PEMDAS poisoning

Many students come to 7th grade with a pernicious problem.  I call it “PEMDAS poisoning”. Many have incorrectly learned to over-rely on PEMDAS as a mnemonic and check list to compute long, multi term expressions.  The convention of solving from left to right among the inverse operations, (square/root, or multiply/divide or add/subtract) is NOT learned by the majority of incoming 7th graders.  The problem persists into high school.  Students doggedly use PEMDAS as a check list and do not see the need to work from left to right. They are also unaware of other grouping symbols (vinculum, square root , absolute value bars…) other than parenthesis. 

The problem is compounded by the teaching of order of operations in a vacuum; devoid of any context.  Students are expected to simplify such expressions as 72 – (6+3)+15/3x5 as a form of Sudoku, a stand-alone puzzle that has no further application but to say they have done it.  This takes away a students’ ability to use common sense to check her answer.  If order of operations is embedded in formulas for compound shapes, or a model for solving story problems then students can rely on their grasp of what sort of answer is in the ballpark as a preliminary check for correctness. 

I think the remedy is for educators to build context and teach from there.  I have a series of questions that I'm developing to try it out, I'll let you know how it unfolds.

There is a great rant to accompany mine at http://www.youtube.com/watch?v=y9h1oqv21Vs.  Check it out!