Questions and protocol
We decided to pose an order of operations question to adults in the community. We thought the biggest misconception would be that people think you always perform multiplication before division (and that you would perform addition before subtraction). We thought the second most popular mistake people would make would be to perform all the operations left to right. When we created the problem we made sure the answer would come out to be a whole number if they did the problem correctly, or if they did one of the misconceptions we were expecting, and got an incorrect answer.
We showed them the problem and asked “Could you please solve this math problem?” We told them that they could either explain as they went or work out the whole problem and then explain it at the end. We agreed not to say anything to them while they were doing it. when they were done, we asked why they did it the way they did. We asked “Do you remember anything from school that helped you know what order to perform the operations?” . If they say PEMDAS or some international variation, we ask them to explain what the letters meant. If their answer was correct, we told them it was. If it was incorrect, we asked “If I told you this was incorrect, what would you change?” This is the math question we asked. 6 + 12 / 3 x 2 - (5-3) ^2 The correct answer is 10. If they did every operation left to right they would get 8. If they thought they do multiplication first because M comes first in PEMDAS, they would get 4.
We showed them the problem and asked “Could you please solve this math problem?” We told them that they could either explain as they went or work out the whole problem and then explain it at the end. We agreed not to say anything to them while they were doing it. when they were done, we asked why they did it the way they did. We asked “Do you remember anything from school that helped you know what order to perform the operations?” . If they say PEMDAS or some international variation, we ask them to explain what the letters meant. If their answer was correct, we told them it was. If it was incorrect, we asked “If I told you this was incorrect, what would you change?” This is the math question we asked. 6 + 12 / 3 x 2 - (5-3) ^2 The correct answer is 10. If they did every operation left to right they would get 8. If they thought they do multiplication first because M comes first in PEMDAS, they would get 4.