Thursday, September 3, 2015
Tell me about Order of Operations
This week I would like for you to tell me about order of operations. Explain in complete sentences what order of operations means to you. Tell me about common misconceptions students have when applying order of operations. Explain how you would help the students fix these misconceptions.
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When I was younger, back in grade four, I learned about an 'Order of Operations'. I didn't really understand what it was, but I figured out the main thing I needed to know for math - multiplication and division is done before addition and subtraction. I looked a lot smarter than many of the others, who hadn't quite figured this out yet. I had no clue what 'parentheses' or 'exponents' were, and they looked very daunting. So, I completely disregarded that portion.
ReplyDeleteIn fifth grade, I learned something called 'PEMDAS'. Later that year, I also learned it was called 'Please Excuse My Dear Aunt Sally'. Confused by the latter and having memorized the former, I took 'PEMDAS' to heart. I still didn't really understand parentheses or exponents, but it was much easier for me to remember the acronym. Everyone else had caught onto the math pattern, but I still maintained as much dominance as I could grade-wise.
Then came sixth grade, the first time math became even slightly challenging. I made a grand total of *drum roll please* 1 B! The order of operations wasn't a big deal to me, because I still wasn't using it. Sure, I learned how to distribute, but that was it and it messed with my head in the fact it WASN'T the PEMDAS. Regardless, I still scored well.
Seventh grade forced a thinking process to actually USE the order of operations. Even though I (in all honesty) did not really listen in my math class, I understood it had reached a different level I had to retrain my brain to understand. Parentheses became important, and exponents slowly rose out of uselessness. I only ever listened (or understood) the concepts when a fellow math student, especially an intelligent one, explained them.
Come this new year of eighth grade, and I think I've got it down. The concepts suddenly make sense and I'm paying attention to them. The exponents confuse you for a while if you think to treat them like the Distributive Property of Multiplication instead of their actual priority level, and a few times I've still caught myself trying to add before I multiply.
So, getting to the essence of the question. The order of operations is a subconscious thing, really, until you get to the parts you haven't focused on yet, like exponents. I think a lot of students don't pay enough attention to order of operations (I'm including myself in that group), mainly because they're still trying to subtract from the parentheses without thinking, or dividing a number before applying it to the proper power. It needs to get to the point where you don't think about the order, and it's automatic. You COULD use the acronym or such, but that makes it appear as multiplication BEFORE division and addition BEFORE subtraction when they're grouped together. Therefore, the only thing I feel would be fit is just grinding students on the order of operations until they've got it. Unpopular, yes, but effective.
I end this note with one last thing: kids, addition surrounded by parentheses is still before division. Thank you for your time.
Caleb saner core 4 a lot of kids get confused with pemdas because of the multiplying and subtracting dividing and adding because of PEMDAS and you can fix that by telling kids not to fallow that and order of operations mean to me is a helpful and only way to do big problems with variables and multiplying and adding and division and subtraction in one big problem
ReplyDeleteWhen it comes to order of operations I pretty much get them, I feel like their pretty easy to me but I know some other kids don't get it as much as I do. The one thing I don't get when it comes to order of operations is the negatives. I think a lot of kids get confused with negatives with dividing, multiplying, adding, and subtracting. To help kids out with that problem is to take it slow at first. Then you have to do the ones in the brackets and then do them in the parentheses. And then you have to do dividing and multiplying and it depends which one is first. And same goes with adding and subtracting. And has to do with that it has to be on the left.
ReplyDeleteColin Denehy
ReplyDeleteWhen I first learned Order of Operations, I was overwhelmed. I could not wrap my brain around the topic. I didn't start really getting it until 6th Grade. One of the most common misconceptions is that brackets and parentheses dont go in the same category. I know I've messed this up several times. We were taught PEMDAS order Please Excuse My Dear Aunt Sally for so long that they stick in our minds. When we get to a problem with brackets, we are totally confused. Another common misconception is that the square root sign is not apart of the parentheses category. This goes along the same lines of the first misconception. We need to start learning a different way, so we can do better in the future. If we learn about this earlier on, we could stop the confusion from ever happening.