tag:blogger.com,1999:blog-15868947.post2360622604264522740..comments2024-04-03T04:11:01.081-07:00Comments on Halfway There: Pattern-matching and hand-holdingZenohttp://www.blogger.com/profile/09058127284297728552noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-15868947.post-59946868900664430692008-08-06T15:00:00.000-07:002008-08-06T15:00:00.000-07:00Physics students have no problem with this expansi...Physics students have no problem with this expansion. They all know c is the speed of light.The skepTickhttps://www.blogger.com/profile/03437104069644740816noreply@blogger.comtag:blogger.com,1999:blog-15868947.post-43479147638678782122008-08-06T12:07:00.000-07:002008-08-06T12:07:00.000-07:00Oh - I forgot the anecdote.Supposedly the calculus...Oh - I forgot the anecdote.<BR/><BR/>Supposedly the calculus exam at my uni years ago broke a few heads by asking people to find the derivative of a function given in terms of x(f).Jens Knudsen (Sili)https://www.blogger.com/profile/14078875730565068352noreply@blogger.comtag:blogger.com,1999:blog-15868947.post-47429926023693523782008-08-05T14:10:00.000-07:002008-08-05T14:10:00.000-07:00I honestly can't remember how the problems were se...I honestly can't remember how the problems were set twelve years ago when I took calculus.<BR/><BR/>But I'm shaking my head in disbelief now. (Prolly doesn't help that I was directed to http://notalwaysright.com/ earlier today.)<BR/><BR/>If I'm being honest though, I wouldn't be surprised if I couldn't do it, myself, without prompthing now. I'd very likely forget the coefficients and even at my best I often 'diffegrated' when doing derivatives. And I have <I>no</I> recollection of how to estimate the bounds on the error term.Jens Knudsen (Sili)https://www.blogger.com/profile/14078875730565068352noreply@blogger.comtag:blogger.com,1999:blog-15868947.post-40938464232137966972008-08-05T01:42:00.000-07:002008-08-05T01:42:00.000-07:00It sounds like another case of favoring textual su...It sounds like another case of favoring textual substitution in lieu of understanding the concepts.Yoohttps://www.blogger.com/profile/08964658430856685576noreply@blogger.comtag:blogger.com,1999:blog-15868947.post-37375300962333328962008-08-05T00:13:00.000-07:002008-08-05T00:13:00.000-07:00I think the problem is that x is a variable. Thus ...I think the problem is that x is a variable. Thus the statement "at x=c" is so counterintuitive that the<BR/>students become confused (and rightly so since x is not c). If you focus on "around x=c" instead and hit them over the head with it a few<BR/>times they will probably do better.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-15868947.post-73106905755182292502008-08-04T20:21:00.000-07:002008-08-04T20:21:00.000-07:00I'm guilty of this sort of thing myself. Various s...I'm guilty of this sort of thing myself. Various second-year physics courses have scrubbed it out of me, but I've gotten the impression at various times that what's needed is for instructors to explicitly introduce students to various permutations of ways to ask the question (by way of examples), then throw them something <I>really</I> convoluted on the exam. Repeated application should improve their pattern-matching.<BR/><BR/>This is assuming that the students' little brains can handle that information in a reasonably time period. This may be a flaw in my suggestionâ€¦Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-15868947.post-68505834215104141392008-08-04T19:51:00.000-07:002008-08-04T19:51:00.000-07:00Sorry. The post got published before it was finish...Sorry. The post got published before it was finished. You saw a stub.Zenohttps://www.blogger.com/profile/09058127284297728552noreply@blogger.comtag:blogger.com,1999:blog-15868947.post-33411438309877166922008-08-04T18:53:00.000-07:002008-08-04T18:53:00.000-07:00I don't think I get it.I don't think I get it.Anonymousnoreply@blogger.com