The yearly discussion of mnemonics is (unfortunately) in full swing on the AP Calculus discussion group this week. I may be to blame for staring it with a mention of SOHCAHTOA. I was trying to make a point about learning the concepts verses memorizing something that will get you the answer with no understanding.
Some things do have to be memorized, no two ways about it. And I can live with SOHCAHTOA or the title of this post as a way of remembering the right triangle definitions of the trig functions. The thing is I can't spell SOHCAHTOA without saying to myself "Sine: opposite over hypotenuse, cosine: adjacent ..." so for me there's no point to that one. But I can see where it may help an Algebra 1 student.
Then there are useless mnemonics like LAND and GOR mentioned in my last post. These really do more harm than good.
Other mnemonics I'd rather avoid. For example "Please prepare my dinner Aunt Sally" or PPMDAS or PEMDAS for short. Here an understanding of the underlying reasons, the concepts if you will, are essential to anyone doing arithmetic (A rat in Tommy's house, etc) or algebra. The parentheses are there to show you what to do first; and you need to know that. Powers indicate repeated multiplication so just think of
as 
which you have to know anyway, as with multiplication and division before addition and subtraction which should become automatic. (The mnemonic leaves out the "from left to right" part anyway.)FOIL is a particularity bad one. It falls apart as soon as you try to multiply a binomial by a trinomial.
Formulas are better learned in words that tell you what to do. To this day when I differentiate a quotient I'm saying to myself, "denominator times the derivative of the numerator minus the numerator times the derivative of the denominator all divided by the denominator squared." That's the way I've always told my classes to memorize the formula.
This one which showed up today on the AP Calculus EDG and is one I could live with: DAMMIT (Dispise all mathematical mnemonics, instead THINK).
Just my opinion. Do what works for you. So for now Hi-De-Low..
In integration by parts, the acronym LIATE helps in determining which parts should be u and dv. (One stills needs to know the formula for parts.) L = natural log, I = inverse trig., A = algebraic expressions, T = trig., and E = exponent (base e). The most left part has precedence for u, and the other part is dv.
ReplyDeleteFor example, integral of x^2*ln(x)dx, we should let u = ln(x) and dv = x^2dx because L is left of A in the acronym. (Of course, more discussion should go around this kind of example in foreshadowing the derivatives of u and the integrals of dv.)
Lin:
ReplyDeleteOne of the mnemonics I hate the most is "y = mx + b" because it traps so many of my students into thinking that x is always the input, y is always the output, and that slope is change of y over change in x. I have almost made a fetish out of emphasizing formulae using words. Thus the formula for a line should be read as, "output = (slope)(input) + (output intercept) and the formula for the slope is slope = (change in output)/(change in input). Students who think about lines this way do not get tripped up by my problem about xylophone production versus years, where x is naturally the output variable and y is naturally the input variable.
Jeff