Sunday, April 29, 2007

sec tan cos sin 3.14159 - Math Team Cheers and Math Mnemonics

[You may want to read the comments for this post. Some useful devices to help students recall important rules/facts from trig & calculus.]

Regardless of whether one approves of giving students mnemonics to help them recall various math facts or terms, students do use some of these and, in fact, don't we all! I know many math teachers detest PEMDAS because it can mislead students but the 'positives may outweigh the negatives'!
Here are a few of my favorites, some of which I've devised and some I've learned from creative teachers and students. I know some of you have your own pet phrases - pls share!!
With the May SATs only a few days away, perhaps one of these will stick in a student's head and help...

1. Zero is a WEIRDO (last 2 letters need to have a strikethrough)
Ok, here's how this works: Each letter helps students recall an important fact about the number ZERO which many students seem to forget almost daily! I'll start you off - try to guess the rest:
W: Whole (i.e., Zero belongs to the set of whole numbers)

2. Spell the word 'WHOLE'. The middle letter reminds us that ZERO is WHOLE and (E)VEN.

3. INTEGER (underline the N, E, and G) - to help students recall that integers can be NEGative.

4. PRIME (strikethrough the letter I, circle the last letter 'E.')
This may help students recall that 1 (the letter I) is not defined to be a prime number; further, there is only one (E)ven prime. Lame yes, but the lamer the better.

5. F)M Some students still listen to their favorite FM station.
This is to help them recall that a (F)ACTOR 'goes into' a (M)ULTIPLE. Thus, 4)12 suggests that 4 is a factor of 12, while 12 is a multiple of 4. Ok, stop groaning!

6. (From one of my outstanding Algebra teachers E.S.):
Permutations are Picky
Combinations don't Care (about order).

7. 'If you're Y's, you go to the top' or RISE rhymes with Y's (and things that RISE always end up on TOP).
These silly statements may help them recall that, in the formula for slope, the y's are in the numerator.

Now it won't be hard to top these, so go ahead...


jonathan said...

the FM bit may be dated....

Dave Marain said...

i agree jonathan!
so come up with an AIM/mp3/ipod/chocolate phone/blackberry/trio mnemonic!
Hey, whatever works, right?

Puckhead said...

For Geometry Class:
Draw a diagonal line through the S in Supplementary, put a one in front of S, and put a loop on top of the U to create a 0 and you have 180pplementary

Draw vertical line closing off the C and creating a 9 and you have

Jonathan said...

I used to make up lousy ones for myself: C comes before S in the alphabet, Comp. is smaller than Supp...

Dave Marain said...

thanks 'puckhead' and jonathan!
some interesting ideas...
the bottom line is that humans remember things in a variety of ways and often the sillier the association, the better it sticks.
Here are a couple of others:
(cos,sin) on unit circle: another C before S alphabetically!
Supplementary Straight...

Actually, there are a couple of others (more graphic organizer or pattern than mnemonics) I really like for trig and calculus that some students will use on tests:

1. For deriv and antideriv of sin and cos:
Place sin at 12:00, cos at 3:00, -sin at 6:00, -cos at 9:00.
Going 'clockwise', you have the derivatives, going 'counter-clockwise' you have the 'anti'derivatives! I guarantee that if you offer this, 25% or more will place this at the top of their papers!

2. The amazing SQRT pattern for the unit circle in trig (I'll use R for square root)
R(0)/2 R(1)/2 R(2)/2 R(3)/2 R(4)/2
Now try to explain that one!