There are two interpretations of "relatively prime" for three (or more) numbers A,B,C. a) Coprime (in pairs): All pairs have GCD=1. GCD(A,B)=GCD(A,C)=GCD(B,C)=1. b) No divisor >1 for all the numbers. GCD(A,B,C)=1. The triple 2,3,4 satisfies (b) but not (a). (a) -> (b). Naturally, the likelihoods of (a) and (b) are different. ----- Math Education, Miscellaneous Thoughts If we want to teach logical thinking, let's design a Logical Thinking course. We can probably come up with something that makes sense to 8th graders. Does it make sense to spend class time teaching, say, long division? There seems to be some conflation of arithmetic with mathematics. There are several different ways to solve two linear equations in two unknowns, and the underlying ideas can be explained in ten minutes. The reporter's inability to assist his daughter with her math homework is curious. This might be evidence that some intelligent people really can't do math. There's a wide range of skill level and interest in math: Maybe we should abandon teaching the same math to everyone in fourth grade. There's no shortage of smart people. We don't need to find all of them. Much of higher math is only justifiable as art, with a very small audience. As an airplane passenger, would you rather your designer had studied number theory or fluid mechanics? What if he plays the flute? Or windsurfs? I was pleased to see that US math students have reached par with the Hungarians, although perhaps the Hungarians are less pleased. Is there an accurate way to do a meanigful test valid across countries? Technical question: Design a method for balancing a checkbook, something more than "recheck all your arithmetic". Is the influx of smart people into the US making the rest of the world dumber? It's more fun to teach a class where the students want to be there. Why have we organized the world to teach algebra to the bored? One problem with this discussion is we've heard most of it many times before. I'll offer a prize of $1 for the first new thought on the subject. Rich rcs@cs.arizona.edu