In TERC it isFuzzy math was designed to make math "accessible" to large segments of the population which in the view of the fuzzy math creators were hitherto marginalized by rigorous math instruction. But by taking math out of "math", everybody loses.
*joining not addition
*separating not subtraction
*bits and pieces and not fractions
*capacity and not volume
*it is what the calculator displays and not decimals.
*it is "landmarks" rather than ALL the numbers in the decimal system.
*it is turns and not angles and degrees.
*it is write a story and not write the equation.
*it is draw pictures and not show a true effective reusable strategy.
Saturday, April 21, 2007
New math language
In a post called Math for poets, Linda Moran cites the comments from a mother and scientist that illustrate how traditional math terms are being swept away by fuzzy math. Apparently, terms like angles and degrees are too taxing:
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5 comments:
As a (high school) math teacher, I think I like to use terms such as "turn" for angle and whatnot... not to replace standard mathematical terminology, but to provide a simpler way of understanding... as a stepping stone. I often talk etymologies with students, so that students mentally see why, for example, geometry is 'the measure of the earth'.
My point is, I find no offense in the words that fuzzies choose to describe the concepts... it's just the use (replacement) of those words for the standard mathematical terms.
Furthermore, I have no problem with showing students the lattice method for multiplication (although I show it to high school students as a topic of interest, not a teaching method), but for first-time learning I stand for standard algorithms.
But analogies are a classic way to make mistakes teaching math. Perhaps it works for high school students who are sophisticated enough to understand that the map is not the territory, so to speak, but certainly it's dangerous with younger students.
I remember being taught something idiotic in 2nd grade about the "greater than" symbol and the "less than" symbol. It was something about a fish, or a mouth, or the big fish eating the little fish, or something. It was bizarre and unintelligible. My take away of it was that a carat like this: <
referred to some mouth eating something, and so I reasoned, the bigger number was large enough to eat the littler number, so
8 < 5 was a true expression meaning "8 is greater than 5".
Now, I understand this is merely an anecdote, but a lot of children make up relatively elaborate explanations for subjects they were mistaught. Math is specific for a reason. Analogies lose accuracy and specificity.
Why not expand the concept!
Let's teach Latin instead of English grammar?
That way we'll know the basic "concepts" of language and learn how to talk gooder.
I see the reasoning behind "no analogies" -- but ask yourself why teachers redefine things or describe them in different ways or use different concepts. If everyone just understood <, > we wouldn't have multiple definitions! The problem is that kids get them confused all the time. I was taught that the large opening was toward the larger # and the small point pointed at the smaller number. That's still far easier for me than "reading" them from right to left.
Uhhh, left to right!
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