tag:blogger.com,1999:blog-7718462793516968883.post7932154142710800603..comments2021-04-10T08:19:35.051-04:00Comments on MadMath: Basic Logic ErrorsDeltahttp://www.blogger.com/profile/00705402326320853684noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-7718462793516968883.post-45233759261041408062015-03-15T19:55:40.224-04:002015-03-15T19:55:40.224-04:00My pleasure! I get to clarify that a few hundred t...My pleasure! I get to clarify that a few hundred times a year, so I've got that pretty well practiced. :-)Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-63946014528771603702015-03-15T16:09:35.679-04:002015-03-15T16:09:35.679-04:00Oh, wow! Yeah, I got that 2^3=-8 was crazy, but I ...Oh, wow! Yeah, I got that 2^3=-8 was crazy, but I legit could not see the problem with -5^2=25. I had no idea that for a negative base, you needed to enclose the whole thing in parentheses, else it would be assumed that you'd multiply the final exponentiation of the positive base by -1. I assume I knew that at some point, since I started as a math major and made it through a year of that before switching... but then again, my grades weren't great! (grin) Thanks!LWSCHURTZhttps://www.blogger.com/profile/06635573516962732975noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-64814811822332881482015-03-15T13:17:41.385-04:002015-03-15T13:17:41.385-04:00Actually, in revising my basic arithmetic lectures...Actually, in revising my basic arithmetic lectures, I just wrote a quick primer on these issues (in a 1-hour block that usually floats around the schedule as an "optional" lesson). And in my algebra classes I introduced a diagnostic where the first question is: "If Alice is happy, then Bob is sad. Which of the following cannot happen? (4 permutations)", which turned out to be one of the hardest things on that diagnostic. If that turns out to be correlated with final results, then I may start injected that same 1-hour logic primer into all my remedial classes. <br /><br />Anyway, in item #1 above, I'm assuming you can see 2^3 = -8 as being nutso (and we do get it). The thing with -5^2 = 25 -- which I claim is the single most common, simple error in algebra -- is that for a negative base you need to write it in parentheses (a statement and example of which is always physically on the board as I'm quizzing students about #1). <br /><br />A juxtaposed negative sign is the same as multiplying by -1, so in truth: -5^2 = (-1)5^2 = (-1)25 = -25 (by order of operations: exponent happens first, then the negative multiplication). If someone wants to square -5, then it must be written: (-5)^2 = (-5)(-5) = 25. Even students with calculators are likely to overlook this, type it into the calculator without parentheses, and so when asked "what is -5 squared?" come back with the incorrect (but correct for what they typed) -25. Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-62505370683220487382015-03-15T06:05:30.746-04:002015-03-15T06:05:30.746-04:00I have trouble with students being unable to read ...I have trouble with students being unable to read logical statements in LOGIC classes. Sigh. But a few comments on these examples:<br /><br />#1) To my chagrin, I can't figure out what's wrong, here, and I know I'm reading the logic right. Apparently, my definition of "base" is incorrect. Could it be that some students are having the same problem?<br /><br />#2) That one, I hope, arises from the equivocal nature of "need" in the vernacular, where it is often conflated with "desire" or "want." Of course, I have noticed that students struggle a lot more with the "necessary/sufficient" distinction than I would have thought.<br /><br />#3) That one is just sad.LWSCHURTZhttps://www.blogger.com/profile/06635573516962732975noreply@blogger.com