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This post shows clearly that geometric intuition (other, perhaps, than drawing a parabola crossing - or not crossing - the X-axis) is not helpful at all underst
by Koshkin 6y ago
This post shows clearly that geometric intuition (other, perhaps, than drawing a parabola crossing - or not crossing - the X-axis) is not helpful at all understanding and solving a quadratic equation, while elementary algebra indeed can and does; the imaginary unit, then, appears naturally as the square root of the negative unit (which leads to the need to extend the reals); if anything, the approach that you advocate would make the kid's head spin (no pun intended) with the result being the total loss of the ability to think about things in a simple and natural way.
- jacobolus 6y agoHaha. I said essentially «there are many concepts involved which will take months to unpack, irrespective of which approach is taken, but in good faith here are some sketchy descriptions of what pictures you might draw if you wanted to start with a graphical interpretation ...» To which you responded essentially «your sketch summary consisting of a few picture-free paragraphs aimed at an expert audience doesn’t completely describe all of a complicated set of ideas to a naïve middle school student anywhere near as well as 2 semesters of introductory algebra class does at covering a more limited subset of the same ideas, therefore it must be useless.» This after you earlier proposed an approach to complex numbers that optimistically will first be accessible for typical 3rd year undergraduate math majors. This conversation is absurd. But all the best to you.