659:, and is basically what TMott is talking about (and what I meant when I said FOILing is "easily extended"). Although... I guess "true" distributing requires two separate steps where you first distribute one polynomial (in parentheses) over the terms of the other, then distribute again to get rid of the parentheses (hence the term "double distributive property" mentioned in the article). What I was talking about is essentially a shortcut where you see the pattern and skip the first distributing step. TMott, it seems to me you were really talking about the same thing I was. BTW, a different way of looking at it, although completely equivalent of course, is called the "vertical format" and works the way most people learned to multiply numbers bigger than 10 on paper, by first lining them up vertically. -
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multiplication. It is mixing two different concepts, but I agree with KSmrg that the point is to remind students there will be 4 terms. A student has the four-letter acronym pounded into his head, and unraveling the meaning of each letter follows quickly. I wasnt ever confused by what "first" stood for, and I really dont remember it ever being an issue in junior high algebra class. (I do remember being annoyed that teachers would say complex multiplication and FOIL are entirely different processes, as though you had to then learn a completely new rule...) -
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understanding of symbolic manipulation already. The FOIL rule is simply a shortcut for the (slightly) longer process of distributing. When you learn how to multiply polynomials of any number of terms, you either see what's actually going on at that point and then don't worry about it anymore, or you never really get it and don't go into a field that requires you to know much mathematics. In either case, the use or non-use of the term "FOIL" is moot. -
1542:. This method has a similar limitation to the FOIL method: it does not generalize in any obvious way to cubics, whereas solving by estimating where the curve crosses the X-axis does. I would not however call the rote formula "phony," despite the fact that it is not easily memorized whereas the method of intersection with the X-axis is (not that I've forgotten the rote method, although I prefer to think of it as solving (
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The article should simply say that FOIL is an acronym for a mnemonic with a basic description of what it refers to, then link to an exposition about multiplying polynomials which should lie elsewhere. It's not POV, it's not denigrating the term, it's not ignoring it, it's just describing what it is.
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Pointing this out in the article would almost certainly be seen as pushing a POV. Citing a "respected" source criticizing the method... well, that would be acceptable. As for your remarks about the way people learn mathematics, I believe they apply more to teachers and state education officials than
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the students themselves, since people usually have very little say in how they learn algebra: they simply "attempt to learn" it the way their teachers "attempt to teach" it. FWIW, as a math tutor in Austin, TX, for 10 years, tutoring mostly high-school seniors and college students — that is, mostly
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FOIL is sufficient to expand this product if you creatively combine it with associativity and recursion. It might be instructive to include this tidbit to show how one could apply FOIL to expanding the product with two multiplicands with three summands each. (And, btw, thanks KSmrq for adding the
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on mathforum.org as an example of student confusion. I think it's a good one. The student is confused because all of a sudden there are three multiplicands and no eight-letter acronym to help. But from the wording of the reply, I think "Doctor Ian" misunderstood the student's confusion (though I
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Yeah, it seems you were talking about the same thing, but missing the part about it not being FOIL anymore. But the phrase could certainly use some attribution to a reputable source, and I haven't been able to locate one. Is there a well regarded textbook regarding teaching algrebra you know of? I
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Though the “monkey face” description is cute and somewhat enlightening, it doesn't seem to appear anywhere else on the web, and its tone is hardly encyclopedic. I have therefore removed it from the article. However, I have retained the wonderful graphic and placed it at the top of the article.
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I was taught in junior high to use the FOIL rule, and later in college I learned that when you tutor students in algebra (even college students), they understand much better when you use words like "FOIL", "cross multiply", "SOH-CAH-TOA" (which I still use :), and "Lo-dee-hi minus Hi-dee-lo over
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As a search of the Web will confirm, the FOIL idea is discussed at many educational sites (some training teachers) and incorporated into textbooks. Two objections are: (1) this introduces a new isolated fact to memorize rather than relying on the already-learned distributive law, and (2) it only
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the generalized version of foil is simple for a mathematician: given: A=(a1+a2+a3+....an) B=(b1+b2+...bm) then A*B=ΣΣai*bj ... Which bascially means, multiply every term in one, by every term in the other. Add them all up. Make an array to keep track if you have to. ... I'd probably add the
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How new is the FOIL method? The oldest (only) reference in the article is 1997. If it's a new pedagogical device then it's not too surprising to see it meeting some resistance, especially by those opposed to learning by memorizing rules. (My impression is that memorization has been making
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Should the article mention that the name "FOIL" is a childish usage? I never heard of it until I'd been an undergraduate for more than three years and I attempted to help someone in an algebra course. It's clearly one of those mnemonics used only by those whose way of attempting to "learn"
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I can attest to its use in the 70's. So many worked up over a mnemonic for a simple shortcut limited to binomial multiplication. The only aspect I don't like about it is the perception that it is some type of algebraic property or rule rather than a shortcut for the distributive property. I
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common (in the southern U.S., at least), and in my experience doesn't really correlate at all with one's mathematical maturity. By the way, note that I do not tutor
Algebra I precisely because it's just too hard to explain certain algebraic concepts if the student doesn't have some basic
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A student who approaches this will know he is trying to multiply two factors together, so "first" means he will multiply the first terms of each factor together. When it comes to inside-outside... well, that's just a pictoral view of the other two things he needs to do to finish off the
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of the terms in FOIL is irrelevant; the point of the mnemonic is to help students remember the four terms of the result. Apparently their brains would explode if asked to understand and use the distributive law twice, especially since the pieces are not numbers but symbolic monomials.
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know what the possible terms are, and then what do you need a mnemonic for? The objections are fair and I wouldn't mind them being in the article, but I can think them up myself and thus don't really need them. What I would have liked an encyclopedia to tell me, however, is how the
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that this is the way we were taught math in the united states. rather than yelling at us for being childish, please understand, many of us lacked teachers who would actually take the time to explain the theorem and WHY foil works. we were just taught it, pure and simple.
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of the rule imagine that it helps. At the moment the article describes the rule in a way that invites ridicule ("The name comes from the order of multiplying terms of the binomials", when the order is immaterial? And "The FOIL dance"???) and it is quite likely that it
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I definitely agree with the article. FOIL avoids any kind of reasoning or understanding of what's going on. Extending it is confusing, because then it's no longer FOIL. To teach a general method without using FOIL, you could, for example, first explain why
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method may not be applicable, it is easily extended to polynomials with more terms. Besides, how else is one supposed to learn to muliply polynomials? What could this other "general method" be that would be useful to beginning algebra students? -
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If you weren't ever confused by what "first" stood for, it means that you understood what was going on, beneath the rote-learning. Congratulations. But, given that you possessed that understanding, what did you need a mnemonic acronym for, then?
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and then estimate where it crosses the X axis, easily verified by back substitution. But that's not how I learnt to find the roots half a century ago, instead we were taught to "complete the square," from which we then derived the rote formula
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I'm asking what it is the mnemonic is a mnemonic FOR. For (a+b)(c+d) "first" might just as readily mean ab as it might mean ac, and if you have another way of remembering which of the ones this is, what use is there left for "FOIL"?
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Oh, I'm not arguing for deletion. I'm just genuinely puzzled why this can help anybody remember anything relevant at all. The words "first" and "last" do not really tell what the terms they are supposed to imply are, unless you
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applies to a product of binomials. I find those compelling objections, and would like to see them mentioned in the article; however, my only sources are opinions stated on Web forums, which
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in which the terms of the folded-out product comes. Could somebody please link to it? I fail to imagine a distributive law that could feel halfway natural and still dictate an internal order between the O and I terms.
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Is there really much more to add to this article? I'm kind of new to the whole wikipedia thing and I was looking for something I could expand in and find the FOIL article. It looks fairly complete to me, any comments?
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It is commonly taught, but is often frowned upon because the method does not work for higher order polynomials, and thus instead of actually teaching a general method, it is an example of learning by rules instead of
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No, I still don't get it. If the brains in question are that prone to exploding, what good does a rote like FOIL do at all? A word like "first" or "inner" is not meaningful unless you
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How about "first summand in each multiplicand", "outer summands in each multiplicand", and so on. In a classroom setting, this is usually replaced with pointing with one's fingers.
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for the order! And won't brains start exploding anyway the first time they are expected to follow an argument that happens to expand such a multiplication in FIOL order? –
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This method was frowned upon by my high school math teacher by the fact that it can cause confusion and errors when answer expression with positive/negative numbers.
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Lo-Lo" (for the quotient rule of derivatives). They may make pure mathematicians cringe, but these are mneumonics used by non-mathematicians to learn the rules. -
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can only speculate). He simply launches into a discussion of his own understanding (but does offer some sage advice along the way that shouldn't be ignored).
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If you have concrete references to relevant parts of the educational literature, please do add them to the article and provide a summary of their arguments. –
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Well that is a very common sentiment. I forgot to mark down any source that mentions it, but it is certainly common. I'll see what I can do to dig one up. -
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I'm seriously confused: What is this rule about? Appears to be some weird kind of algebra with a non-commutative addition where one needs to remember the
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That would be criminally misleading: it would teach the non-fact that the product of a1+a2+...+an and b1+b2+...+bm consists of terms of the form ai*bj
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Consider a news item that says "Between May 2000 and August 2005, Brazil lost more than 132,000 square kilometers of forest—an area larger than Greece"
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FOIL has been much debated, discussed, railed against, defended in the educational literature. This article, surprisingly, has none of that. --
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something of a comeback recently in educational circles.) But in what sense is the method "phony?" When I look for the roots of a quadratic
1353:..beautifull? ugly?...thing if I knew how to flesh out those sigmas. beautifull to a mathematician; ugly to the typical algebra student.
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The term "FOIL rule" is rarely used, "FOIL method" is an order of magnitude more common. I suggest moving the article accordingly. --
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Hypnotize yourself and regress back to a time in your life when words like "commutative" and "distributive" meant nothing to you. The
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may be able to go to the university bookstore and look for one. Also, I couldn't find any article that actually explains
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two things are a and b, and so forth. And once you do know what the point it, "FOIL" gives no additional information
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where for each term there is a common principle that is applied uniformly to (1...n) and (1...m) to select i and j
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I've upgraded the rating to "Start" since this is not a stub article. Is it B-worthy? I'm tempted to say so. -
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I think you do understand, you just don't like it. Fair enough; but we're not endorsing, we're reporting.
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topics on
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I think there should be some articles that explains the negative aspect of this rule. Thanks,
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know that you're supposed to take products of one term from each multiplicand. Indeed, if you
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Please help fix the broken anchors. You can remove this template after fixing the problems. |
1306:(O+I). How sad for the teachers; how bizarre for the students. One teacher-of-teachers says
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essentially have the same sentiments expressed by dcljr. The last 3 sentences say it all.
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979:"FOIL" is an English word. "FIOL" is not. That's the only reason "O" comes before "I". -
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ridicule, but I would like to see the other side of the argument, too. Whatever it is. –
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ie. (x + 3)(x - 7) = the answer could be incorrect by the confusion of the minus sign.
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Foil is pretty much the same thing as taking an outer product of two arrays.
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can somebody fix the erros which seem to be examples. as of this current date
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It seems that for complex multiplication the rule "FLOI" is taught! That is (
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This article links to one or more target anchors that no longer exist.
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but do not attempt to include the whole process of factorization here
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A quick Google search confirmed this. I have moved the article.
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an algebra class, I understand: the "general method" is simply
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Possibly the history of the subject? A see also section? --
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501:Then show why
499:
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295:case-sensitive
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257:Mid-importance
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18:Talk:FOIL rule
14:
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2:
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1627:Vaughan Pratt
1620:
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1599:
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1589:
1588:Vaughan Pratt
1585:
1581:
1577:
1573:
1569:
1565:
1561:
1557:
1553:
1549:
1545:
1541:
1537:
1533:
1529:
1525:
1521:
1517:
1512:
1508:
1504:
1500:
1496:
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1488:
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1481:
1476:
1471:
1466:
1462:
1457:
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1450:
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1445:Michael Hardy
1442:
1434:Childish term
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1427:
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1199:
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936:
935:factorization
932:
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922:
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884:
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835:
832:
829:
826:
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767:
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758:
754:
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748:
744:
740:
739:69.234.165.36
736:
728:
724:
720:
716:
712:
700:
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696:
692:
688:
684:
672:
667:
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658:
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619:
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483:
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368:
363:
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352:
351:
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345:Frowned upon?
344:
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324:
317:
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296:
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286:
279:
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71:
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52:
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38:
34:
29:
28:
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1731:
1703:— Preceding
1699:
1683:96.224.43.92
1679:
1659:
1624:
1583:
1579:
1575:
1571:
1567:
1563:
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1547:
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1535:
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1498:
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1490:
1486:
1464:
1460:
1440:
1437:
1385:
1366:
1350:
1340:
1335:this article
1332:
1303:
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1261:
1228:
1098:
1093:
1088:
1037:
1033:
1029:
1025:
1007:
997:
963:
961:
938:
914:
913:
911:
806:
786:
729:
704:
679:
657:distributing
656:
652:
361:
359:
353:
348:
328:
325:We cant help
301:
293:Anchors are
290:
256:
212:
148:Low-priority
147:
107:
73:Low‑priority
51:WikiProjects
1656:Monkey face
1355:24.18.8.160
1342:tableau.)
733:—Preceding
709:—Preceding
123:Mathematics
114:mathematics
70:Mathematics
41:Start-class
1750:Categories
1441:memorizing
1302:) = (F−L)+
1094:proponents
777:TeaDrinker
687:Polynomial
1709:Danielhhs
1465:extremely
915:Supuhstar
757:factoring
355:concepts.
232:Education
219:education
175:Education
1717:contribs
1705:unsigned
1603:JackOL31
1418:Marasama
1099:deserves
958:Confused
747:contribs
735:unsigned
723:contribs
711:unsigned
653:teaching
1382:Math ed
1153:grubber
1121:grubber
1089:already
1026:already
789:grubber
715:Mlw1235
259:on the
150:on the
1586:). --
1530:where
1461:adults
1391:(Talk)
1038:except
1030:didn't
1000:WT:WPM
807:Contra
695:Taxman
382:Taxman
47:scale.
1732:math
1562:² + 2
1550:)² =
1538:² − 4
1470:dcljr
1344:Lunch
1312:KSmrq
1282:) = (
1202:Lunch
1067:KSmrq
1034:first
1013:KSmrq
1008:order
998:From
981:dcljr
964:order
943:Lunch
761:dcljr
701:Stub?
661:dcljr
636:TMott
367:dcljr
362:exact
1738:talk
1713:talk
1687:talk
1667:talk
1646:talk
1631:talk
1607:talk
1592:talk
1582:² −
1554:² −
1518:= (−
1505:² +
1489:² +
1475:talk
1449:talk
1422:talk
1373:talk
1359:talk
1310:. --
1308:this
986:talk
766:talk
759:. -
743:talk
719:talk
666:talk
372:talk
336:talk
291:Tip:
221:and
1663:Jim
1642:Jim
1526:)/2
1388:C S
941:.
900:. —
853:to
251:Mid
142:Low
1752::
1740:)
1719:)
1715:•
1689:)
1669:)
1648:)
1633:)
1609:)
1594:)
1584:ac
1574:+
1572:ax
1566:+
1564:bx
1560:ax
1556:ac
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1522:±
1509:+
1507:bx
1503:ax
1501:=
1493:+
1491:bx
1487:ax
1451:)
1424:)
1375:)
1361:)
1300:bc
1296:ad
1290:)+
1288:bd
1284:ac
1271:)(
1011:--
1002::
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830:12
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745:•
725:)
721:•
685:.
599:…
554:…
470:…
432:…
338:)
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1473:(
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1357:(
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1292:i
1286:−
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870:5
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565:k
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538:(
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530:2
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443:k
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416:+
411:1
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403:(
400:a
374:)
370:(
334:(
310:.
263:.
154:.
53::
20:)
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