
Re: Teaching Dev Mathematics Conceptually: practical ideas
Posted:
Feb 18, 2009 3:32 PM


Well, I don't think the expression 3^2 is undefined if  is properly defined. It should be read as the opposite of 3^2 which is clearly negative 9 or 9. The  symbol has three different meanings depending on context. In front of a natural number it means "negative", in front of anything else it means "opposite". If it is between 2 things it means subtract. Since no books except mine bother to define the symbol it leaves everyone confused.
wayne
Quoting Philip Mahler <mahlerp@middlesex.mass.edu>:
> On 2/18/09 1:21 AM, "Jonathan Groves" <JGroves@Kaplan.edu> wrote: > >>> Ahh, but PEMDAS is not arbitrary, Phil. Think about >>> how we'd have to write out polynomials if the order >>> convention were different. It is a convention, but >>> it's not arbitrary. > > Good point. > > It does look like multiplication preceding addition developed naturally from > the algebraic notation which started to develop in the 16th century. Because > yes, it really isn't arbitrary, I agree. > > But we've also shown that PEMDAS, which I do use a lot in teaching, isn't > perfect. It is not a complete definition of algebraic syntax. > > We've seen in these (very helpful for me) discussions that things like a/bc > and a/b(c) are handled differently by different pieces of technology. Indeed > I would get nervous if I saw the expression a/bc somewhere. > > Also, the infamous 3^2, which I still would like to ban as an illdefined > expression, or at least so confusing it's not worth the trouble. > > Phil > > > **************************************************************************** > * To post to the list: email mathedcc@mathforum.org * > * To unsubscribe, email the message "unsubscribe mathedcc" to > majordomo@mathforum.org * > * Archives at http://mathforum.org/kb/forum.jspa?forumID=184 * > **************************************************************************** >
**************************************************************************** * To post to the list: email mathedcc@mathforum.org * * To unsubscribe, email the message "unsubscribe mathedcc" to majordomo@mathforum.org * * Archives at http://mathforum.org/kb/forum.jspa?forumID=184 * ****************************************************************************

