I tutor students from a few different schools/districts and I have found that I now have to ask them if they use PEMDAS, GEMS, or GEMA. And just last week I learned about GEMDAS. If you search Pinterest you will find that some people have very strong opinions about this topic. I have read some good blog posts about order of operations lately and it has me thinking.
One of the main points I have seen for moving away from PEMDAS for some teachers has been that students can become confused about the actual order of operations if they follow PEMDAS as a series of 6 steps. For example, given the expression 12 – 6 + 7, if you solve left to right you will get 13 for your answer. If you solve addition first then subtraction you will get -1 for your answer. So, which is correct? The correct order of operations is to solve addition and subtraction left to right, so the correct answer is 13. The point some educators have made about PEMDAS is that some students think that addition is always done before subtraction because they think of the mnemonic device as a series of 6 steps with addition coming before subtraction. However, most of the students I work with have been taught correctly that addition and subtraction should be done left to right.
Another argument I have seen against PEMDAS is that P stands for “Parenthesis” leaving students with an incomplete understanding of grouping symbols. In GEMS, the G stands for “Grouping” symbols which is more complete. This is a good point. However, most of my students have been taught that P stands for Parenthesis and other grouping symbols and they seem to do well with that.
Since I am not in the classroom this year I do not have to actually take a stand for one acronym over the other. I actually have to know them all, since it is in the best interest of my students to make sure they understand when and how to use whichever method their teacher uses. I think the important thing to remember is whichever acronym you choose to use as a teacher, is to make sure your students know how it works! I asked my 10th grade daughter which acronym she uses and she said she was taught PEMDAS, but now she doesn’t use it because she knows what order to work in. I think that is the end goal anyway, to get our students to understand and remember the order of operations so they can successfully solve math problems.
I would love to hear what other teachers have to say on the topic of PEMDAS…