Mnemonic abbreviations – only as necessary
Abbreviations. Shortenings. Zakrasheniya. And all variety of cutesy ways to remember mathematical details. I don’t go for them. Not when the mathematical principles would be just as clear (or clearer) without them.
I don’t like:
- FOIL. (special case; don’t we know how to distribute?)
- Please Excuse My Dear Aunt Sally (misleading in multiple ways)
- All students take calculus (huh?)
I once depended on “sinus-minus” but now think it is silly. And I still need “A student earning B’s is not on probation” but I am getting to the point where it might go bye-bye soon. But I think my students will still benefit from it.
And I do write:
complementary
complementary
qomplementary
(that q is a 9 with a straight spine) which I learned from a teacher who learned it from a kid – but now it’s just a gag – my students already know the difference between complementary and supplementary.
Anyway, do you know some cutesiness that is useful? More examples of uselessness?
JD2718 
I agree with you on FOIL and Aunt Sally, but I’m embarrassed to admit I don’t even know what the others you mentioned mean. (Okay, the “qomplementary” one I can figure out.) As for useful mnemonics, well, I still occasionally rely on good ol’ Indian chief Sohcahtoa.
What’s the harm in using FOIL? I also find that ASTC is helpful, not to replace conceptual understanding, but as a shorthand. I use “All Students Take Courses” instead of ” … Calculus,” since not all students take calculus. I also find sohcahtoa quite helpful. I would say that sohcahtoa, especially, is beyond the criticism that the mnemonic is replacing understanding, since the definitions of sine, cosine, and tangent are simply facts that need to be memorized – that is, there’s nothing magic about sine being defined as the length of the opposite leg divided by the length of the hypotenuse.
a student told me last quarter
that “sohcahtoa” has the expansion
“silly old hippie, chillin’ at home, tripping on acid”.
i can enlighten denise as to “all students take C”
(where C is “calculus”, “classes”, “care” …):
of the 6 trig functions, All are positive in quadrant I,
Sine (& its reciprocal) is positive in Q.II
(and the others are negative),
Tangent (& its reciprocal) is positive in Q.III,
& Cosine (&c) is positive in Q.IV.
but of course this is all perfectly obvious
if one but knows that sin(t) is a y co-ordinate
and cos(t) the corresponding x co-ordinate.
oh, and SOHCAHTOA abbreviates
sine = opposite/hypotenuse,
cosine = adjacent/hypotenuse,
tangent = opposite/adjacent.
pretty useful for beginners as it seems to me,
though a colleage told me not long ago
that whenever he grades an exam
with the property that the student has written
“SOCAHTOA” at the top of page one,
that exam always turns out to have a very low score.
what i *don’t* know is the one about a student
earning b’s. hmm. googling. no apparent help.
i learned it
“Some Old Hippie Caught Another Hippie Trippin’ On Acid”
it was kinda funny because my math teacher replaced “Acid” with apples, but made it obvious and implied that it was acid.
I’d forgotten most of these, though Aunt Sally is ringing a bell (my daughter met her this year in fifth grade), as is SOHCAHTOA.
Math is not subject I need mnemonics for, so they haven’t stuck with me like the way ROY G. BIV, Oh Be A Fine Girl Kiss Me* or “only one c is necessary” have.
Now what would be really useful would be if someone would come up with a good mnemonic for when to use “which” or “that.”
— Rachel
* Otherwise known as “Only Bungling Astronomers Forget Generally Know Mnemonics” or “Only Boring Astromomers Find Gratification Knowing Mnenonics.”
And it looks like I could use a mnemonic for spelling mnemonic…
Distribution of terms
A Student = All – subject
Earning B’s = Non – both
Is Not = some are – neither
On Probation = some are not – predicate
Remembering which terms are distributed is not easy. A few kids master the underlying principles (wonderful!) but most need the mnemonic. I use it too.
I forgot SohCahToa, and I do like Vlorbik’s version, which is new for me. I use this one, and find it useful. What is sine and what is cosine is rather arbitrary.
FOIL is, imho, useless. Why memorize when the first principle, distribution, is clear?
Further, a good handle on double distribution makes factoring much, much easier. And finally, banning FOIL, and I actually ban it, catches kids attention with a clear message that even those who know something are not going to skate by on prior knowledge.
SOHCAHTOA is the only one I know/use. Many of the others I didn’t recognize at all (sinus-minus??) In general I think understanding should trump memorization in math (and science, and everywhere else possible). But Jonathan, how do you “ban” FOIL? Require them to show an intermediate step?
okay … i looked up distribution of terms
and *still* don’t get it. never mind.
I don’t like any of them. In the end they learn the mnemonic, but they can’t tell you why it works.
And, I don’t understand the students’ b’s and probations either.
Hm, distribution is tough. Let’s start by considering “categorical propositions” These are statements of the form Q subject C predicate where Q = quantifier and C = copula. We limit our quantifiers to “all,” “no,” “some,” and “some/not”
A term (subject or predicate) is distributed (and here I use my own words, which might be wrong) if we know something definite about the term.
For example: All j are k or All cows are herbivores. In these statements, j and cows are “distributed” since we have something that about cows and j. Herbivores and k are not distributed, since we know nothing concrete about either.
Another example: No m are n, or No Buicks are reindeer. In this case, we know that membership in m implies no membership in n, so m is distributed, but also we know that membership in n excludes membership in m, so n is also distributed. (In words, we now know something concrete about all reindeer)
Does this help at all? Do we need a full post/set o posts?
no. really. by “never mind”, i mean … you know.
i already speak logic fluently and all this fuss
takes me back to 7th grade where they tried
to get us to learn about “parts of speech”
like nouns, verbs, adjectives, usw.
since i could already speak and write english
at least as well as the teachers, i figured
they were just trying to push us around
to prove they could. i still figure that, actually.
of course, when i began academic study
of a foreign language, i finally saw the point
of breaking things down in this way.
but, doggone it, we oughtn’t to teach logic
as if it were a foreign language … unless,
god help us, we’re teaching philosophy
instead of mathematics …
ASTC is silly. Much easier to do is to remember the unit circle and the facts that a positive number divided by a positive number is positive, etc. I think that that particular mnemonic takes so much explanation that a student might as well memorize what’s actually going on.
I still use SOHCAHTOA myself, though, despite having learned about these functions ten years ago and being a grad student in mathematics.
As for mnemonics to remember the order of operations — inevitably people seem to use them incorrectly. I’m a big fan of just using too many parentheses whenever anything is the least bit unclear.
Vlorbik, for the math-y part of logic, I am with you. Those categorical syllogisms are another thing.
And Isabel, we are on the same page.
think of a good one for astc?
Not having English as first language I have no idea of most of the mnemonic devises you talk about (I only know the O Be A Fine Girl Kiss Me) but as a teacher I hate mnemonics. When out students are done in school the will not be multiplying fractions, they will not “Multiply by the exponent, and then reduce it by one”. Most of them will not use most of the math we teach. Math is just a handy tool to use while we try to make them learn how to THINK and you don’t do that by using mnemonic devises.
My weapon of choice towards my student is the “why?” question, if they cant answer that question they are not allowed to use that rule. The first year they hate me for it, they hate me for forcing them back down to a level they understand when they can do (without understanding) so much more. After about a year they start to see the point, after two they appreciate it and when they after three years leave my care I get a lot of thanks but best of all are the e-mails I get from former student going to university who can compare with other students. I get an extra kick when someone studying something not directly connected to math like history writing me to thank me for forcing them to think and connect.
The fight in the beginning is a major one, the word “hate” isn’t to strong, but I think they hate “it” not “me”. Every year I get calls from parents questioning what I am doing “But they learned this is 5th grade…” to which I answer “Yes, they learned this is 5th grade but now I want them to understand it”. I once had a group of parents force the school to have a big meeting about me to either get me removed or change my methods but was saved by my 3rd year students that defended me diligently.
/Per