Absolute Value: Magnitude of a Number
Date: 11/24/97 at 23:36:12 From: Ann L. Triplett Subject: Absolute value I have just visited this Web site for the first time, and view it as an important potential resource. I have just started teaching developmental (remedial) math part time at a community college (it's my second semester), so I am actually teaching K-12 material. I find that I don't have enough experience to field some of my students' questions about how they could use this in real life. (Ironic, since I have worked since 1981, first at Federal Express and then as a consultant, now part time - so I SHOULD have some experience using MATH in real life/business). They stumped me today - I could not think of a single time I have used the concept of ABSOLUTE VALUE in my work - any ideas where they may run into it ? Ann Triplett - Arlington, TX
Date: 12/08/97 at 14:04:52 From: Doctor Mark Subject: Re: Absolute value Hi Ann, Since I teach remedial math at my state college (twice per term), I feel your pain... Absolute value is one of those things that really doesn't have any applications, in a strict sense. Said another way, it has lots of applications. Let's see why. The best way I have found of describing absolute value is that the absolute value of a number is just the number, ignoring the sign. That is, it's sort of like being colorblind. People who are colorblind don't see colors, and people who are "absolute valuers" are "minus sign blind": they don't see minus signs. Of course, this only holds for single numbers, not combinations like 5 - 3, or variable quantities like - x. The main mistake that students make regarding absolute value (which I actually prefer to call the "magnitude," since it's shorter) of a number is that they treat it by analogy: since |-5| = 5, it must follow that |5| = - 5. That is, they think that absolute value means "change the sign," not "ignore the sign." There are just not that many situations in which you are supposed to "ignore" the sign of a number, because the sign of a number is just as important as the number next to the minus sign (which, of course, is the absolute value of the number!). On the other hand, there are, in some sense, lots of situations in which the absolute value rears its head. The reason that its use is not apparent is that we denote the sign of a number by some word, like "increase by," "decrease by," or "fell by," followed by the absolute value of the number. For instance, suppose the temperature went from 55 degrees to 32 degrees. We say that "the temperature dropped by 23 degrees". What we mean is that the change in temperature [which is *always* (final temperature) - (initial temperature)] was 32 - 55 = - 23 degrees. But we express that as "it dropped (the "-") by 23 (the absolute value) degrees." That is, in English, we use words to denote the sign of the number, and absolute value to designate the magnitude of the number. Similar considerations apply to profit/loss, income/expense, and so on. So in some sense, the absolute value is used all the time. You might consider subscribing to the <math-teach> mailing list, also run by the Math Forum (for how to subscribe, see "About this discussion"): http://mathforum.org/kb/forum.jspa?forumID=206 There you can interact with other college faculty, and with K-12 mathematics teachers, and post your questions. I am a pretty active member of that group, and if you post any pedagogical/why do we need this/what's this good for types of questions there, you will probably get responses from me. -Doctor Mark, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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