Math Arguments

Is this rational?

Can complex numbers be categorized into rational and irrational, or is it only the real numbers that get divided that way? What do you think about this idea?

Must irrational numbers be real? If you think so, how do you reconcile the various definitions of irrational?

If you don't think so, why do we seem to perpetuate this idea with students that irrationals are composed entirely in the real number system...perhaps not by stating that directly, but by using representations such as the ones below?







This next is an extra credit project for a college teacher prep program ... these students obviously don't know their subject all that well and this "teacher" is no better. "Hands On Math: Burn The Textbooks, Shred The Worksheets, Teach Math." is the blog motto.




Are the visual organizers getting in the way of the understanding?