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Only 23% of students answered this question correctly! Only 23% of the end products of our K-12 education system can answer this simple problem. 23%.
This problem is classified as Low Complexity:
This category relies heavily on the recall and recognition of previously learned concepts and principles. Items typically specify what the student is to do, which is often to carry out some procedure that can be performed mechanically. It is not left to the student to come up with an original method or solution.
This is about as simple an algebra problem that I can think of that I'm still willing to call real algebra. I think it's safe to say that if you can't do this problem, you do not possess a profound understanding of algebra.
These kids are our NCTM babies. Kids whose entire learning of math occurred under the auspices of the NCTM's standards.
8 comments:
I can't do this problem.
Or, rather, I might be able to do it, but I would be discovering it. I don't know it.
This is something parents need to know about the SAT Math test: you can't lay a glove on a 700 without knowing algebra 2.
You may not even be able to lay a glove on a 600.
When I took a sample SAT test I probably got nearly every algebra 1 item right; I missed all of the function questions.
My score was a range of, iirc, 560-620.
Here's the post.
I always hated function problems.
I always have to remember that f(x) = y
I work so much better in two variables.
rory
well, I intend to master them!
But I agree; I have trouble making that jump from "x" and "y" to a function problem.
inflexible knowledge
A function is a special case of x and y. Any equation can be written with x and y but it is not necessarily a function. Only equations that pass the test for functionality can be written with f(x).
For example: x^2+y^2=1 is a circle with radius one. This is not a function. But the upper half or lower half is a function. Solve for y. You get y=sqrt(1-x^2). Since this is a funtion, you can write f(x)=sqrt(1-x^2)
It's funny how people can react so differently to the same things - I used to love functions.
I remember when I was doing Math Olympiad in jr. high, I would create a 'shortcuts' in especially vexing problems by lumping them into discrete units, and mark them with homemade symbols like a diamond, or a bullseye. When we finally got to functions in algebra, one of my biggest difficulties was forcing myself to use the standard f(x) notation instead of a bunch of random little squiggly lines. While I immediately saw the benefit of the standard notation (particularly when it came to nested funtions - "let's see, what does the diamond inside a circle next to a little weiner dog facing left mean again?"), it was still quite the adjustment.
At least I know I'm not alone - in college I had one econ TA who never quite mastered the greek alphabet, so he would often refer instinctively refer to the various leters by his own made-up names. To be honest, though, I have to admit that 'whathoozit' is far, far more evocative than 'sigma'.
I think this partly explains why discovery learning is both so tempting and so dangerous. The constructivists would point to my experience and say, "See! He learned it on his own, and retained it as a result!" This is true. What they overlook, however, is that my rudimentary, self-taught techniques were useful for only the most rudimentary problems, and that my retention of those techniques actually hurt me later on when I instinctively tried to apply them later on in situations they were wholly unsuited to.
interesting....
I haven't grokked functions; it'll be interesting to see if I do here in Algebra 2.
I was never taught functions - nothing at all - so the question is whether I can self-teach.
If not, I'll have to find a course somewhere.
Probably at WCC.
oh my gosh
I just stumbled across this post while searching for something else, and....wow
this is a REALLY easy problem
Takes about two days of SAT prep to learn this.
That's not quite fair; it does take a while to remember that f(x) is the same thing as y.
Nevertheless, "low complexity" is right.
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