> There are different skills, but are they that different? > The closest area to good mathematics I can think of is > grammar. Development of concepts does not need repetition > after the concepts are learned.
True; however, I would argue that the relationship between grammar and math is not apparent at first to most students. They see themselves as "i'm good at writing" but "i'm not good at math". Otherwise, all good english grammar students would be good mathematicians. It is the relationship that is missing; the mathematicians seem to see it, the english majors don't seem to get it. For the lucky few who figure out the similarities, the world has just become that much simpler -- the rest are left divided into two worlds "english/art/history majors" (good memory) and "math/science/etc. majors" (good conceptualization). The world of education is currently too "sink or swim". > Reading "good books"? Is this at all academic? There > is lots to learn about the universe; this does not mean > that SOME time should not be spent on literature. As for > writing book reports, after a couple of reasonable ones > have been written, MAYBE there should be another one > occasionally. Busy work may have some uses for those > whose mental abilities are not too great, but not for > the ones who can think. As for doing math, see my > comment on your next paragraph. Busy work isn't what i'm advocating; i'm simply saying that one can never write "too well" that one cannot improve what-so-ever. I think that writing book reports, forces one to organize one's thoughts about a topic one might have just read. It also forces one to think about the issues that are discussed in the book. It forces one to practice writing, and with sufficient exposure, one naturally becomes more agile (so that ideally, book reports don't take up as MUCH of one's time because we become better/faster). It also forces us to summarize the key information in "our own way" that is similar to "memorization" except that we have given it sufficient thought that it becomes "our own". Once something becomes "owned" it can be used. Finally, reading books on our own (without emphasis on "we're learning chapter 1 today") provides ample opportunity to get in a broad range of coverage, that is simply not possible if we are stuck reading a textbook on a chapter-by-chapter basis (e.g., history... where we are forced to read a single textbook, and just because that author is a difficult read, we end up getting stagnated when we could just as well pickup another book by another source, whose writing more closelly matches our comprehension style). > This not only makes it hard to keep up, > >but I suspect promotes ADD (attention deficit disorder). > > Wrong. Those with ADD have the genetic makeup which keeps > them from tolerating lengthy periods on any subject. Also, > bright, and especially gifted, children are bored by slow > presentations and busy work. They do not need, and should > not have to do, "easy problems". True, ADD may be genetically predisposed; however, my point was that teaching multiple subjects, many of which we could learn on our own if we were so inclined, is simply a waste of valuable time that could be better spent on become good at the fundamentals (which I suppose you refer to as 'concepts' and 'structure'). As an extreme thought experiment, I simply cannot believe that if we took a hypothetical student and forced him/her to spend 4-6 hours/day (reading, writing, and doing) math, they wouldn't automatically become "quantitative" people after a time (at least for the sake of becoming quantitative enough to function in society, if not to become full-fledged mathematicians). It surprises me that with all the emphasis on american history in schools, there are still people (esp. natives of the US) who will venture to "guess" that the first president of the united states was "thomas jefferson". > I do not object to SOME time devoted to arithmetic skills, > AFTER the concepts are understood. How many really good > mathematicians do we lose by teaching those skills, and > telling children that they do not have mathematical ability > if they cannot calculate rapidly and accurately? By arithmetic, I was simply referring generally to learning of mathematics, not rapidly or accurately crunching numbers. I apologize for the confusion. > This would give us a solid 3-4 hour block of time > >per subject per day and I think that makes a huge difference (compared to 1 > >hour of each subject, with no time to really think or ask questions that may > >come up after prolonged thinking). > > I still believe that any prolonged period of study should > be by the student at his or her convenience. I do not > approve even of 75 minute classes, and I do not think that > a conceptual class should meet more than 3 times per week. My point exactly, i'm simply saying that classes should not be lecture-driven. They should be Q&A only, with maybe time for 1 lecture at the beginning of every week (or something) to introduce the required concepts. Self-study should be promoted more, and having teachers "around" is useful to facilitate fluid discussions that will help a student overcome conceptual barriers. So teachers as consultants, rather than lecturers. A student shouldn't feel like he/she is learning "to go to class and pass the test", but because he/she feels the "relevancy" of whatever is being learnt, and at the same time doesn't feel like they are in a "sink or swim" environment. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
