tag:blogger.com,1999:blog-7322734145373546886.post2682224137131962708..comments2024-09-16T02:08:16.815-07:00Comments on Coming of Age in the Middle: Exponent NegativityAnonymoushttp://www.blogger.com/profile/12503110737663642101noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-7322734145373546886.post-7881522570932522062012-10-15T08:52:53.411-07:002012-10-15T08:52:53.411-07:00I feel that this comment summarizes the struggles ...I feel that this comment summarizes the struggles of many of our Algebra students:<br /><br />"The other thing I learned is this: if an integer is negative, you can stick it at the bottom of a fraction under a one, and it magically becomes positive. I don't know why, but if I simply accept this and apply it, my homework answers are right."<br /><br />Many students are taught a Bob Lochelhttp://mathcoachblog.wordpress.comnoreply@blogger.comtag:blogger.com,1999:blog-7322734145373546886.post-43491307960940339922012-03-31T17:45:01.925-07:002012-03-31T17:45:01.925-07:00I recently tweeted about how (many, not all) adult...I recently tweeted about how (many, not all) adults have no shame in bragging about how terrible at math they are or were when they were in school. However, we never hear an adult brag they can't read. This devalues numeracy. <br /><br />I think you are spot on. It's human to not know everything. Too many teachers are fearful they will be 'exposed' and wind up passing along Tales In Educationhttps://www.blogger.com/profile/17613178432615965613noreply@blogger.comtag:blogger.com,1999:blog-7322734145373546886.post-67674440647564687962012-03-12T21:00:44.298-07:002012-03-12T21:00:44.298-07:00Jessica, I posted this on Twitter, because you are...Jessica, I posted this on Twitter, because you are like any of my students who don't feel like "math is their thing," but you are able to articulate your struggles and frustrations so eloquently, honestly, and understandably. Please keep learning math for the sake of us math teachers!Timon Piccinihttp://mrpiccmath.weebly.comnoreply@blogger.comtag:blogger.com,1999:blog-7322734145373546886.post-1964031299695173142012-03-11T11:10:46.101-07:002012-03-11T11:10:46.101-07:00Wow! I have math peeps! And I get it! Thanks, ever...Wow! I have math peeps! And I get it! Thanks, everyone!!!Anonymoushttps://www.blogger.com/profile/12503110737663642101noreply@blogger.comtag:blogger.com,1999:blog-7322734145373546886.post-39594788283068958212012-03-10T09:51:01.613-08:002012-03-10T09:51:01.613-08:00x^0 = 1 is a requirement in order that the exponen...x^0 = 1 is a requirement in order that the exponent rules you've developed make sense. See http://mathforum.org/dr.math/faq/faq.number.to.0power.html<br /><br />The same is true of negative exponents. The "why" is because it extends the rules from the other cases in ways which make sense. This happens often in mathematics. We develop rules, and to make the rules work, we extend themDavidhttps://www.blogger.com/profile/08098221991466148258noreply@blogger.comtag:blogger.com,1999:blog-7322734145373546886.post-61389348330354776762012-03-10T01:48:13.614-08:002012-03-10T01:48:13.614-08:00Nothing triggers my compulsion to try to explain t...Nothing triggers my compulsion to try to explain things more strongly than a phrase like "I accept that it's a rule", so here's a go:<br /><br />http://minrk.posterous.com/the-law-of-conservation-of-exes<br /><br />I hope that doesn't end up just increasing your confusion and/or frustration.Min RKhttps://www.blogger.com/profile/06786006279154837800noreply@blogger.comtag:blogger.com,1999:blog-7322734145373546886.post-4842559451137335692012-03-09T18:29:39.101-08:002012-03-09T18:29:39.101-08:00The why is actually fairly manageable.
When you m...The why is actually fairly manageable.<br /><br />When you multiply two exponents with the same base you add the powers. x^2 * x^3 = (x*x)*(x*x*x) = x*x*x*x*x = x^5 = x^(2+3)<br /><br />When you divide, you subtract the exponents. 3^5/3^3 = (3*3*3*3*3)/(3*3*3) = 3*3 = 3^2 = 3^(5-3).<br /><br />x^0 can be written as x^(2-2) = x^2/x^2 = 1, because any value divided by the exact same value is alwaysSarahBhttps://www.blogger.com/profile/01699795594479465816noreply@blogger.com