PEMDAS? Really?

Why do we continue insisting on teaching students to use the rigid rules of PEMDAS, also known as the Order of Operations?  Most students have trouble with this mnemonic because they think they should do all the multiplication, then division, then addition, then subtraction in that order.

The other issue is that people often get confused when there are multiple groupings within a problem because students sometimes forget to do all of the operations within the associated groupings.

I just read something I do not agree with fully but the author pointed out we should have students think of 8 - 2 + 1 as 8 + (-2) + 1 so they get the correct answer.  Rather than doing all the addition first rather than the addition or subtraction based on which is found first, second, etc so many see this problem as 8 - (2+1) or 8 - 5 = 3. 


In another article, it has been pointed out that parenthesis and group symbols are not actually operations but containers for the operations so its important for students to understand that the math needs to be done inside these groupings first following the proper order.  If there are grouping symbols inside of grouping symbols inside of grouping symbols, I was taught to begin inside the inner most grouping symbol but students often get confused with which grouping is the inner most one.

Furthermore, another artist pointed out that order of operations do not work the same if the problem is written in reverse Polish Notation which I have not used since I got rid of an HP calculator.  The same author stated we really need to quit teaching order of operations in this manner, rather help them develop the feel for solving numerical problems.

Another person classified PEMDAS as a computational strategy, a strategy and not a set of rules to be followed in stone.  I like thinking of it as a strategy rather than a set of rules because it encourages a bit more flexibility and less adherence to  a rigid application of rules.

One big thing I've noticed is that students arrive in high school having learned to do the order of operations incorrectly.  Sometimes I manage to correct their misconceptions but other times, I cannot change them and they continue applying the "rules" in the wrong way.  It would be nice if elementary teachers could teach this topic properly so students arrived knowing how to use these strategies properly.

Let me know what you think, I'd love to hear.  Have a great evening.