intimate familiarity is the fact that all across this country, 2/3 of community college students need remedial algebra, and 2/3 will never-ever pass it. Even with hundreds of research projects every year, no one's significantly improved on this.)
There should be a Millenium/Randi-style million-dollar prize for anyone who claims that everyone can learn algebra or programming, because it simply isn't true.
"The Kantian philosophical argument for preventing cruelty to animals is that our actions towards non-humans reflect our morality — if we treat animals in inhumane ways, we become inhumane persons. This logically extends to the treatment of robotic companions."
Is Kant's argument actually the basis for why our society recognizes some rights of animals? Probably not. Thank you for overlooking the far more compelling arguments of Descartes, Locke, Rousseau, Bentham, Martin, Schopenhauer, Darwin, Cobbe, Kingsford, Mill, Salt, Lind, etc.
This kind of thinking is basically Stockholm Syndrome writ very large.
Let's say you asked people a thousand years ago, "Would you want to live with a king?". I'm sure the vast majority would have said "no", and come up with a bunch of reasons why that would be personally undesirable and socially perilous. The reasoning is so transparently irrational it's ludicrous.
"Note that this is not for backing up and restoring data you need to have available on a live basis. This is for truly *archive* data--data you don't need on a day-to-day basis but might need to retrieve in special cases. It will not, generally speaking, be a backup at all; it's your primary store of this data."
But doesn't that seem like an inherent problem? I can see outsourced, online storage as one redundant element in a backup system; but trusting it as a primary store of data, not so much.
Except that that is not actually correct. It's learning to manipulate the symbols of one particular branch of maths. You can do plenty of maths without arithemtic and percentages. In fact it won't help with geopetry for instance. Or boolean logic (I used to love messing around with logic gates when I was a kid. I never thought of it as maths, but it is). I'm not denying that being able to work with numbers is useful, and understanding percentages is handy, but that is not what much of maths is about.
Saying that numbers are "the symbols of one particular branch of maths" is pretty much the total opposite of their actual status. Numbers are everywhere except for limited niche purposes. It's necessary for any writing or applications in the modern world, like calculus, probability, statistics, etc. Logic is a prerequisite to math but not included in math (e.g., where I went to school it was taught in the philosophy department). Geometry, your example, was initiated by concerns of length, area, volume, etc.
I, personally think you have disproven yourself with that claim. You were already fluent by year 7. You could already happily write new stories. You didn't have to be drilled in the minutae of sentance structure to do those things. Likewise, you don't have to have memorised massive multiplication tables to do geometry or understand or probe Pythagorus's theorem. In fact, Pythagorus proved it before algebra or positional number systems even existed.
You can achieve a novice-level of functionality at a natural language; to go further, to engage in conversations on how to debug pieces of writing, to be understood without expecting others to spend great effort filling in your gaps, you need to understand the grammar of the language. (As an aside, you've got at least 9 misspellings in the piece of text I've quoted from you so far.)
Your facts about Pythagoras are, like, way off. Positional number systems (using 60's as on our clocks and angle measurements) were used in ancient Babylon (~3000 BC) thousands of years before Pythagoras (~500 BC); in fact, Babylonian tablets exist showing the values for Pythagorean triples all those centuries earlier. Other comments on Pythagoras: (1) The Pythagorean theorem is fundamentally about a notion of area; if you don't understand that as a quantity I can't imagine how the theorem is meaningful; (2) if you want to work on the Pythagorean theorem as he did, in words and without algebraic symbols, be my guest, but it's so immensely inefficient you'll spend your whole life and no one else will be able to communicate with you; and (3) the Pythagoreans were deeply interested in issues of number -- in fact, their entire philosophy revolved around it, and their single most earth-shaking discovery was that a certain triangle must have an irrationally-valued side:
"In ancient Greece the Pythagoreans considered the role of numbers in geometry. However, the discovery of incommensurable lengths, which contradicted their philosophical views, made them abandon abstract numbers in favor of concrete geometric quantities, such as length and area of figures. Numbers were reintroduced into geometry in the form of coordinates by Descartes, who realized that the study of geometric shapes can be facilitated by their algebraic representation, and whom the Cartesian plane is named after. Analytic geometry applies methods of algebra to geometric questions, typically by relating geometric curves and algebraic equations. These ideas played a key role in the development of calculus in the 17th century and led to discovery of many new properties of plane curves. Modern algebraic geometry considers similar questions on a vastly more abstract level."
I worked in video games and yes: logic, discrete math, linear algebra are all musts.
More importantly, as a current math teacher it's literally freaked me out in the past few weeks how many former high school classmates have gotten in touch with me and all said something very similar along the lines of, "I really wish I knew more math; it's holding me back at my job that I don't know more; I have to hire people to do this job for me". In the past few weeks, they have been: an Artist, a Photographer, a Business Web Developer, a History teacher, etc.
FTA -- "Are the results the product of chance? To address this question, Dunning calculated the p-value for each font. Grossly simplified, the p-value is an assessment of the likelihood that the particular effect we are looking at (e.g., the effect produced by Baskerville) is a result of a meaningless coincidence. [10] The p-value for Baskerville is 0.0068 [snip explanation of P-values]... The conservative approach is to divide 5 percent by the number of tests. Thus, the p-value to dismiss chance falls to 0.0083."
While being a bit unclear on what's being tested or how (no stated null hypothesis, etc.; not surprising for the mass-media New York Times), the thing that's really sketchy is how this comes after this arbitrary weighting of "strong agree" as +5, "strong disagree" as -5, etc., generating single scores for each font which are wildly more divergent that the initial raw agreement bar-charts. I suspect that if P-values are allegedly being computed for these decorated scores, then the results would be invalid (I'd love to know what statistical test he thinks can be run on arbitrarily mangled scores like that).
Let's run a two-proportions z-test on this data -- I'm looking at Weiss Introductory Statistics, Procedure 12.3, but you can also see the procedure here. The hypotheses are Ho: Baskerville has the same proportion in agreement as other fonts, versus Ha: Baskerville has a different proportion in agreement from other fonts; this is a two-tailed test, since we didn't know in advance whether it should be higher or lower. For Baskerville x1=4703 (number agreeing), n1 = 7536 (total number surveyed), so p1^ = 0.624 (sample proportion agreeing); for other fonts x2 = 23265, n2 = 37988, p2^ = 0.612. The pooled proportion is pp^ = (x1+x2)/(n1+n2) = 0.614. The standard error is SEE = sqrt(pp^(1-pp^)*(1/n1 + 1/n2)) = 0.00793. So the test-statistic z-score is z = (p1-p2)/SE = 1.47. And the P-value for a two-tailed test is P = 2*F(-|z|) = 2(0.0708) = 0.1416 (this last from a table lookup).
In conclusion: While the article claims a P-value of 0.0068, and that we should require a P-value of less than 0.0083 to indicate strong evidence for the article's hypothesis, when I do a simple proportion test, the P-value is actually much higher: P = 0.1416. In my book this is interpreted as "weak or no evidence" -- obviously much higher than the customary 5% cutoff, even ignoring the need to divide by the number of tests. So it appears that we do not have statistically significant evidence for the article's findings.
"Most people can realize what can be automated. That's why most people don't like repetitive tasks, that they know could be automated. That's how a lot of so called progress has happened."
My experience is exactly the opposite. When I'm in an intro computer course and say, "If you ever find yourself doing a repetitive task on a computer, then you're using it wrong; try to find a hotkey, or a script, or a batch process, or think if you can program something to do it instead", they look at me like I have two heads. I think most people are comforted by repetitive tasks and feel confident and secure with them.
Universities do not and should not be teaching foreign languages. They teach reading, the general practice. They teach the theory behind writing. They teach grammar. But they don't teach "French" or "German".... oh wait, no, the opposite is true, I wonder why that is?
"I read both trilogies and will get around to reading the third eventually."
I've read the first two trilogies many times. I read the first book of the later series and the writing and plot was so shockingly awful it was like biting into a rotten egg.
Still Images, Audio Recordings, Video, and Related Computer Files
NASA still images; audio files; video; and computer files used in the rendition of 3-dimensional models, such as texture maps and polygon data in any format, generally are not copyrighted. You may use NASA imagery, video, audio, and data files used for the rendition of 3-dimensional models for educational or informational purposes, including photo collections, textbooks, public exhibits, computer graphical simulations and Internet Web pages. This general permission extends to personal Web pages.
"What do you find most annoying or gratifying about Firefox these days?"
The most annoying thing is that I'm stuck with a yellow "Some plugins used by this page are out of date" warning bar at the top of Firefox at all times. Reason: I've got Flash 10.1, which is identified as out-of-date, but I'm running Firefox on Windows 2000, for which no newer version of Flash exists. There is no way to just shut off these warnings that I've been able to find. So, that's quite annoying.
FTA: "For example, it seems that indicators of corruption increase and political cooperation unravels when a period of instability or violence is imminent."
Why do articles like this act as though "violent acts" were the essential force, and "corruption" some kind of indicator symptom? I submit that the latter is the cause and the former the resulting symptom.
The article includes this viewpoint, but you have to get all the way to the very last paragraph to see it -- "But perhaps revolution is the best, if not the only, remedy for severe social stresses. Gintis points out that he is old enough to have taken part in the most recent period of turbulence in the United States, which helped to secure civil rights for women and black people. Elites have been known to give power back to the majority, he says, but only under duress, to help restore order after a period of turmoil. “I'm not afraid of uprisings,” he says. “That's why we are where we are.”"
My interpretation: Social politeness did not spring up out of nowhere accidentally. There are good reasons for it. One is: The expected value to myself, if I were to correct some total stranger -- and risk their displeasure, argumentation, lost time, possible hostility -- is pretty much nil.
What do I care if some doofus loudmouth on the bus, or a convenience store, or a random psychological experiment I got thrown in, thinks they're funny or has nutjob political or religious beliefs? The chance of my opinion changing them is close to zero. Aside from that, the time and hassle expense to my day is probably significant; the chance of their reacting in a defensive and hostile manner is pretty high. Aside from that, my chance of running into them again ever in my life, such that I receive some later benefit is also nil. Hence the politeness protocol of smiling noncommittally and getting the hell away from them.
(Side issue: I've never understand "road age" of the ilk "I'll teach that bastard a lesson!". Given someone that cuts you off, you'll never see them again, so any lesson you could conceivably give won't generate you any benefit. Let 'em go and maximize your distance from the crazies.)
Now, if someone is being truly irrational and is an intimate of yours, such that you have to deal with them all the time, then the equation changes; being honest with them will hopefully improve your mutual relationship and time spent together. Conjecture -- Perhaps a society which increases mobility, depersonalization, and time spent with strangers has a propensity to become more and more dishonest and delusional.
Actually he does say, "I say this as a writer and social scientist whose work relies heavily on the use of numbers." I read this as meaning he has to use statistics and its prerequisite of algebra. He just assumes every other profession (historians, doctors, artists, etc.) are a bunch of neanderthal trench-diggers who probably aren't really doing anything sophisticated.
I very much disagree with Lockhart's renowned piece. Let's just stick with the subject of algebra (as identified in the NY Times article today). Yes, the vast majority of community college students (for example) fail out due to inability to pass this one subject.
From my perspective, the analogy is this: Basic numerical handling (decimals, percents) is just learning the symbols of math, equivalent to letters of the alphabet. Basic algebra (variables, order of operations, relations of operations, being able using a formula) is equivalent to the grammar of math, very similar to when I took 7th grade English and was drilled on identifying parts of speech, diagramming sentences, etc. You need this stuff before you can even read any useful modern anything, before you can have a conversation about anything interesting mathematically. I don't see any way to teach letters-of-the-alphabet (number notation) or grammatical-sentence-structure (algebraic variables & operational relations) that can usefully pretend to be discovering this stuff for the first time or training people to be researchers. The notation really is arbitrary, and simply has to be learned and cemented before meaningful literature/conversations (math) can take place. It is this level that Prof. Hacker is disputing as necessary; the one thing he's right about is that the majority of our fellow citizens are demonstrably unable to succeed at it today.
Likewise, my girlfriend is currently learning Chinese for the first time. She simply has to spend hours every week learning new vocal tones, vocabulary, and drilling writing characters over and over again to ingrain them. It's simply fallacious to pretend that it's unnecessary to do the grunt work of initially learning new (and arbitrary) symbols and structure for any new language.
Slashdot Mirror
"Almost anyone can grasp algebra 1"
The fact is this is just totally false. There are a million teachers in the U.S. trying a thousand different teaching techniques and no one has any better than about a half success rate. Yes homework, no homework, personal drills, group work, project-oriented, detailed writing exercises, exploratory work, no one can make a dent in the success rate. (My intimate familiarity is the fact that all across this country, 2/3 of community college students need remedial algebra, and 2/3 will never-ever pass it. Even with hundreds of research projects every year, no one's significantly improved on this.)
There should be a Millenium/Randi-style million-dollar prize for anyone who claims that everyone can learn algebra or programming, because it simply isn't true.
"Fact: The answer to every rhetorical question is 'yes'".
That's the after-comic to this SMBS strip: http://www.smbc-comics.com/index.php?db=comics&id=2708
And I would say the same for human infants undergoing circumcision.
"If our system doesn't change we are gonna have ever growing masses of poor and unemployed and that is when things traditionally get nasty."
No problem, the automatic security drones will take care of that for you.
"The Kantian philosophical argument for preventing cruelty to animals is that our actions towards non-humans reflect our morality — if we treat animals in inhumane ways, we become inhumane persons. This logically extends to the treatment of robotic companions."
Is Kant's argument actually the basis for why our society recognizes some rights of animals? Probably not. Thank you for overlooking the far more compelling arguments of Descartes, Locke, Rousseau, Bentham, Martin, Schopenhauer, Darwin, Cobbe, Kingsford, Mill, Salt, Lind, etc.
Immanuel Kant was an old pissant, etc., etc.
"without a king", that is.
This kind of thinking is basically Stockholm Syndrome writ very large.
Let's say you asked people a thousand years ago, "Would you want to live with a king?". I'm sure the vast majority would have said "no", and come up with a bunch of reasons why that would be personally undesirable and socially perilous. The reasoning is so transparently irrational it's ludicrous.
"Note that this is not for backing up and restoring data you need to have available on a live basis. This is for truly *archive* data--data you don't need on a day-to-day basis but might need to retrieve in special cases. It will not, generally speaking, be a backup at all; it's your primary store of this data."
But doesn't that seem like an inherent problem? I can see outsourced, online storage as one redundant element in a backup system; but trusting it as a primary store of data, not so much.
"Is personal liberty the inevitable victim of advanced civilization?"
I kind of think so, yes. Not to the degree it's being victimized right now (drug war), though.
"After all, there are a lot of examples of 'experts' who got it completely wrong in the past."
That's a good example of survivor bias.
Except that that is not actually correct. It's learning to manipulate the symbols of one particular branch of maths. You can do plenty of maths without arithemtic and percentages. In fact it won't help with geopetry for instance. Or boolean logic (I used to love messing around with logic gates when I was a kid. I never thought of it as maths, but it is). I'm not denying that being able to work with numbers is useful, and understanding percentages is handy, but that is not what much of maths is about.
Saying that numbers are "the symbols of one particular branch of maths" is pretty much the total opposite of their actual status. Numbers are everywhere except for limited niche purposes. It's necessary for any writing or applications in the modern world, like calculus, probability, statistics, etc. Logic is a prerequisite to math but not included in math (e.g., where I went to school it was taught in the philosophy department). Geometry, your example, was initiated by concerns of length, area, volume, etc.
I, personally think you have disproven yourself with that claim. You were already fluent by year 7. You could already happily write new stories. You didn't have to be drilled in the minutae of sentance structure to do those things. Likewise, you don't have to have memorised massive multiplication tables to do geometry or understand or probe Pythagorus's theorem. In fact, Pythagorus proved it before algebra or positional number systems even existed.
You can achieve a novice-level of functionality at a natural language; to go further, to engage in conversations on how to debug pieces of writing, to be understood without expecting others to spend great effort filling in your gaps, you need to understand the grammar of the language. (As an aside, you've got at least 9 misspellings in the piece of text I've quoted from you so far.)
Your facts about Pythagoras are, like, way off. Positional number systems (using 60's as on our clocks and angle measurements) were used in ancient Babylon (~3000 BC) thousands of years before Pythagoras (~500 BC); in fact, Babylonian tablets exist showing the values for Pythagorean triples all those centuries earlier. Other comments on Pythagoras: (1) The Pythagorean theorem is fundamentally about a notion of area; if you don't understand that as a quantity I can't imagine how the theorem is meaningful; (2) if you want to work on the Pythagorean theorem as he did, in words and without algebraic symbols, be my guest, but it's so immensely inefficient you'll spend your whole life and no one else will be able to communicate with you; and (3) the Pythagoreans were deeply interested in issues of number -- in fact, their entire philosophy revolved around it, and their single most earth-shaking discovery was that a certain triangle must have an irrationally-valued side:
"In ancient Greece the Pythagoreans considered the role of numbers in geometry. However, the discovery of incommensurable lengths, which contradicted their philosophical views, made them abandon abstract numbers in favor of concrete geometric quantities, such as length and area of figures. Numbers were reintroduced into geometry in the form of coordinates by Descartes, who realized that the study of geometric shapes can be facilitated by their algebraic representation, and whom the Cartesian plane is named after. Analytic geometry applies methods of algebra to geometric questions, typically by relating geometric curves and algebraic equations. These ideas played a key role in the development of calculus in the 17th century and led to discovery of many new properties of plane curves. Modern algebraic geometry considers similar questions on a vastly more abstract level."
http://en.wikipedia.org/wiki/Geometry#Numbers_in_geometry
I worked in video games and yes: logic, discrete math, linear algebra are all musts.
More importantly, as a current math teacher it's literally freaked me out in the past few weeks how many former high school classmates have gotten in touch with me and all said something very similar along the lines of, "I really wish I knew more math; it's holding me back at my job that I don't know more; I have to hire people to do this job for me". In the past few weeks, they have been: an Artist, a Photographer, a Business Web Developer, a History teacher, etc.
FTA -- "Are the results the product of chance? To address this question, Dunning calculated the p-value for each font. Grossly simplified, the p-value is an assessment of the likelihood that the particular effect we are looking at (e.g., the effect produced by Baskerville) is a result of a meaningless coincidence. [10] The p-value for Baskerville is 0.0068 [snip explanation of P-values]... The conservative approach is to divide 5 percent by the number of tests. Thus, the p-value to dismiss chance falls to 0.0083."
While being a bit unclear on what's being tested or how (no stated null hypothesis, etc.; not surprising for the mass-media New York Times), the thing that's really sketchy is how this comes after this arbitrary weighting of "strong agree" as +5, "strong disagree" as -5, etc., generating single scores for each font which are wildly more divergent that the initial raw agreement bar-charts. I suspect that if P-values are allegedly being computed for these decorated scores, then the results would be invalid (I'd love to know what statistical test he thinks can be run on arbitrarily mangled scores like that).
Let's run a two-proportions z-test on this data -- I'm looking at Weiss Introductory Statistics, Procedure 12.3, but you can also see the procedure here. The hypotheses are Ho: Baskerville has the same proportion in agreement as other fonts, versus Ha: Baskerville has a different proportion in agreement from other fonts; this is a two-tailed test, since we didn't know in advance whether it should be higher or lower. For Baskerville x1=4703 (number agreeing), n1 = 7536 (total number surveyed), so p1^ = 0.624 (sample proportion agreeing); for other fonts x2 = 23265, n2 = 37988, p2^ = 0.612. The pooled proportion is pp^ = (x1+x2)/(n1+n2) = 0.614. The standard error is SEE = sqrt(pp^(1-pp^)*(1/n1 + 1/n2)) = 0.00793. So the test-statistic z-score is z = (p1-p2)/SE = 1.47. And the P-value for a two-tailed test is P = 2*F(-|z|) = 2(0.0708) = 0.1416 (this last from a table lookup).
In conclusion: While the article claims a P-value of 0.0068, and that we should require a P-value of less than 0.0083 to indicate strong evidence for the article's hypothesis, when I do a simple proportion test, the P-value is actually much higher: P = 0.1416. In my book this is interpreted as "weak or no evidence" -- obviously much higher than the customary 5% cutoff, even ignoring the need to divide by the number of tests. So it appears that we do not have statistically significant evidence for the article's findings.
"If you work daily and pay your bills you are a civilian..."
Thank you for the seed of a capitalist dystopia sci-fi story. Let's hope we never actually get there.
"Most people can realize what can be automated. That's why most people don't like repetitive tasks, that they know could be automated. That's how a lot of so called progress has happened."
My experience is exactly the opposite. When I'm in an intro computer course and say, "If you ever find yourself doing a repetitive task on a computer, then you're using it wrong; try to find a hotkey, or a script, or a batch process, or think if you can program something to do it instead", they look at me like I have two heads. I think most people are comforted by repetitive tasks and feel confident and secure with them.
Universities do not and should not be teaching foreign languages. They teach reading, the general practice. They teach the theory behind writing. They teach grammar. But they don't teach "French" or "German".... oh wait, no, the opposite is true, I wonder why that is?
"Ya you basically learn two throw away languages, but then can learn two useful languages withount too much trouble."
Apparently their policy is also to not teach a specific language like English, eh?
"I read both trilogies and will get around to reading the third eventually."
I've read the first two trilogies many times. I read the first book of the later series and the writing and plot was so shockingly awful it was like biting into a rotten egg.
Low-key, and yet just deeply terrified me. Seemed pretty concrete and realistic. It's all downhill. Every hope is dashed.
Using NASA Imagery and Linking to NASA Web Sites
Still Images, Audio Recordings, Video, and Related Computer Files
NASA still images; audio files; video; and computer files used in the rendition of 3-dimensional models, such as texture maps and polygon data in any format, generally are not copyrighted. You may use NASA imagery, video, audio, and data files used for the rendition of 3-dimensional models for educational or informational purposes, including photo collections, textbooks, public exhibits, computer graphical simulations and Internet Web pages. This general permission extends to personal Web pages.
http://www.nasa.gov/audience/formedia/features/MP_Photo_Guidelines.html
"What do you find most annoying or gratifying about Firefox these days?"
The most annoying thing is that I'm stuck with a yellow "Some plugins used by this page are out of date" warning bar at the top of Firefox at all times. Reason: I've got Flash 10.1, which is identified as out-of-date, but I'm running Firefox on Windows 2000, for which no newer version of Flash exists. There is no way to just shut off these warnings that I've been able to find. So, that's quite annoying.
FTA: "For example, it seems that indicators of corruption increase and political cooperation unravels when a period of instability or violence is imminent."
Why do articles like this act as though "violent acts" were the essential force, and "corruption" some kind of indicator symptom? I submit that the latter is the cause and the former the resulting symptom.
The article includes this viewpoint, but you have to get all the way to the very last paragraph to see it -- "But perhaps revolution is the best, if not the only, remedy for severe social stresses. Gintis points out that he is old enough to have taken part in the most recent period of turbulence in the United States, which helped to secure civil rights for women and black people. Elites have been known to give power back to the majority, he says, but only under duress, to help restore order after a period of turmoil. “I'm not afraid of uprisings,” he says. “That's why we are where we are.”"
My interpretation: Social politeness did not spring up out of nowhere accidentally. There are good reasons for it. One is: The expected value to myself, if I were to correct some total stranger -- and risk their displeasure, argumentation, lost time, possible hostility -- is pretty much nil.
What do I care if some doofus loudmouth on the bus, or a convenience store, or a random psychological experiment I got thrown in, thinks they're funny or has nutjob political or religious beliefs? The chance of my opinion changing them is close to zero. Aside from that, the time and hassle expense to my day is probably significant; the chance of their reacting in a defensive and hostile manner is pretty high. Aside from that, my chance of running into them again ever in my life, such that I receive some later benefit is also nil. Hence the politeness protocol of smiling noncommittally and getting the hell away from them.
(Side issue: I've never understand "road age" of the ilk "I'll teach that bastard a lesson!". Given someone that cuts you off, you'll never see them again, so any lesson you could conceivably give won't generate you any benefit. Let 'em go and maximize your distance from the crazies.)
Now, if someone is being truly irrational and is an intimate of yours, such that you have to deal with them all the time, then the equation changes; being honest with them will hopefully improve your mutual relationship and time spent together. Conjecture -- Perhaps a society which increases mobility, depersonalization, and time spent with strangers has a propensity to become more and more dishonest and delusional.
In my defense, I voted for not-Obama in the 2008 primary. But that's useful added detail, thank you.
Actually he does say, "I say this as a writer and social scientist whose work relies heavily on the use of numbers." I read this as meaning he has to use statistics and its prerequisite of algebra. He just assumes every other profession (historians, doctors, artists, etc.) are a bunch of neanderthal trench-diggers who probably aren't really doing anything sophisticated.
P.S. "professor emeritus" = old senile dude (IME)
I very much disagree with Lockhart's renowned piece. Let's just stick with the subject of algebra (as identified in the NY Times article today). Yes, the vast majority of community college students (for example) fail out due to inability to pass this one subject.
From my perspective, the analogy is this: Basic numerical handling (decimals, percents) is just learning the symbols of math, equivalent to letters of the alphabet. Basic algebra (variables, order of operations, relations of operations, being able using a formula) is equivalent to the grammar of math, very similar to when I took 7th grade English and was drilled on identifying parts of speech, diagramming sentences, etc. You need this stuff before you can even read any useful modern anything, before you can have a conversation about anything interesting mathematically. I don't see any way to teach letters-of-the-alphabet (number notation) or grammatical-sentence-structure (algebraic variables & operational relations) that can usefully pretend to be discovering this stuff for the first time or training people to be researchers. The notation really is arbitrary, and simply has to be learned and cemented before meaningful literature/conversations (math) can take place. It is this level that Prof. Hacker is disputing as necessary; the one thing he's right about is that the majority of our fellow citizens are demonstrably unable to succeed at it today.
Likewise, my girlfriend is currently learning Chinese for the first time. She simply has to spend hours every week learning new vocal tones, vocabulary, and drilling writing characters over and over again to ingrain them. It's simply fallacious to pretend that it's unnecessary to do the grunt work of initially learning new (and arbitrary) symbols and structure for any new language.