tag:blogger.com,1999:blog-7718462793516968883.post2400517846859976380..comments2022-07-30T07:38:11.860-04:00Comments on MadMath: Words Matter!Deltahttp://www.blogger.com/profile/00705402326320853684noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-7718462793516968883.post-46625635228230927132012-09-11T01:45:41.745-04:002012-09-11T01:45:41.745-04:00Thanks for the comment and appreciation on that po...Thanks for the comment and appreciation on that point. <br /><br />Just today (first day of fall semester for me), I did my usual 1st-class handout of the definitions of terms for my remedial algebra class. One girl comes up at the end and profusely thanks me for it, saying, "I begged my last teacher to tell me what these terms meant, and he said don't worry about that, just do the problems." And my mouth went agape and I started thinking about going to find someone to throttle!Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-89628975798122033672012-09-11T01:42:35.367-04:002012-09-11T01:42:35.367-04:00Wow, what a great observation! I hadn't heard ...Wow, what a great observation! I hadn't heard of Maxima before, but awhat a fascinating lesson to draw from it and your work.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-15575505363545518182012-09-10T20:04:51.551-04:002012-09-10T20:04:51.551-04:00Your realization that this implied thing that you ...Your realization that this implied thing that you "always do to it" is somewhat useless if taught came to me one day, too. For a bit I used symbolic math software -- both Maple and MathCad, they both use the same engine (or at least used to at the time). The results were usually presented simplified in a certain way, and it seemed to "agree" with how things were expected of us in high school maths.<br /><br />I then started using the open source Maxima, and there the default simplifications were rather minimalistic. Maxima had me explicitly invoke various kinds of simplifications. At first it seemed like a drag, and I thought it was some kind of a drawback. Eventually it came to me that perhaps, just perhaps, the nice form of "usual" or "common" high-school simplification is not very useful except in said high-school math setting. That's because I was using symbolic maths in engineering, and how you'd want the final symbolic result presented was really application specific. Different kinds of post-processing "simplification" applied to different subject areas and types of problems.<br /><br />There were times when sorting by highest monomial exponent in sums monomial products made the expression unreadable in the context of a problem. Other times taking out common factors would make it blow up to half a page and make it equally unreadable. Various simplifications of rationals/fractions would also backfire. Almost every simplification you'd think of, that we were expected to apply as a matter of fact to produce "clean" final results, would backfire once, and then keep backfiring when one delved deeper into a particular kind of problems. Eventually I realized that pretty much every symbolic math problem that I was solving in grade school was engineered to be amenable to certain mechanistic approach in solving it, including mindless application of simplifications. Real life turned out to be a nice eye opener.<br /><br />Coincidentally, I agree with Unknown's love for applied math. I couldn't make the heads nor tails of maths until I could apply it.---https://www.blogger.com/profile/02360963065007021231noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-67745710578280919072012-09-10T19:09:51.261-04:002012-09-10T19:09:51.261-04:00'...that for any given algebraic expression, t...'...that for any given algebraic expression, there's some implied thing that you always "do" to it'<br /><br />That's some heavy, hammer-beating-nail-on-head stuff right there, Delta. Many people seem to suffer from this disease and it limits their ability to succeed in advanced math courses and hard-science.<br /><br />It's also worth noting that math teaches essential problem-solving skills, critical thinking skills, visualization skills, and other abilities useful for life that have nothing to do with solving an equation.<br /><br />I think part of the problem is that we teach math as a completely isolated subject through algebra II/trig. Most people end their studies at about this point and think "well that was interesting but a complete waste of time."<br /><br />I find that math is a lot more interesting and digestible in the context of physics lab, real-world examples, and word problems. I didn't really understand algebra until I got to calculus and put all those esoteric techniques to use. I didn't understand series and Fourier analysis until I took engineering courses and was exposed to useful and meaningful applications of math.<br /><br />Going back to your point, I fully agree that many math problems don't make it clear what you're being asked to do. I have no supporting evidence, but I also believe that poorly-worded problems can lead to an apparent inversion of intelligence in the class where the students who don't really know what they're doing can at least memorize the mechanics and the more capable (but bored) students don't recognize the limited scope of the question and give a wrong correct answer.Unknownhttps://www.blogger.com/profile/05018937822711944070noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-43161930734580397002012-02-20T15:03:22.729-05:002012-02-20T15:03:22.729-05:00Here's a related anecdote. First day, first pr...Here's a related anecdote. First day, first problem in my sophomore statistics class looks like this -- "The following table provides percentages of U.S. adults, by educational level, who believe that evolution is a scientific theory well supported by evidence... Do you think that this study is descriptive or inferential? Explain your answer."<br /><br />Answer -- "Inferential, because the reported results are for all 'U.S. adults', not restricted to a sample or survey."<br /><br /><br />So last year this prompts one student to ask: "Do you you always do it like that?" And I'm somewhat at a loss for words, but what I say is, "No, you have to read the problem and do whatever it asks you to do." And the student in question had apparently never confronted that issue.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-45010119034971679482012-02-20T02:23:32.427-05:002012-02-20T02:23:32.427-05:00^ I fully agree!^ I fully agree!Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-5372479670618854412012-02-19T21:26:40.722-05:002012-02-19T21:26:40.722-05:00Well said, Delta
I hope elementary teachers read ...Well said, Delta<br /><br />I hope elementary teachers read this too - it's not just algebra questions that are crap in many places. In fact, some even recommend teaching students to look for "key words" so they can ignore the rest - AAARRRGGGHHH!<br /><br />Let's start a revolution about teaching math so our students UNDERSTAND it, not so they learn a bunch of tricks to answer questions quickly. :)ProfPetehttps://www.blogger.com/profile/12575502626496101245noreply@blogger.com