tag:blogger.com,1999:blog-2433841880619171855.post2587791577153256629..comments2024-03-27T21:09:44.320+00:00Comments on Pat'sBlog: Student Confusion about Order of OperationsUnknownnoreply@blogger.comBlogger5125tag:blogger.com,1999:blog-2433841880619171855.post-29593289612683095312009-10-03T15:06:12.758+01:002009-10-03T15:06:12.758+01:00Poor handwriting is another factor to consider. I ...Poor handwriting is another factor to consider. I don't know how many times I have pointed out to students that "1/2a" just doesn't cut it when what they really mean is "(1/2)a". They can't even read their own work from one line of a problem to the next.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-68024395434497920862009-09-27T17:33:18.635+01:002009-09-27T17:33:18.635+01:00Sue,
I don't think it will ever go away... i...Sue, <br />I don't think it will ever go away... in my web page notes I have "The symbol "÷" is called an obelus, and was first used for a division symbol around 1650. The invention is often credited to British Mathematician John Pell but I have also seen credit given to J H Zahn, Teutsche Algebra (1659). The colon, ":", was used as a fraction symbol, and later as a division symbol by Liebnitz around 1685 in much the same fashion as the obelus, "8:4=2". " and later in the same article, "Cajori remarks that De Morgan recommended the use of the / in 1843, and although he continued to use : in his subsequent works, his advice was taken up by Stokes from 1880 and several others. Some years later the National Committee on Mathematical Requirements (1923) opined, "Since neither ÷ nor :, as signs of division, plays any part in business life, it seems proper to consider only the needs of algebra, and to make more use of the fractional form and (where the meaning is clear) of the symbol /, and to drop the symbol ÷ in writing algebraic expressions." and yet here we are in the 21st century and it is still around.Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-27392556033263972362009-09-27T16:46:11.526+01:002009-09-27T16:46:11.526+01:00We (mathematicians) have tried to use visual cues,...We (mathematicians) have tried to use visual cues, so that multiplication and division group more tightly on the page than plus and minus, and exponents more tightly yet. <br /><br />And then we have stupid textbooks that use the bar and dots symbol for division in order of operations problems, which I have *never* seen otherwise.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-13745883558377756422009-09-27T16:16:18.151+01:002009-09-27T16:16:18.151+01:00In typical Canadian fashion we (generally) combine...In typical Canadian fashion we (generally) combine the American and UK acronyms and teach 'BEDMAS.' Does anyone use "index" for exponents and teach PIDMAS or BIDMAS? :)<br /><br />Pointing out these issues is really useful - it is unfortunate that some teachers hard-headedly insist when teaching this stuff that it is completely consistent and free from any contradictions. Far better to realize (and point out) that, just with natural language, context is important. The notation we use is a shorthand for what could be made completely rigorous - thanks to convention we can use our notation more freely. The struggle to learn these conventions is the struggle to attain fluency, a challenge in any language.dan.mackinnonhttps://www.blogger.com/profile/13603404133431327842noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-35618167636955009182009-09-27T16:13:39.399+01:002009-09-27T16:13:39.399+01:00This comment has been removed by the author.dan.mackinnonhttps://www.blogger.com/profile/13603404133431327842noreply@blogger.com