Date: May 17, 1995 10:46 PM
Author: Karen Dee Michalowicz
Subject: Re: order of operations, history
I have been looking at the history of orders of operations.

One source, Florian Cajori's A History of Mathematical

Notations, talks about the discussion in America at the turn of

the century about expressions where there is both a division

and multiplication. In fact, his book, first printed in l929,

says "If an arithemetical or algebraical term contains division

and multiplication, there is at present no agreement as to

which sign shall be used first...Other textbook writers direct

that multiplications in any order be performed first, the

divisions as they occur from left to right (ref.Slaught and

Lennes, High School Algebra, E.ementary Course, Boston l907).

The term a/bxb is interpreted (in Fisher's Text-Book of

Albegra, l898) as (a/b)xb. An English committee (The Report of

the Comittee on the Teaching of Arithmetic in Public Schools,

l917) recommends the use of brackets to avoid ambuiguity in

such cases."

So, I find that a general consensus on the order of operations

on numbers was still developing 65 years ago.

Cajori's book has a wealth of information about mathematical

notation which I find very interesting. I got it and many

other of my math history books "for a song" from Dover

Publications.

--

Cheers!

Karen Dee

Math History Lives!

Karen Dee Michalowicz VQUEST Math Lead Teacher/Trainer

Upper School Mathematics Chair Virginia Quality Education

The Langley School in Sciences and Technology

1411 Balls Hill Rd, McLean, VA

22012 USA

703-356-1920(w) E-Mail: kmichal@pen.k12.va.us

Fax: (703) 790-9712 --or-- KarenDM@aol.com