On Dec 30, 2013, at 2:41 PM, Joe Niederberger <firstname.lastname@example.org> wrote:
> More to the point -- your "proof" here isn't good enough. > In your parenthetical "reasons" you are essentially assuming the usual law of signs. That doesn't pass muster if your goal is to prove that no other law of signs is possible.
It?s a ?consistency? proof. Students in algebra do not yet have sufficient background to justify these things deeply with formal analysis.
If I were to guess, you confuse the emotion of math with its pedagogy.
I claim that the pedagogy is universal, while the emotion is up to the individual.
emotion - what you like about math, which varies from student to student.
pedagogy - how mathematical awareness builds in a student, any student.