tag:blogger.com,1999:blog-8231784566931768362.post1858132459306603953..comments2017-08-14T07:12:08.201-04:00Comments on MathNotations: Top Ten Lists of Common (Student) Math Errors!Dave Marainhttp://www.blogger.com/profile/13321770881353644307noreply@blogger.comBlogger12125tag:blogger.com,1999:blog-8231784566931768362.post-15697083715417688942008-02-20T12:25:00.000-05:002008-02-20T12:25:00.000-05:00Cecil,Yes, √0 = 0. I meant that students thi...Cecil,<BR/>Yes, √0 = 0. I meant that students think it's undefined! Sorry for my lack of clarity. I was listing common errors but I should have made that clearer so one doesn't take it as a fact.Dave Marainhttps://www.blogger.com/profile/13321770881353644307noreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-5801781330272183822008-02-20T10:54:00.000-05:002008-02-20T10:54:00.000-05:00Dave:Isn't the function f(x) = sqrt(x) defined at ...Dave:<BR/>Isn't the function f(x) = sqrt(x) defined at x=0??, i.e., sqrt(x) = 0.cecil kirkseynoreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-4202000477819620232008-02-19T01:50:00.000-05:002008-02-19T01:50:00.000-05:00∫_a^b f(g(x))g'(x) dx = ∫_a^b f(u) du.∫_a^b f(g(x))g'(x) dx = ∫_a^b f(u) du.Eric Jablownoreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-29582168498934805372008-02-16T15:23:00.000-05:002008-02-16T15:23:00.000-05:00good one, jonathan!I attempted to prevent this com...good one, jonathan!<BR/>I attempted to prevent this common transposition by requiring that students write the extra step:<BR/>√25 ⋅ √3, but no instructional technique works with all students all the time! (It did work some of the time with some students...)<BR/><BR/>We could probably devote an entire book to negatives, which is why I often told my algebra students:<BR/>SUCCESS IN ALGEBRA = THINKING 'NEGATIVELY'!Dave Marainhttps://www.blogger.com/profile/13321770881353644307noreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-68184551156801293312008-02-16T14:54:00.000-05:002008-02-16T14:54:00.000-05:00canceling part of a sum. Do it in my class, and al...canceling part of a sum. Do it in my class, and all partial credit on that question is voided. <BR/><BR/>How about √(75) = 3√5 ?<BR/><BR/>But of course the most common student error is the magically disappearing minus sign...jd2718http://jd2718.wordpress.com/noreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-64318636933967844722008-02-16T10:57:00.000-05:002008-02-16T10:57:00.000-05:00jackie--Luv it!Sometimes, students simply don't si...jackie--<BR/>Luv it!<BR/>Sometimes, students simply don't simplify far enough. They will leave<BR/>an answer with √1 in their answer! And, of course, √0 is undefined.<BR/>Who is keeping track of these!Dave Marainhttps://www.blogger.com/profile/13321770881353644307noreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-38382991312262789132008-02-16T10:08:00.000-05:002008-02-16T10:08:00.000-05:00Simplifying errors with radicals: ((6)^.5)/2= 3^.5...Simplifying errors with radicals: <BR/><BR/>((6)^.5)/2= 3^.5Jackiehttps://www.blogger.com/profile/16859831037023994373noreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-30223764683429911572008-02-16T09:18:00.000-05:002008-02-16T09:18:00.000-05:00mathfr3d--for one who is not a math teacher, you f...mathfr3d--<BR/>for one who is not a math teacher, you found a 'classic!'<BR/><BR/>tc, eric--<BR/>We could have an entire section devoted to L'Hopital's and limits in general!<BR/>A classic: (1+1/n)^n → 1<BR/>Ah, those fun indeterminate forms!<BR/><BR/>Keep 'em coming folks.<BR/>This list should be endless...Dave Marainhttps://www.blogger.com/profile/13321770881353644307noreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-79320470529372659752008-02-16T08:48:00.000-05:002008-02-16T08:48:00.000-05:00So is the error of using l'Hôpital's rule without ...So is the error of using l'Hôpital's rule without checking that the numerator and denominator have limits 0 (or ∞).Eric Jablownoreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-75545843986595706362008-02-16T08:44:00.001-05:002008-02-16T08:44:00.001-05:00Another one:(x-2)(x+3)=(x-2)(2x+5)Cancel (x-2) fro...Another one:<BR/><BR/>(x-2)(x+3)=(x-2)(2x+5)<BR/><BR/>Cancel (x-2) from both sides, and get x=-2.<BR/><BR/>TCAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-16040976789330301442008-02-16T08:44:00.000-05:002008-02-16T08:44:00.000-05:00I'm not a math teacher but dividingand multiplying...I'm not a math teacher but dividing<BR/>and multiplying inequalities with <BR/>negative values is often a source of<BR/>errors:<BR/><BR/>-2 > 2x --> 1 > -xMathfr3dnoreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-86034619391340675662008-02-16T08:40:00.000-05:002008-02-16T08:40:00.000-05:00In particular, the error (f/g)' = f'/g'seems to in...In particular, the error <BR/><BR/>(f/g)' = f'/g'<BR/><BR/>seems to increase after the students get exposed to L'Hospital's rule. <BR/><BR/>TCAnonymousnoreply@blogger.com