I am thinking through what generally, I am sort of laughing saying this now, mathematics addicting. I think if the same psychological arts could be applied to gaming as applied to mathematics, we'd likely have a lot more mathematically inclined people, and I don't mean making cheesy mathematics shoot em up type games, but at least translating the addiction/stimulus hooks to mathematics in education might prove to be an aid?!
Anyways, where more individually tailored educational systems I suspect may prove greater relative to larger scale education systems, are that metrics can be made of a students progress in terms of proficiency/deficiencies, and then education can be tailored to target specific areas while maintaining a students interest in terms of success/reward stimulation, or whatever reward system applicable to maintaining a student's more long term interests and drive. Obviously not making problem solving too easy, nor making them too hard, but appropriately structuring learning where a student's achievement level happens to be centered at. Anyways I've already heard of educational systems now arising that are structured exactly in this way, which are more 1 to 1 focus oriented in terms of academics instead of being scaled large relative to any larger 20 or 30 to 1 student to teach ratios. The more ideal ratio possibility is a very small student to teacher ratio system, and generally where the teacher/instructor can constantly monitor a students progress and then re calibrate teaching according to the rate of achievement at a given progression. Artificial intelligence systems will likely be able to actively handle and aid progression metrics likely in the future, so that more often I would suspect we are likely to see in the future, students that could be taught (as horrifying as this could be to some) generally by the aid of computing systems alone...although even so, human instructors could see positive benefits in terms of measuring aids to something like performance and so forth. I would expect as technology progresses likely in our future, our children may be much better educated not less relative to us, and not only better educated, but also living better.
As to education, nowadays, I am seeing a lot of stuff out there that provides generally not only the equivalent of free k-12 education (at this point I am not sure if its comprehensive as a substitute to primary education), but also college level education likewise, or basically without formally having a paper diploma, you could likely achieve the academic merits of such. I also see that online education could serve a role in filling preparatory gaps where those in more disadvantaged situations could have increased likelihood of closing these gaps to be on par with other students at a given academic institution, or hopefully as digital divisions between wealthier and poorer potentially close rank, the information access being similar means that online education possibilities could change educational culture for the have nots that hadn't the skills or level of education to get into higher ranked institutions, or merely getting into higher level institutions period.
As to a form of liberalization theory on this bit, this is actually a boon to a democracy in my opinion from a sociological standpoint, one because if you want to tap the potential power of your civilization, it means you provide more people with better quality education not less, because that in turn translates into much greater synergistic power potential for a given civilization which has more people educated to handle higher skilled labor and higher level technology work that are hopefully more likely to be critical thinking and articulate enough so as not to be easily socially controlled especially on the point of lies, distortions, and so forth (a bit of sermonizing I know)...of course, I am not sure on the later point this always turns out to be true, but at least one should hope the better educated are neither so ignorant, and especially on the matters of liberal arts education, that there is at least something of better rounded ness in one's living conditions and personal choice making?! Its not just about the job and money...but well being too!
I am not so certain that drastic changes need be made to a given educational system, just because it appears to be failing, that is, in terms of overhauls to teaching many different conceptual viewpoints, although I am not so certain that is problematic to teaching either. While some might complain by the presence in remedial education, in higher level mathematics, it seems that re working a problem using alternate methods/models could be a possible practice...for instance, in checking work, if you obviously hadn't had an answer key, you were working through new concepts, but wanting to verify a problem's solution that could alternately be worked under older concepts that you were more familiar with...of course, maybe it is something of American thing as the aphorism goes, 'If it ain't broke don't fix it!' Or whatever method that works is the right way, and hence any other way of going about doing the same thing over again could be considered as obfuscating the problem at hand. The problem is that when we are set in thinking about the same sets of problems in the same ways, and handling them in that way in some repetitive way over and over again. Immediately I couldn't offer that at times, I weren't much the same in terms of personality, that is, if having solved a problem I might ignore a problem that involved more unfamiliar territories of geometric relations over familiar relations that I were already acquainted. Admittedly, I am suspect most of America would fail horribly at someone attempting to teach classical geometry owing to the Greeks in its entirety, that is where much relations that we could be familiar with in modern physics/engineering are heavily inclined to principles of trigonometry, and yes, we might have some versing on things like the relation of angles between parallel lines, and intersecting non parallel lines, but I scarcely recalled in high school math much of what I might have learned beyond this. Admittedly, when I peruse modern geometry books, which at times recalls geometry of antiquity, looks at times very foreign in principle with heavy and extensive use of length ratios which certainly relate sine, cosine, and so forth ratios, but without in principle using them in the same ways. As it turns out theory of relativity were owing heavy in inspiration I believe to something like Minkowski spaces, or Klein geometries, or being able to at least in theory consider space in a different way relative to the Euclidean notions that we might have, and of course, in terms of problem modeling...if you could think differently about a problem so that you weren't thinking rectangles even translating in motion to solve these sorts of problems, you might consider alternately about a space where two intersecting straight lines in such space have not one but two points of intersection, can you visualize what sort of space that is?! In order for a civilization to assert itself, of course, it needs thinkers that can diverge from a given group in appreciating different modes or ways of thinking about a particular problem, that is, being able to conceptually re visualize problems, or being willing to embrace alternative structures, that aren't merely ignored because we think one way of doing things is the best way and only way end of story! Of course, then one should ask are we trying to gear the next generation of students in the manner of being theoretical scientists?! No, but then there may be some emotional practicality to this, and this relates to being able to work through situations while truly listening to other feedback while neither being insistent on solely applying solutions in rigid ways. At least from a psychological standpoint if we are more likely to listen and work to see that alternate means of solving problems can be done, we may be more likely to be not only possibly better problem solvers but also more diplomatic in our approach to handling problem solving.
I am not so certain that drastic changes need be made to a given educational system, just because it appears to be failing, that is, in terms of overhauls to teaching many different conceptual viewpoints, although I am not so certain that is problematic to teaching either. While some might complain by the presence in remedial education, in higher level mathematics, it seems that re working a problem using alternate methods/models could be a possible practice...for instance, in checking work, if you obviously hadn't had an answer key, you were working through new concepts, but wanting to verify a problem's solution that could alternately be worked under older concepts that you were more familiar with...of course, maybe it is something of American thing as the aphorism goes, 'If it ain't broke don't fix it!' Or whatever method that works is the right way, and hence any other way of going about doing the same thing over again could be considered as obfuscating the problem at hand. The problem is that when we are set in thinking about the same sets of problems in the same ways, and handling them in that way in some repetitive way over and over again. Immediately I couldn't offer that at times, I weren't much the same in terms of personality, that is, if having solved a problem I might ignore a problem that involved more unfamiliar territories of geometric relations over familiar relations that I were already acquainted. Admittedly, I am suspect most of America would fail horribly at someone attempting to teach classical geometry owing to the Greeks in its entirety, that is where much relations that we could be familiar with in modern physics/engineering are heavily inclined to principles of trigonometry, and yes, we might have some versing on things like the relation of angles between parallel lines, and intersecting non parallel lines, but I scarcely recalled in high school math much of what I might have learned beyond this. Admittedly, when I peruse modern geometry books, which at times recalls geometry of antiquity, looks at times very foreign in principle with heavy and extensive use of length ratios which certainly relate sine, cosine, and so forth ratios, but without in principle using them in the same ways. As it turns out theory of relativity were owing heavy in inspiration I believe to something like Minkowski spaces, or Klein geometries, or being able to at least in theory consider space in a different way relative to the Euclidean notions that we might have, and of course, in terms of problem modeling...if you could think differently about a problem so that you weren't thinking rectangles even translating in motion to solve these sorts of problems, you might consider alternately about a space where two intersecting straight lines in such space have not one but two points of intersection, can you visualize what sort of space that is?! In order for a civilization to assert itself, of course, it needs thinkers that can diverge from a given group in appreciating different modes or ways of thinking about a particular problem, that is, being able to conceptually re visualize problems, or being willing to embrace alternative structures, that aren't merely ignored because we think one way of doing things is the best way and only way end of story! Of course, then one should ask are we trying to gear the next generation of students in the manner of being theoretical scientists?! No, but then there may be some emotional practicality to this, and this relates to being able to work through situations while truly listening to other feedback while neither being insistent on solely applying solutions in rigid ways. At least from a psychological standpoint if we are more likely to listen and work to see that alternate means of solving problems can be done, we may be more likely to be not only possibly better problem solvers but also more diplomatic in our approach to handling problem solving.
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