tag:blogger.com,1999:blog-491174673971804494.post7397249616026848240..comments2024-03-22T01:06:23.845-07:00Comments on Confessions of a College Professor: Common Core and Fractions, Part 2Doomhttp://www.blogger.com/profile/04528555392898760692noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-491174673971804494.post-41609486223553170612014-07-19T18:13:20.591-07:002014-07-19T18:13:20.591-07:00Square roots by hand isn't much fun, but Metho...Square roots by hand isn't much fun, but Method 2 of Wikihow explains it clearly. Google "square root by hand method" to get there.<br /><br />Most public schools, like college, have 'two track' system. So, it's possible some students in a school learn long division, while others learn how to make shoebox displays.Doomhttps://www.blogger.com/profile/04528555392898760692noreply@blogger.comtag:blogger.com,1999:blog-491174673971804494.post-75691614531479122932014-07-19T15:12:57.526-07:002014-07-19T15:12:57.526-07:00Knowing stuff like prime numbers & what number...Knowing stuff like prime numbers & what numbers are highly composite (like 12) can be very handy. Also seeing stuff like a number being a perfect square, cube, or half/quarter of something or double/treble/5x/10x something. I am glad that when I was attending middle school in the mid-1990s, we still did things that 'old style' way you describe. I can't imagine how they teach decimal division these days. Do they teach short division in schools along with long? Now doing square root simplification by hand I never learnt. I would like to learn it though.Jesshttps://www.blogger.com/profile/17151299421522255994noreply@blogger.comtag:blogger.com,1999:blog-491174673971804494.post-48704517501741370482014-06-06T07:23:03.664-07:002014-06-06T07:23:03.664-07:00That's as good a way as any to multiply fracti...That's as good a way as any to multiply fractions, but students have been trained to think "multiplication is harder than addition". They're so blown away by addition of fractions that they figure the reason so little time is spent on multiplying that it must be impossible, and few ever learn it, at least to judge by what I see on papers.Doomhttps://www.blogger.com/profile/04528555392898760692noreply@blogger.comtag:blogger.com,1999:blog-491174673971804494.post-78341165534046156372014-06-06T02:07:00.738-07:002014-06-06T02:07:00.738-07:00Shouldn't that more complicated but elegant wa...Shouldn't that more complicated but elegant way be left for when students start taking algebra, where they'll need to know what a greatest common factor is in order to factorise polynomials and simplify rational expressions?<br /><br />Also, about simpler ways of handling fractions, is it frowned on everywhere (not just in schools) to multiply fractions by going straight across (multiplying the numerators and denominators) then simplifying the resulting product fraction? I've found this way to be easier for me, even though it does take longer. Oddly, I'm more likely to mess up when cross-cancelling! This is been an issue teachers have seen me deal with for many years now. They do not like seeing say 3/4 * 6/21 = (3 * 6)/(4 * 21) = 18/84 = 9/42 = 3/14.Jesshttps://www.blogger.com/profile/17151299421522255994noreply@blogger.comtag:blogger.com,1999:blog-491174673971804494.post-84871256705034786422014-05-01T14:51:10.422-07:002014-05-01T14:51:10.422-07:00I thought about mentioning GCF ("Greatest&quo...I thought about mentioning GCF ("Greatest"), but decided tossing that in there would be piling on confusion onto what is already a ridiculously complicated algorithm.<br /><br />I'm not sure I agree with the archdruid on many things; the whole "oil is melted dinosaurs" theory has siginficant issues. I really don't see humans forgetting bookkeeping skills, and I promise you, even if computers shut down tomorrow, and every single textbook burned, we'd have some rebuilt log tables within a short period of time...assuming nobody would just copy<br /><br />If it's such a fear, I guess someone could start printing books on plates of steel or something? A total industrial collapse is possible (I politely concede), but "Mad Max" is just not as likely for the world as real-world Somalia. I'm just not willing to believe humanity is that incapable on every level.Doomhttps://www.blogger.com/profile/04528555392898760692noreply@blogger.comtag:blogger.com,1999:blog-491174673971804494.post-86773205968018020852014-05-01T10:59:45.450-07:002014-05-01T10:59:45.450-07:00In industry, we had the saying "If it works, ...In industry, we had the saying "If it works, don't fix it." The traditional methods of teaching arithmetic, such as multiplication tables and handling fractions as described in the previous post, worked. It put men on the moon. It built ships, bridges, and aircraft. It created whole new industries such as electronics and computing. It runs cities and countries.<br /><br />Educationists, however, insist that they must "improve" things by meddling with what has been proven to be effective. I shudder to think what would have happened to me had I been taught fractions in the method you just described.<br /><br />It certainly explains why many of my students couldn't do basic arithmetic and they were recent high school graduates.<br />Quarter Wave Verticalhttps://www.blogger.com/profile/03173446011323023116noreply@blogger.comtag:blogger.com,1999:blog-491174673971804494.post-71792984669205074772014-05-01T10:43:03.853-07:002014-05-01T10:43:03.853-07:00Maybe a century back adding fractions could have b...Maybe a century back adding fractions could have been taught this way (i.e., taking the LCM). But these days the students just don't have practice at calculating LCMs and HCFs (highest common factors); count yourself lucky if they know the multiplication tables. Your way is the easiest.<br /><br />The old computational skills have gone out the window. Even school teachers these days usually cannot calculate square roots by hand. <br /><br />I think the Archdruid has it correct here:<br /><br />"Computer-free mathematics. Until recently, it didn’t take a computer to crunch the numbers needed to build a bridge, navigate a ship, balance profits against losses, or do any of ten thousand other basic or not-so-basic mathematical operations; slide rules, nomographs, tables of logarithms, or the art of double-entry bookkeeping did the job. In the future, after computers stop being economically viable to maintain and replace, those same tasks will still need to be done, but the knowledge of how to do them without a computer is at high risk of being lost. If that knowledge can be gotten back into circulation and kept viable as the computer age winds down, a great many tasks that will need to be done in the deindustrial future will be much less problematic." <br /><br />http://thearchdruidreport.blogspot.com/2014/01/seven-sustainable-technologies.htmlAAhttps://www.blogger.com/profile/13242448989166177843noreply@blogger.com