OFFICE MEMO: Dick Pilgrim Date: Wed, 24 Sep 1997 16:08:48 -0700 To: firstname.lastname@example.org From: email@example.com (Dick Pilgrim) Subject: Re: order of operations
I just received a phone call from a middle-school teacher regarding an order of operations question. She was challenged by a parent regarding the correctness of her interpretation of the expression [80(15) -: 6(10] where -: represents the division symbol - not a fraction bar or backslash. The parentheses are as shown. The teacher was using the textbook (umpteenth edition of Dolciani) convention we could refer to as PEDMAS
* Date: 19 Sep 97 08:42:10 -0400 (EDT) * From: Ron Ferguson <firstname.lastname@example.org> * Subject: Order of Operations ----- * I would guess the scheme described in your book is the venerable * "Please Excuse My Dear Aunt Sally (Parentheses, Exponents, Multiply, * Divide, Add, Subtract) where each unpunctuated operation is done left * to right before the next operation is done.
The parent insisted that the correct result is 20 while the teacher used 2000 as the result. My interpretation, pre-computer/calculator, leads to 2000 *but* using a TI82/85 and entering as shown above gives 20 while the entering it as 80*15/6*10 gives 2000.
Due to a hectic beginning of classes, I just got to the last two days digest of math-teach this afternoon right after our conversation. It looks as though we need to either more carefully define our order of operations 'rules' or, more reasonably, be careful about punctuation in expressions to avoid ambiguity. The reason I say "more reasonably" is that perhaps this will lead some textbook authors of beginning algebra books to eliminate the "god-awful' expressions invented only to trip up students.
--------------- Dick Pilgrim Mathematics Diagnostic Testing Project University of California, San Diego email@example.com Ph: (619)534-3298 Fax: (619)534-1011 "Be well, do good work, and stay in touch" Garrison Keillor ---------------