“Please Excuse My Dear Aunt Sally” or PEMDAS is a new concept being introduced to the fifth grade students this year. It’s been a few years (okay, more than a few years) since I have last worked with this concept, but I remember the mnemonic as standing for “Parentheses, Exponents, Multiplication, Division, Addition, Subtraction”, aka “Order of Operations.” Not only have we learned this, but we have also learned about brackets and braces as well. Some problems that we have encountered have been relatively straight-forward, while others have been on the somewhat tricky side. So, several nights ago, this was one of the problems on the homework:
24 – (8/2) + 6 =
I always do out the answers before starting to correct the problems. I calculated that the answer should be 26. Sitting down to correct the work on Wednesday evening, the first student had 26 for an answer. So far, so good. But the next five students had 14 for an answer. Clearly, there was a difference of opinion on the correct answer. Since, I am always subject to making my own errors, I wasn’t sure. Since I have been getting ready for an observation, I was recently reading over “22 Verbal Events in a Class that Lets Kids Get Smart.” One of the suggestions was to for students to take initiative to explain another student’s thinking, including how they might have made an error. So, I decided not to make that answer right or wrong and put it in front of the class for discussion.
On this rainy Thursday, I started our math class by putting that problem on the ActivBoard and put down 26 and 14 as a possible answer. I asked for volunteers to explain how someone may have arrived at 26 for an answer. “You divide 8 by 2, which is 4, then you subtract 4 from 24 which is 20 and add 6 which is 26. As soon as that student finished, over half the class raised their hands, saying “no, you do addition before subtraction, remember PEMDAS. Addition comes before subtraction. So, 8 divided by 2 = 4, 4 + 6 = 10, and 24 – 10 = 14. Another girl raised her hand and said she had a similar question on this problem the night before and her father had looked it up on the internet, where he said that addition and subtraction are treated equally and one should do the operation from left to right. More mass confusion rang throughout the room. But, you taught us PEMDAS, addition is before subtraction.
Quickly, I decided to phone a friend, in this case our math specialist Mrs. Link. She shortly came downstairs and respectfully listened to the “26” camp and the “14” camp. She listened to the student who talked about her dad’s research and nodded that she agreed with that theory. Again, more confusion. Always diplomatic, Mrs. Link announced to the class that was going to consult with some other math experts and see if she could clarify the confusion. Off she headed, and we tried to settle down to do some place value work.
After about five minutes, Mrs. Link returned, a book in her hand, to deliver her “ruling.” Everyone waited for her to open up her “Math on Call” book. Opening up to section 208, she started to read the definition that multiplication and division are treated equally and are solved from left to right as are addition and subtraction. A learning moment for us all for sure. I thanked her for her work in searching out the truth for us. She headed back upstairs again and we were left to work on some addition and subtraction problems before lunch.
Since lunch was next, I headed upstairs to talk with Mrs. Link. She commented on the students’ passion for discussing math. Too often, the students just sit there passively and are not actively engaged. Not these 20 students (3 were out today). They were passionate in their views, they challenged each other’s views, and they willingly admitted (as did I) that they were confused. I felt that this was a learning moment for us all. Sometimes, it is not about being right, it’s about learning from one another and being passionate about your views. I don’t think that any one of us will ever think about PEMDAS again without thinking about this great learning experience.