Excuse Aunt Sally … part II

Sometimes, an experience in class illustrates a concern.

In today’s beginning algebra class, we were doing order of operations with signed numbers … the first problem for students to do had a quotient and then a product.  MANY students in class were convinced that they needed to multiply first; their rationale was “PEMDAS” — where multiply clearly comes before divide. The problem looked like -16 ÷ (-4) ·2; not very complex … and more than half the class insisted on multiplying -4 and 2 before dividing.

Now, it is true that the type of problem involved is not that important; it’s not needed to model any situation, does not find any reasonable answer, and does not support future learning (outside of order of operations).  The correct answer for this particular problem is not very valuable.

However, our students should be developing a coherent system of knowledge.  In an earlier post, I suggested that “Dear Aunt Sally be Excused” from all math classes; my rationale was that PEMDAS directly causes confusion in algebraic reasoning.  This post is further suggesting that PEMDAS is not very functional even within the original domain of use (order of operations, no variables).

I am becoming more convinced that “PEMDAS” should be avoided in all mathematics classes … whether it is school mathematics or college mathematics.  PEMDAS is short-sighted and misleading; PEMDAS does not support an organized system of understanding.  PEMDAS harms students in the long term, and somewhat in the short-term.

 
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1 Comment

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  By Holly, September 30, 2011 @ 2:17 pm

  I am no great expert, but it seems to me that these students have learned order of operations under an oversimplification, at the very least, of PEMDAS, or a gross misuse (or a mnemonic grab by students)? I never saw any great evidence of change on the department’s test results for how PEMDAS was taught/learned. However, when I learned order of operations, I think we were given very simple operations first, such as 2 + 4, 7 x 2, to confirm the way we had done it in earlier grades. This affirmed the ‘left to right’ nature of order of operations. Then we added in the PEMDAS, with the ‘take-home’ being something like: “Order of operations is PEMDAS and left to right” (or left to right and PEMDAS). Shortfalls aside, I think that is the ‘correct’ use of PEMDAS.

  I think we were also given homework problems at least 20 in quantity to help reinforce the examples we saw in class. I am curious as to what’s caused the change–if you’ve seen one over the years, as remembering PEMDAS, in mnemonic form or no, can be helpful but must be used with good judgment and not blindly.

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