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There's a few problems with the article. The rules argument he makes could instead be made for the more useful field of computer programming. Also, the reducti

There's a few problems with the article. The rules argument he makes could instead be made for the more useful field of computer programming. Also, the reductionist paradigm is dead. It worked for finding laws of physics and some chemistry, but otherwise, in the most useful fields of today, like biology/materials/chemistry (high throughput methods), computer vision, search engines etc. the automated creation of hypotheses through machine learning is winning out. Conrad Wolfram gives a talk about the need for math education reform http://www.youtube.com/watch?v=60OVlfAUPJg http://www.youtube.com/watch?v=60OVlfAUPJg He uses the term mathematics, but completely removing that term and replacing it with computer programming and machine learning should be done. They sound cooler and this step will remove all the baggage and ill-will mathematics has in society. That way, all mathematics teachers can be simply removed from high schools and colleges and replaced with computer programmers. Estonia is one of the few enlightened places on this subject with their introduction of programming as mandatory from year 1 in k12. Almost the entire high school drop out rate can be attributed to maths teaching, and their is no solid empirical proof of it's utility over programming (the practice of "science" hasn't been applied to "maths" itself). http://en.wikipedia.org/wiki/Mathematical_anxiety http://en.wikipedia.org/wiki/Mathematical_anxiety The same argument can be made for a number of other subjects, such as chemistry (why teach the periodic table?), languages (we have google translate and should taxpayers be funding this unproductive activity), and others (everything should be reexamined in light of search engines and instant information access). The only useful subjects in k12 are probably - computer programming, including machine learning/statistics - physical education, - communication (reading/writing/public speaking/socialization) - general studies (trivia like history, geography, astronomy), - personal finance - physical crafts (3d printing, woodshop, cooking)

capnrefsmmat 14y ago
I'm curious how you would replace mathematics with programming. My undergraduate thesis project involves a lot of programming, but I also had to determine that I can detect anomalous gamma spectra through some linear algebra, a correlation matrix, an assumption of Poisson-distributed counts, and a chi^2-distributed anomaly statistic. This gives me a statistically well-founded way to detect anomalies. Would you have me replace this process with some sort of automated machine learning, hoping it could produce better results than a special-purpose algorithm?
- marshallp 14y ago
  Even if your argument is true, that maths is needed for that particular task, it doesn't justify teaching it to 99% of people. Also, the math you mention could have been taught as a set of computer programming functions (taught in a few hours) rather than how it's traditionally taught (as s semester long class or sequence of classes). Black box machine learning might have given you better method than your whatever you're currently doing. And it would be done in a automated manner, with human effort just focusing on collecting data. I'm assuming whatever you're done is being done/has been done by many 1000s people as well. That's a tremendous waste of time. Even if the method you outline is better than what machine learnig would have found, it only needed to be done once (or a few times - marketplace) and exposed as an api.
  - Thrymr 14y ago
    How do you choose the black box if you don't understand the problem? It's not as if there exists a single black box for all possible problems.
    - marshallp 14y ago
      That's missing the point entirely. I'm pretty sure you don't know the exact materials and the process for making the shoes you might be wearing. There are probably no shoe factories left in america. They same applies to the black box machine learning, very very few people need to know of what goes on under the hood. edit: I don't know if you changed your comment, but black boxes exist that can solve any problem (neural nets for example).
      - Thrymr 14y ago
        That might be true for some very general (or common) problems (though I have doubts about that as well), but it can't possibly be true for a specialized problem such as the one described. How do you train a model if you don't understand the problem? You can't just say "unsupervised learning" and expect your algorithm to come up with a full understanding of the physics involved. (And no, I have not edited my comment.)
pbhjpbhj 14y ago
>Almost the entire high school drop out rate can be attributed to maths teaching, and their is no solid empirical proof of it's utility over programming // Can you point out the parts in the Wikipedia page that wouldn't apply if you teach programming and machine learning. I'm not quite sure if mathematics is a superset of computer programming or will prove to be a subset. Either way we probably want to teach people algorithms to handle basic numerical functions (addition/addition/addition and addition) - why do you think it will matter if we call this learning by a different name? We'll probably want to take more of an abstract computer scientific approach than a "programming" approach that would need to focus on the stack to some extent, once you make those abstractions then you've got pure arithmetic haven't you? In chemistry the periodic table is the means to categorise chemical knowledge isn't it. A sort of learning technique? Languages I feel are useful but that state support should probably concentrate on major languages to foster cooperation between people groups, cultural understanding, mobility of workers. I like your K12 subject list and appreciate the focus on utility.
- marshallp 14y ago
  You don't need the teaching of abstract concepts. Why not just let students roam free with "programming", a set of api's, so they can roam with free with creativity. Why even teach arithmetic? Just given them the arithmetic computer functions and let them play around with it. As students build games or whatever else they'll discover the concepts that you might consider important themselves. What use is the periodic table for almost anyone. Teaching the periodic table should be left for someone wishing to pursue research in chemistry, maybe as a 20 year old. The basic skills that chemists probably use today, like computer programming, would have been ingrained throughout k12.
Thrymr 14y ago
I find the idea of replacing "mathematics" in the curriculum with "computer programming" rather baffling. As important as programming is in our world, only a small fraction of high school graduates are going to need to do what we currently think of as "programming", while everyone will need to interact with technology and understand the world quantitatively. That calls for a much broader view of math and technology education than just "programming", even including machine learning and statistics. Also, expecting anyone to have any kind of understanding of machine learning and statistics without a real grasp of what is currently considered "mathematics" doesn't make any sense to me. You're going to need algebra and linear algebra at minimum, and probably calculus as well, to have a chance at meaningful use of ML models.
- marshallp 14y ago
  Why do people need to know the under the hood stuff. As I mentioned in my other comment, we have the concept of division of labour. Also, programming and machine learning will increasingly be most of what people's job description. In fact, in my extremest viewpoint, I think even programming is on it's way out and machine learning will the majority of people's work. Or put more simply, giving computers a few examples. Already, with things like the Baxter robot from Rethink Robotics, and mechanical turk from amazon, we're seeing what the future of work will be like. The computers will just figure out things extrapolating from the choices we make.
  - Thrymr 14y ago
    I actually agree with you that programming may be on its way out for the majority of people. I can't agree with sweeping away all of mathematics, including arithmetic and algebra, as "under the hood stuff" for K-12 students.
    - marshallp 14y ago
      Algebra (the art of rearranging equations) is not necessary anymore (you just need to know how to realize how things can be quantified - the naming of variables of computer programming). Arithmetic beyond use of calculator is useless. Maths as traditionally taught is the leading cause of high school dropouts rates and probably a lot more damage than tahat (people who might have been scientists turning to arts instead).
rayiner 14y ago
I think formal logic and statistics should be subjects you can't get out of middle school without.
defen 14y ago
From reading your HN comments, you seem like the kind of person who has a small axiomatic set of principles, and then attempts to fit the world to those principles. Without going into the merits/demerits of that approach, I'd at least like to point out that it occasionally leads to absurd conclusions - such as replacing language courses with Google translate. Do you really think that Google translate is a feasible way to converse with someone in a foreign language? Or, for translating literature? Here is the opening paragraph of War and Peace, computer translation vs human. Note that Google translate assumed the whole thing was French, and left the Russian parts untranslated, so I had to manually translate the Russian words. Italics represent words originally in Russian. Google translate: Еh, my prince. Genoa and Lucca are only appendages of, the manor, Buonaparte family. No, I warn you that if you do not tell me that we have war, even if you allow yourself to overcome all infamies, all the atrocities of this Antichrist (my word, I think) - I do you know more, you are no longer my friend, you are no longer my faithful servant, as you say. Ну, hello, hello. I see that I frighten you, sit down and talk. Richard Pevear and Larissa Volokhonsky translation: Well, my prince, Genoa and Lucca are now no more than possessions, estates, of the Buonaparte family. No, I warn you, if you do not tell me we are at war, if you still allow yourself to palliate all the infamies, all the atrocities of that Antichrist (upon my word, I believe it) - I no longer know you, you are no longer my friend, you are no longer my faithful slave, as you say. Well, good evening, good evening. I see that I'm frightening you, sit down and tell me about it
- marshallp 14y ago
  Is it the responsibility of the taxpayer to fund the education for the leisure activity of the upper middle classes (speaking with foreigners or reading translated literature). The education system that exists today (k12 + college) is a McReplica of what aristocratic people of earlier centuries considered fit for their children (who would never actually need to work). We're living the enviousness of the middle classes of a century ago (this same principle applies to the McMansions). It has no relation to what a more perfected reality could be. With respect to google translate, I think we'll see a lot of improvements. I expect to see human level performance within 5 years (it's a "let the computers run long enough" + "enough data" problem).

capnrefsmmat 14y ago

I'm curious how you would replace mathematics with programming. My undergraduate thesis project involves a lot of programming, but I also had to determine that I can detect anomalous gamma spectra through some linear algebra, a correlation matrix, an assumption of Poisson-distributed counts, and a chi^2-distributed anomaly statistic. This gives me a statistically well-founded way to detect anomalies. Would you have me replace this process with some sort of automated machine learning, hoping it could produce better results than a special-purpose algorithm?

marshallp 14y ago
Even if your argument is true, that maths is needed for that particular task, it doesn't justify teaching it to 99% of people. Also, the math you mention could have been taught as a set of computer programming functions (taught in a few hours) rather than how it's traditionally taught (as s semester long class or sequence of classes). Black box machine learning might have given you better method than your whatever you're currently doing. And it would be done in a automated manner, with human effort just focusing on collecting data. I'm assuming whatever you're done is being done/has been done by many 1000s people as well. That's a tremendous waste of time. Even if the method you outline is better than what machine learnig would have found, it only needed to be done once (or a few times - marketplace) and exposed as an api.
- Thrymr 14y ago
  How do you choose the black box if you don't understand the problem? It's not as if there exists a single black box for all possible problems.
  - marshallp 14y ago
    That's missing the point entirely. I'm pretty sure you don't know the exact materials and the process for making the shoes you might be wearing. There are probably no shoe factories left in america. They same applies to the black box machine learning, very very few people need to know of what goes on under the hood. edit: I don't know if you changed your comment, but black boxes exist that can solve any problem (neural nets for example).
    - Thrymr 14y ago
      That might be true for some very general (or common) problems (though I have doubts about that as well), but it can't possibly be true for a specialized problem such as the one described. How do you train a model if you don't understand the problem? You can't just say "unsupervised learning" and expect your algorithm to come up with a full understanding of the physics involved. (And no, I have not edited my comment.)

pbhjpbhj 14y ago

>Almost the entire high school drop out rate can be attributed to maths teaching, and their is no solid empirical proof of it's utility over programming // Can you point out the parts in the Wikipedia page that wouldn't apply if you teach programming and machine learning. I'm not quite sure if mathematics is a superset of computer programming or will prove to be a subset. Either way we probably want to teach people algorithms to handle basic numerical functions (addition/addition/addition and addition) - why do you think it will matter if we call this learning by a different name? We'll probably want to take more of an abstract computer scientific approach than a "programming" approach that would need to focus on the stack to some extent, once you make those abstractions then you've got pure arithmetic haven't you? In chemistry the periodic table is the means to categorise chemical knowledge isn't it. A sort of learning technique? Languages I feel are useful but that state support should probably concentrate on major languages to foster cooperation between people groups, cultural understanding, mobility of workers. I like your K12 subject list and appreciate the focus on utility.

marshallp 14y ago
You don't need the teaching of abstract concepts. Why not just let students roam free with "programming", a set of api's, so they can roam with free with creativity. Why even teach arithmetic? Just given them the arithmetic computer functions and let them play around with it. As students build games or whatever else they'll discover the concepts that you might consider important themselves. What use is the periodic table for almost anyone. Teaching the periodic table should be left for someone wishing to pursue research in chemistry, maybe as a 20 year old. The basic skills that chemists probably use today, like computer programming, would have been ingrained throughout k12.

Thrymr 14y ago

I find the idea of replacing "mathematics" in the curriculum with "computer programming" rather baffling. As important as programming is in our world, only a small fraction of high school graduates are going to need to do what we currently think of as "programming", while everyone will need to interact with technology and understand the world quantitatively. That calls for a much broader view of math and technology education than just "programming", even including machine learning and statistics. Also, expecting anyone to have any kind of understanding of machine learning and statistics without a real grasp of what is currently considered "mathematics" doesn't make any sense to me. You're going to need algebra and linear algebra at minimum, and probably calculus as well, to have a chance at meaningful use of ML models.

marshallp 14y ago
Why do people need to know the under the hood stuff. As I mentioned in my other comment, we have the concept of division of labour. Also, programming and machine learning will increasingly be most of what people's job description. In fact, in my extremest viewpoint, I think even programming is on it's way out and machine learning will the majority of people's work. Or put more simply, giving computers a few examples. Already, with things like the Baxter robot from Rethink Robotics, and mechanical turk from amazon, we're seeing what the future of work will be like. The computers will just figure out things extrapolating from the choices we make.
- Thrymr 14y ago
  I actually agree with you that programming may be on its way out for the majority of people. I can't agree with sweeping away all of mathematics, including arithmetic and algebra, as "under the hood stuff" for K-12 students.
  - marshallp 14y ago
    Algebra (the art of rearranging equations) is not necessary anymore (you just need to know how to realize how things can be quantified - the naming of variables of computer programming). Arithmetic beyond use of calculator is useless. Maths as traditionally taught is the leading cause of high school dropouts rates and probably a lot more damage than tahat (people who might have been scientists turning to arts instead).

rayiner 14y ago

I think formal logic and statistics should be subjects you can't get out of middle school without.

defen 14y ago

From reading your HN comments, you seem like the kind of person who has a small axiomatic set of principles, and then attempts to fit the world to those principles. Without going into the merits/demerits of that approach, I'd at least like to point out that it occasionally leads to absurd conclusions - such as replacing language courses with Google translate. Do you really think that Google translate is a feasible way to converse with someone in a foreign language? Or, for translating literature? Here is the opening paragraph of War and Peace, computer translation vs human. Note that Google translate assumed the whole thing was French, and left the Russian parts untranslated, so I had to manually translate the Russian words. Italics represent words originally in Russian. Google translate: Еh, my prince. Genoa and Lucca are only appendages of, the manor, Buonaparte family. No, I warn you that if you do not tell me that we have war, even if you allow yourself to overcome all infamies, all the atrocities of this Antichrist (my word, I think) - I do you know more, you are no longer my friend, you are no longer my faithful servant, as you say. Ну, hello, hello. I see that I frighten you, sit down and talk. Richard Pevear and Larissa Volokhonsky translation: Well, my prince, Genoa and Lucca are now no more than possessions, estates, of the Buonaparte family. No, I warn you, if you do not tell me we are at war, if you still allow yourself to palliate all the infamies, all the atrocities of that Antichrist (upon my word, I believe it) - I no longer know you, you are no longer my friend, you are no longer my faithful slave, as you say. Well, good evening, good evening. I see that I'm frightening you, sit down and tell me about it

marshallp 14y ago
Is it the responsibility of the taxpayer to fund the education for the leisure activity of the upper middle classes (speaking with foreigners or reading translated literature). The education system that exists today (k12 + college) is a McReplica of what aristocratic people of earlier centuries considered fit for their children (who would never actually need to work). We're living the enviousness of the middle classes of a century ago (this same principle applies to the McMansions). It has no relation to what a more perfected reality could be. With respect to google translate, I think we'll see a lot of improvements. I expect to see human level performance within 5 years (it's a "let the computers run long enough" + "enough data" problem).