I think there's a place for a formal system of education, even if it's not as centralized as the one we have now. We need common places for people to access shared knowledge like fundamental physics and math.
Something like Khan Academy with more contributors and formats.
When the British empire was at its height, any British officer could walk up to another and have common ground for a conversation. Even if they were from opposite sides of the world, they had been given the same education. Some amount of common education goes a long way in facilitating communication.
What a strange article. As someone with a background in the humanities I'm certainly a fan of more creativity and communication, however it wasn't until near the end of college (thanks to a math major roommate) that I finally started to understand the true beauty of mathematics. Still catching up on what I find to be essential math skills I continually feel that US student are completely robbed of a decent math education in k-12 (and for the most part college students as well).
The problem with math, at least in the US, is it tends to be taught by people who really don't understand it themselves, so it becomes an ugly, mechanized process. I remember asking one of my early hs math teachers if it was possible for something infinite to be larger than something else infinite. She just sort of smiled and shrugged her shoulders. Almost a decade later I learned about the cardinality of infinite sets and was finally able to answer my question. The sad thing is that if my hs math teach has said 'well let me show you something...' it would have taken me far less than a decade to not only get my answer but also become fascinated with mathematics.
Finally, the more I've learned and studied the more I've come to see that just about anything interesting you want to do is almost always improved by a solid mathematical understanding of the world. And not just a superficial understanding, but a deep meaningful sense of the mathematical principles that can describe the world around us.
I read it differently. I think the author is saying that mathematicians need to be able to communicate what is interesting and important about mathematics, otherwise no one will bother to pursue it.
What I find interesting about Euclid is that he makes no additional effort to communicate what is interesting an important about mathematics. His proofs have an inherent beauty that is self-evident. Indeed, this self-evident quality is a big part of what makes them so beautiful. Each one is like a perfectly constructed plot.
I was introduced to this my Freshman year in college. I remember thinking "this is absolutely amazing - why didn't anybody tell me about this before?" That sense was shared by every one my classmates, who - universally - felt robbed by their 9-12 education.
To this day I remain angry about the utter mediocrity of math education that strips the work of any sense of historical context, the sequence by which one branch emerged from another, the causes of these developments, and the sense of aesthetic delight that comes from discovering what amounts to new and increasingly powerful uses of human reasoning.
At the same time, I felt deeply fortunate that I got the education I did, realizing how far from the norm it is. I also realize that if you DO have to explain why something is important, it's probably because your audience has lost the story's thread. They've stopped seeing the subject from the inside out, and are just going through the motions to pass the test, get the grade, and move on a.s.a.p. The highly fragmented nature of contemporary curriculum design not only increases the chances of this happening, it virtually guarantees disengagement.
The OP is right to observe that people who truly learn do so in spite of the system, not because of it.
The notion that we "don't need to make a thing out of science and math in K-12 because people will be able to explore it on their own" is somewhat myopic. A significant percentage of Americans, especially those from lower income brackets, don't have broadband in the home. Many more don't have home environments conducive to doing what Bill Gates and others did (keep in mind that Bill Gates grew up in a very wealthy home) as many households may be sharing a computer between family members, etc. Exposing people to science and math in school is absolutely critical.
I had that view of physics initially, despite being very interested in computers and mathematics, because I viewed physics as a really inelegant memorization-based field, that consisted of filing away in your head a bunch of special-case equations for things like "how to determine final position with constant acceleration and constant friction". I disliked it much less when I took a calculus-based physics course in college, where all those miscellaneous equations were exposed as special cases of a few more general relationships.
So all the people who are incapable of calculus can't appreciate pysics? That makes sense. It also restricts appreciation of physics to the top quartile, conservatively.
I don't really know in general; I personally didn't appreciate physics when it was presented to me algebraically in high school, despite getting an A in it. Perhaps it'd be possible with a different way of teaching it; not sure.
Programming is essentially not taught in U.S. high schools (it's sometimes available as an elective which most people don't take and it's almost never taught by someone who had any background in software development).
When I tell most people that I'm a computer programmer, I get blank stares because they just don't have any concept of what it entails. It's completely magic to them and I usually end up describing it as analyzing business problems and translating those requirements into software, but they still don't have a clue as to the actual mechanics of programming since they've never been exposed to it in real life. That, or they ask me if I could take a look at their router and then I have to explain "that's not what I do".
It's probably a "grass is always greener" situation, but I'd often enjoy being able to relate my career to average people who share a minimal amount of common understanding, even if it's just to tell me they hate it. I don't expect education to make people like a subject.
I posted this as a response to a comment, but it fits here too:
I gave the wrong impression. We still need math, physics, and all the fundamentals, but being able to communicate those things is important. People like Neil deGrasse Tyson and Brian Cox are up against a sea of ignorance that's rarely willful.
Making sure all mathematicians and physicists are able to respond to someone outside their field when challenged will help fix that.
I agree with the crux of your post. However, people hone their communication skills on a daily basis, simply by interacting with the people around them. Having a strong pedestal in math and science rely heavily on the educational system. A solid background in these areas make it much easier to understand more complex principles, and to think clearly and logically. It's important to communicate your thoughts coherently, but your ideas, themselves, are more important.
I once heard a high school science teacher from the Bay Area tell a group of new teachers that teaching English isn't the English teacher's job. Teaching literature is the English teacher's job. Teaching English, such as proper spelling and grammar, is every teacher's job.
As an example, he talked about how he would deduct points from his students if they misspelled a science term or forgot a period. Over time, this reinforced the idea that they need to be concerned with spelling and grammar not just in their English class, but all the time.
Disclaimer: He teaches in a district with a high population of ESL students, so communication is a constant topic for them.
I think with formal education no longer being a gatekeeper or exclusive haven of knowledge, ie. with iTunes U and the Khan Academy etc., to be competitive in a global market, future students will need to work hard on things like mathematics and programming in their teens. Not being numerate and having a high aptitude for problem solving and rapid learning will put you at a disadvantage similar to what being illiterate was like 80 years ago.
I have mixed feelings about adding more communication to math textbooks or trying to make the content more accessible. I have been trying to teach myself mathematics over the last couple of years. Here are my findings -
a) Math books offered in Borders/Barnes and Nobles invariably have titles like 'Math for dummies', 'Math made easy', "even you can do math' etc. The content seems excessively shallow and diluted by huge amounts of infographics.
b) I believe the key to writing a good math textbooks is having a good feel for 'pregnant pauses'. Good textbooks have problems and prose that deliberately make the user confront their doubts and then shove them into the pregnant pause, out of which the reader emerges joyful at seeing the entire picture. I believe that writing with such mastery requires experience and skill that is not common.
c) I believe that in specialised subjects you are better off writing for the benefit of the motivated reader because everyone else will rarely be applying the contents of the textbook in real life.
d) By overly simplifying things you rob readers of one of the true joys of mathematics - figuring out a problem that they consider difficult. Unless the reader is addicted to this joy they will find most meaningful real world problems too perplexing to solve.
In short I wish we had more concise and thought provoking textbooks.
I honestly think the author is full of crap. The students I grew up with were either school oriented or not. The students who failed to produce coherent writing in English class weren't excelling in the sciences to say the least. Kids were either there to learn or they weren't and there was very little in-between.
So by emphasizing the english portion of education over more sciences we'd only get more of the same crap at the expense of students who DO want to gain formal education in the sciences. Kids don't see the connection between the education and the practical nature of the knowledge they're fed. Stupid is as stupid does.
I was a gung-ho math/science kid. I pulled 95% in my classes of choice and low 60's in the english classes because I refused to participate in the circle-jerk discussion that was english 30. "Now class can you tell me where the foreshadowing is?", "what was the meaning of this poem?". I'm certain I could have pulled out better marks with the effort but I decided my time in classes was better spent doodling. Having more of my time pushed towards english courses and away from the sciences I'd be hard pressed to say that I'd be half the engineer I am today without it. Hell, too much of that 65% crap and I probably wouldn't have gotten the post-secondary education at all.
Provide the tools children need to make formal decisions about their future and provide the fundamentals they need to get there. You can tell which kids are going to be working with their hands or with their heads pretty early so help them get where they want. Everyone needs a fundamental level of communication but over-emphasising it instead of something more practical to the child will only put us full circle to where we are now but with "sciences" and "english" reversed in the discussion.
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[ 3.7 ms ] story [ 71.4 ms ] threadI think school education keep us away from the real, real enjoyment of beauty, real work that creates real value for the people we love.
Something like Khan Academy with more contributors and formats.
And the fact that you stop there is why the education system still sucks.
The problem with math, at least in the US, is it tends to be taught by people who really don't understand it themselves, so it becomes an ugly, mechanized process. I remember asking one of my early hs math teachers if it was possible for something infinite to be larger than something else infinite. She just sort of smiled and shrugged her shoulders. Almost a decade later I learned about the cardinality of infinite sets and was finally able to answer my question. The sad thing is that if my hs math teach has said 'well let me show you something...' it would have taken me far less than a decade to not only get my answer but also become fascinated with mathematics.
Finally, the more I've learned and studied the more I've come to see that just about anything interesting you want to do is almost always improved by a solid mathematical understanding of the world. And not just a superficial understanding, but a deep meaningful sense of the mathematical principles that can describe the world around us.
I was introduced to this my Freshman year in college. I remember thinking "this is absolutely amazing - why didn't anybody tell me about this before?" That sense was shared by every one my classmates, who - universally - felt robbed by their 9-12 education.
To this day I remain angry about the utter mediocrity of math education that strips the work of any sense of historical context, the sequence by which one branch emerged from another, the causes of these developments, and the sense of aesthetic delight that comes from discovering what amounts to new and increasingly powerful uses of human reasoning.
At the same time, I felt deeply fortunate that I got the education I did, realizing how far from the norm it is. I also realize that if you DO have to explain why something is important, it's probably because your audience has lost the story's thread. They've stopped seeing the subject from the inside out, and are just going through the motions to pass the test, get the grade, and move on a.s.a.p. The highly fragmented nature of contemporary curriculum design not only increases the chances of this happening, it virtually guarantees disengagement.
The OP is right to observe that people who truly learn do so in spite of the system, not because of it.
I dunno. I'm a physicist, and a lot of people tell me "I hate physics" when I tell them what I do. I think K-12 is doing more harm than good.
When I tell most people that I'm a computer programmer, I get blank stares because they just don't have any concept of what it entails. It's completely magic to them and I usually end up describing it as analyzing business problems and translating those requirements into software, but they still don't have a clue as to the actual mechanics of programming since they've never been exposed to it in real life. That, or they ask me if I could take a look at their router and then I have to explain "that's not what I do".
It's probably a "grass is always greener" situation, but I'd often enjoy being able to relate my career to average people who share a minimal amount of common understanding, even if it's just to tell me they hate it. I don't expect education to make people like a subject.
Making sure all mathematicians and physicists are able to respond to someone outside their field when challenged will help fix that.
As an example, he talked about how he would deduct points from his students if they misspelled a science term or forgot a period. Over time, this reinforced the idea that they need to be concerned with spelling and grammar not just in their English class, but all the time.
Disclaimer: He teaches in a district with a high population of ESL students, so communication is a constant topic for them.
a) Math books offered in Borders/Barnes and Nobles invariably have titles like 'Math for dummies', 'Math made easy', "even you can do math' etc. The content seems excessively shallow and diluted by huge amounts of infographics. b) I believe the key to writing a good math textbooks is having a good feel for 'pregnant pauses'. Good textbooks have problems and prose that deliberately make the user confront their doubts and then shove them into the pregnant pause, out of which the reader emerges joyful at seeing the entire picture. I believe that writing with such mastery requires experience and skill that is not common. c) I believe that in specialised subjects you are better off writing for the benefit of the motivated reader because everyone else will rarely be applying the contents of the textbook in real life. d) By overly simplifying things you rob readers of one of the true joys of mathematics - figuring out a problem that they consider difficult. Unless the reader is addicted to this joy they will find most meaningful real world problems too perplexing to solve.
In short I wish we had more concise and thought provoking textbooks.
Here is what Feynman had to say about textbooks: http://www.textbookleague.org/103feyn.htm
So by emphasizing the english portion of education over more sciences we'd only get more of the same crap at the expense of students who DO want to gain formal education in the sciences. Kids don't see the connection between the education and the practical nature of the knowledge they're fed. Stupid is as stupid does.
I was a gung-ho math/science kid. I pulled 95% in my classes of choice and low 60's in the english classes because I refused to participate in the circle-jerk discussion that was english 30. "Now class can you tell me where the foreshadowing is?", "what was the meaning of this poem?". I'm certain I could have pulled out better marks with the effort but I decided my time in classes was better spent doodling. Having more of my time pushed towards english courses and away from the sciences I'd be hard pressed to say that I'd be half the engineer I am today without it. Hell, too much of that 65% crap and I probably wouldn't have gotten the post-secondary education at all.
Provide the tools children need to make formal decisions about their future and provide the fundamentals they need to get there. You can tell which kids are going to be working with their hands or with their heads pretty early so help them get where they want. Everyone needs a fundamental level of communication but over-emphasising it instead of something more practical to the child will only put us full circle to where we are now but with "sciences" and "english" reversed in the discussion.
Yeah, guys like Bill did amazing things compared to those bozos that just took their highschool's computer programming course in the 1970s.