MathExplanationsFromCarolyn < Kitchen

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10-2005: this page needs SERIOUS updating!

functions
dimensional analysis
mixture problems
significant digits

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absolute value 4-10-2006

introducing absolute value

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dimensional analysis 7-23-2005

DanK brought up dimensional analysis in this thread, and it's such a useful idea that I thought we should have a thread to explain what it is, and talk about it and its possible uses in math education.

Here's a very simple example, where dimensional analysis can help you get the right answer.

Suppose a man drives 60 miles in 50 minutes. How fast is he driving?

There are two answers a kid is likely to come up with: the first (and correct) one is 60/50, but a kid might very well come up with 50/60 and not notice he's made a mistake.

Here's how dimensional analysis could help this student get the right answer: he knows he wants a rate for an answer; distance per unit of time. If he thinks of the 60 as '60 miles', and the 50 as '50 minutes', then his two choices are:

(60 miles)/(50 minutes) = 60/50 miles/minute

(50 minutes)/(60 miles) = 50/60 minutes/mile.

This gives him more context to help him choose the right answer. Miles per minute are units that make sense for this answer: minutes per mile don't.

complete post on dimensional analysis

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functions 7-30-2005

On the way home, Colin asked us about the difference between the median, the mean, and the mode of a data set, and what each of them is good for. This is, of course, the sort of thing we love to pontificate about. He then told us that he felt he had never really quite gotten the idea of a function, and asked us to explain it.

It's a smart kid who understands what he doesn't understand. Most adults can't do that very well. [NOTE: THIS IS METACOGNITION Catherine]

Actually, most kids coming into calculus classes are confused by functions. A function is just a black box; you put in an input, and get out an output. What makes it a function is that, when you put in the same inputs, you always get the same outputs. You can't put the same number in the black box and get 2 one time, and 5 the next.

Most texts teach functions using formulas to define the functions; all the functions kids see look like f(x)=3x-5, or g(x)=x/6. But functions don't have to have formulas to go with them; they can defy description by a formula. The only rule is that if you put in the same input multiple times, you get the same output, every time.

The reason kids confuse formulas with functions is that it's hard to define functions that don't use formulas, even though in real life we encounter them all the time. When a function totally defies description with a formula, we often resort to trying to describe it with only a couple of numbers, such as the mean, median, and standard deviation (this is how the whole field of statistics arises).

complete post on functions

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why automaticity? (an explanation of what's involved in solving mixture problems)

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Significant Digits, Part 1

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marketing fuzzy math

-- CatherineJohnson - 30 Jul 2005

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dimensional analysis 7-23-2005

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functions 7-30-2005

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