summary of results
We expected two main misconceptions regarding order of operations. We thought people would remember the mnemonic device "Please Excuse My Dear Aunt Sally" (PEMDAS) but apply it incorrectly by doing parentheses, exponents, then multiplying first because M comes before D in PEMDAS and do adding before subtracting for the same reason. We also expected people to solve all operations left to right like they would read in English text.
Our hypothesis was accurate. We had a few people perform all operations left to right with an answer of 8. The majority of our sample population incorrectly solved the problem by using PEMDAS, BIDMAS, or something similar and did M before D and A before S because that is the order in which it appears in the mnemonic device and got an answer of 4. Every person remembered learning the order of operation process, but couldn't quite remember how to go about it correctly. The people who used the European acronyms BEDMAS and BIDMAS (B stands for brackets and I stands for Indices) tended to do the parentheses first, then the exponents, then did multiplying before dividing just like the people that used PEMDAS. Another interesting European acronym that we discovered in our research was BODMAS (Brackets, Of, Divide, Multiply, Add, Subtract) and several of the Irish people we interviewed used it and got confused about what the O meant. The word Of does not direct them to do exponents and several of them mused aloud that they knew O represented of, but they didn't know how that related to math.
We were pleased with how our interviews turned out. People answered the way we expected them to and demonstrated a true misconception of the order of operations.
We suggest that teachers recreate a device for students so that the order of operations can be easier remembered when the students arrive at (M and D) and (A and S) portions of the problem. The image below we have found in our research to be a very helpful example.
Our hypothesis was accurate. We had a few people perform all operations left to right with an answer of 8. The majority of our sample population incorrectly solved the problem by using PEMDAS, BIDMAS, or something similar and did M before D and A before S because that is the order in which it appears in the mnemonic device and got an answer of 4. Every person remembered learning the order of operation process, but couldn't quite remember how to go about it correctly. The people who used the European acronyms BEDMAS and BIDMAS (B stands for brackets and I stands for Indices) tended to do the parentheses first, then the exponents, then did multiplying before dividing just like the people that used PEMDAS. Another interesting European acronym that we discovered in our research was BODMAS (Brackets, Of, Divide, Multiply, Add, Subtract) and several of the Irish people we interviewed used it and got confused about what the O meant. The word Of does not direct them to do exponents and several of them mused aloud that they knew O represented of, but they didn't know how that related to math.
We were pleased with how our interviews turned out. People answered the way we expected them to and demonstrated a true misconception of the order of operations.
We suggest that teachers recreate a device for students so that the order of operations can be easier remembered when the students arrive at (M and D) and (A and S) portions of the problem. The image below we have found in our research to be a very helpful example.
image from http://www.epcc.edu/CollegeReadiness/Documents/Order_of_Operations_0-40.pdf
