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

And Isabel, we are on the same page.

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.

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 …

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?

And, I don’t understand the students’ b’s and probations either.

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.

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.

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.”

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.