{"id":383,"date":"2012-08-02T13:43:17","date_gmt":"2012-08-02T20:43:17","guid":{"rendered":"http:\/\/www.scholarsonline.org\/Blog\/?p=383"},"modified":"2012-08-02T13:43:17","modified_gmt":"2012-08-02T20:43:17","slug":"calculus-classes-with-a-live-teacher","status":"publish","type":"post","link":"https:\/\/www.scholarsonline.org\/Blog\/?p=383","title":{"rendered":"Calculus classes with a live teacher?"},"content":{"rendered":"

There are many on-line resources for math students these days.\u00a0 There are college\/university level courses, such as those offered by MIT and Stanford.\u00a0 There are \u00a0YouTube videos suitable for high school level study, such as Khan Academy and others.\u00a0 \u00a0There are also many downloadable textbooks and on-line learning aids.\u00a0 A conscientious parent might ask, \u201cWhat is the benefit worth paying for<\/em> in having a live but on-line instructor?\u201d<\/p>\n

The question is both easy and hard for me to answer, because of my varied experience.\u00a0 I have taken classes from teachers in person, via live video links, and on-line.\u00a0 I have also learned material on my own with no teacher to interact with.\u00a0 In previous blog entries, the Drs. McMenomy have discussed the virtues of finding things out on one\u2019s own (\u201cFreedom to fail\u201d and \u201cFailure is not an option\u201d below).\u00a0 So, as a student, why no<\/em>t tackle calculus on your own?<\/p>\n

In an ideal context, you would have all the time<\/em> you needed to explore all of the nooks and crannies, all the dead-ends, of a mathematical subject until you reached the same conclusions as previous generations of mathematicians.\u00a0 Most likely, you\u2019d be a good mathematician then, too \u2013 math certainly requires practice to do well, and you would have had a lot of practice.\u00a0 But independent exploration takes a long while \u2013 unless you are an amazing genius, much more time than a year\u2019s worth of classes.<\/p>\n

So there\u2019s the first reason to have a math teacher:\u00a0 to shorten the time it takes to reach mastery, by pointing out unprofitable dead ends in thought.<\/p>\n

As you learn a subject, you must make mistakes<\/em>.\u00a0 (This is a lesson I personally resisted for a long time \u2013 I wanted to be perfect the first time through.)\u00a0 Because mathematics has a definite sense of \u201ccorrect and incorrect\u201d, of \u201cperfect and imperfect\u201d, it\u2019s not so bad as with Greek or history, where there are matters of style and personal orientation.\u00a0 Proofs, which can convince any sceptic, are not only possible, but expected, at least at times.\u00a0 However, you have to avoid learning the mistakes you make during learning as if they were true<\/em>.<\/p>\n

So there\u2019s the second reason to have a math teacher:\u00a0 to point out the errors in your reasoning and understanding, so that you don\u2019t have to un-learn and re-learn the material involved.\u00a0 This is especially true when there\u2019s very careful reasoning required \u2013 and calculus certainly has areas where it has taken centuries for some very bright people to reach an adequate level of care in reasoning!<\/p>\n

Anyone who has read a textbook (or any other nonfiction book) realizes that not all the material in them is equally important.<\/em> That seems pretty blatantly obvious, but not everyone sees that.\u00a0 I\u2019ve been known to grouse about professors\u2019 pet theories which, while true, aren\u2019t useful, using terms like \u201cacademic fantasies\u201d.<\/p>\n

So there\u2019s the third reason to have a math teacher:\u00a0 someone to point out the crucially important parts, and differentiate them from the merely interesting parts.\u00a0 (OK, I\u2019m not perfect there \u2013 but I try!)<\/p>\n

But perhaps the most critical reason for an outsider\u2019s presence in the learning activity is embodied in the statement, \u201cyou don\u2019t know what you don\u2019t know.\u201d\u00a0 It sounds tautological, until you realize that you can know what you don\u2019t know in some contexts (\u201cI don\u2019t know anything about the aorist in Greek, except that there\u2019s something knowable under that label\u201d), and there are so many situations possibly contrary to fact that you can\u2019t even know them all.\u00a0 (A recent example:\u00a0 \u201cLifetime warranty\u201d \u2013 I knew that sometimes it refers to the buyer\u2019s lifetime, sometimes to the useful life of the product \u2013 but I didn\u2019t know, in the sense that I really believed it in a way that I could act on it, that it might also refer to the lifetime of the company offering the product\u2026)\u00a0 There can be holes in your knowledge that you\u2019re unaware of:\u00a0 intellectual blind spots.<\/p>\n

So there\u2019s the fourth reason to have a math teacher:\u00a0 someone to make sure that your knowledge is reliably complete.<\/p>\n

All that said, no one can practice doing math for you, just as no one can do physical exercise for you.\u00a0 Learning is the goal, and teaching one of many means to the goal.<\/p>\n","protected":false},"excerpt":{"rendered":"

There are many on-line resources for math students these days.\u00a0 There are college\/university level courses, such as those offered by MIT and Stanford.\u00a0 There are \u00a0YouTube videos suitable for high school level study, such as Khan Academy and others.\u00a0 \u00a0There are also many downloadable textbooks and on-line learning aids.\u00a0 A conscientious parent might ask, \u201cWhat […]<\/p>\n","protected":false},"author":470,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-383","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/www.scholarsonline.org\/Blog\/index.php?rest_route=\/wp\/v2\/posts\/383","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.scholarsonline.org\/Blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.scholarsonline.org\/Blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.scholarsonline.org\/Blog\/index.php?rest_route=\/wp\/v2\/users\/470"}],"replies":[{"embeddable":true,"href":"https:\/\/www.scholarsonline.org\/Blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=383"}],"version-history":[{"count":2,"href":"https:\/\/www.scholarsonline.org\/Blog\/index.php?rest_route=\/wp\/v2\/posts\/383\/revisions"}],"predecessor-version":[{"id":385,"href":"https:\/\/www.scholarsonline.org\/Blog\/index.php?rest_route=\/wp\/v2\/posts\/383\/revisions\/385"}],"wp:attachment":[{"href":"https:\/\/www.scholarsonline.org\/Blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=383"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.scholarsonline.org\/Blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=383"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.scholarsonline.org\/Blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=383"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}