Riordon and I were discussing commutativity.
Me: So is subtraction commutative? What's ten take away zero?
Rio: Ten.
Me: And zero take away ten?
Rio: Well, you can't.
Me: You can't‽
Rio: Well, my teacher said you can't.
Me: She did?
Rio: Yes, I said you could because of negative numbers and the teacher said we didn't do those for a couple of grades yet.
(I remember the same thing happening to me when I tried to use division in infant school.) The daft thing is that Rio is quite capable of working in the complex plane. I wonder how I can teach her not to let the school put brakes on her exploration. It bothers me firstly that she'd understood what the teacher said to mean that she should pretend negative numbers didn't exist, and secondly that she then took this to apply to every situation in her life (not just as needed to get by in school maths classes).
Public education?
I take it that Riordon uses the public school system? Inhibiting a student from exercising what they have learned is terrible (that is, as long as it's not how to play with matches
;). What if you talk with her teacher about it? Sure it may seem trivial to the teacher, but keeping a kid in a learning rut (that's what appears to be happening) is a terrible thing to do.
Re:Public education?
marnanel on 2006-02-08T04:23:42
That's right, she's at the local elementary school. I'll mention it to the teacher when I see her; I don't mean to be negative (um, not a deliberate pun) because the teacher's generally doing a fine job, but I don't like this one thing I've heard.
intellectual debt!
> I wonder how I can teach her not to let the school put brakes on her exploration.
0 - 10 + 10 != 10
Very important to understand debt in the modern world.
I'm reminded of kindergarten (0th grade) where we had these 10x10 grids and we had to fill them out with the numbers 1-100. I figured out an assembly-line mode for this busy work where I wrote all of the 10s columns, then all of the 1s columns. I got scolded. Years later I realized that I had implicitly understood the base-ten number system. Math was really stunted for me until 4th grade, where I had the most saintly teacher -- I was playing with triangles and had discovered some relationship (think it was the sum of the angles). When I asked her about it, she seized the opportunity and taught me the Pythagorean theorem on the spot. She later moved into teaching high-school AP classes -- probably more bored in the 4th grade than I was.
