tag:blogger.com,1999:blog-7718462793516968883.post2469127718298387404..comments2023-03-02T12:12:05.847-05:00Comments on MadMath: Faulty FactoringDeltahttp://www.blogger.com/profile/00705402326320853684noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-7718462793516968883.post-88266568448533185402014-03-18T01:48:10.874-04:002014-03-18T01:48:10.874-04:00Well, that does work, and I'd say it's equ...Well, that does work, and I'd say it's equivalent to the standard "factor by grouping" method (including the need to factors negatives with the GCF) -- except that using purely the GCFs from the box leaves it kind of a mystery as to why it works (and loses one place that one can double check). For example, I'd see your problem done as:<br /><br />9x^2-18x+8 <br />= 9x^2-12x-6x+8<br />= 3x(3x-4)-2(3x-4)<br />= (3x-4)(3x-2)<br /><br />So: (1) that's what I see in any algebra textbook, (2) it allows a clear explanation of why the last step works (the common binomial counts as a GCF), and (3) there's an opportunity to double-check if the parenthetical binomials don't match.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-63535750649108693442014-03-17T23:35:06.374-04:002014-03-17T23:35:06.374-04:00I've seen that approach used before and have s...I've seen that approach used before and have similar concerns with students getting problems wrong for the reasons you've noted.<br /><br />A few years ago, I came up with an alternate approach to factoring quadratics that is a decomposition of the box method used to teach FOIL in Algebra 1. It turns out that it is not an original approach--others in history discovered it before me--but it is not commonly taught, or known by most math teachers, because it doesn't show up in most standard high school textbooks.<br /><br />If anyone is curious, you can view a power point of the method at the link below (the second file). Note: when factoring out the GCF in slide 5, you always pull out the sign of the x coefficient, i.e. the GCF of -6x and 8 (for the method to work) is -2.<br /><br />Glenn Laniewski<br />Blog:<br />autismplusmath<br />My method:<br /><a href="http://autismplusmath.blogspot.com/p/the-store.html" rel="nofollow">Factoring Quadratics by the Box Method</a>?https://www.blogger.com/profile/09000980455095316183noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-65843987557712844052014-03-10T17:44:55.846-04:002014-03-10T17:44:55.846-04:00Fascinating! At least I'm not the only one who...Fascinating! At least I'm not the only one who sees this. I get maybe one or two students out of 30 doing this in those classes. I do have to keep a "backup explanation" prepared to engage with students when this becomes an issue.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-9853840783556989562014-03-10T13:26:21.455-04:002014-03-10T13:26:21.455-04:00The first time I saw it, I was blown away. (And it...The first time I saw it, I was blown away. (And it isn't common among my students (CA now, MI previously).) I asked the student to explain what she was doing, and of course she couldn't. I couldn't see why it worked at first. I finally got her to show me enough examples that I figured out the real process, as you show above.<br /><br />I let her use it. (Beginning algebra course, not worth the agony of pushing her to do something else, and she wasn't going to really understand it. Maybe now, 10 years later, I'd choose differently.)Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.com