Teacher Tech blog with Alice Keeler

Paperless Is Not a Pedagogy

Alice Keeler

Forget Order of Operations (PEMDAS) – Here’s Why It’s Okay to Break the Rules

Why do you go left to right? Because a teacher said so? It is the rule? Help your students be more flexible by NOT using order of operations. Ditch PEMDAS!!
Forget Order of Operations (PEMDAS) – Here’s Why It’s Okay to Break the Rules

In math, we’re taught there’s a specific way to simplify problems – the Order of Operations. Remember those “Please Excuse My Dear Aunt Sally” posters? They reinforced PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction), a common way to remember this order. But is this strict sequence the only way to approach math problems? Do we HAVE TO go left to right? Is it possible to start with subtract? What if thinking more flexibly actually deepens our understanding? Could there be more to math than memorizing a catchy phrase?

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Rethinking Order of Operations

Join me (Alice Keeler) February 29th, 2024 for a free workshop with OTIS. Can’t attend live? Register to receive the recording afterwards.

Innovative Strategies Beyond PEMDAS for Deepening Number Sense

I have a secret, I do NOT go left to right when simplifying math problems. For most of my life I kept this a secret, expecting that I would be discovered as being bad at math if anyone found out. Instead, I used number sense strategies. It wasn’t until I read “Mathematical Mindsets” by Jo Boaler that I realized this was not a sign of being bad at math, but rather the opposite!! I am GREAT at math. Instead of mindlessly following memorized steps, I would think about how to make the process easier (for me.) 

Number Sense

Number sense is not being really great at remembering the steps to a math problem. It is the ability to go beyond memorized steps and having an understanding of how the numbers work together and the ability to be flexible with the use of math.

Math instructor Howie Hua shared on social media that his college students were blown away that they were not taught they could use algebra to manipulate the numbers to make subtracting significantly easier. 

I Dislike PEMDAS

Math class, especially in the 21st century, should not be about getting the right answer. Calculators do an excellent job of this. If the goal is answer finding, we can stop torturing kids with irrelevant, non contextualized, made up math problems. 

Math Should Be About Thinking

The problem with PEMDAS and order of operations is that we are taught that it MUST be done this way. For some students, they are actually marked down on their grade if they take an alternative approach. Why do students get order of operations problems wrong? Because they are not thinking! They are trying to go through the steps and possibly making careless mistakes as a result. 

My math department years ago said that when when a students asks “when am I ever going to use this” that we should respond with “We are teaching you critical thinking.” Flatly, we were definitely NOT teaching the students critical thinking. We were teaching them to follow steps and algorithms which is what robots do. 

What Is the First Step?

As a math teacher, how many times have I said to a student “What is the first step?” This implies a memorization of what to do. This can be stress inducing for many students (it is stress inducing for me.)

What Do You Notice?

If instead of “first” remembering the steps students take a breath and analyze the question they will feel more confident and possibly come up with a more flexible solution. 

“What do you notice?” 

Might be a better first question when we support student problem solving. 

Simplify This Expression

4 plus 8 plus 9 plus 6

Order of operations tells us to go left to right. 4 plus 8 is 12. Add 9…. uhhhh the numbers keep getting bigger and is more difficult than if you notice first that 4 + 6 is ten. ❤️ I love 10. 

Register for Free for the Order of Operations Workshop with Alice Keeler

The workshop recording will be made available after the event so please register even if you can’t attend or you missed it. 

Rethinking Order of Operations: Innovative Strategies Beyond PEMDAS for Deepening Number Sense

NIX PEMDAS! Rethinking Order of Operations: Is there a better way to solve than brackets first or left to right? The traditional order of operations, a cornerstone in teaching mathematics, might not be the only way to simplify expressions. These rules, often encapsulated in acronyms like PEMDAS/BEDMAS/GEMS, are deeply ingrained in math education, but they may not always serve our students’ best interests. Join Alice Keeler, an innovative math teacher, as she explores alternative strategies that prioritize number sense and conceptual understanding over rote procedure. This session is a journey towards empowering students to think critically and flexibly about math, breaking free from the constraints of traditional order of operations. 

order of operations is broken when I use 4 plus 6 first and rewrite it as 10 plus 8 and rewrite the 9 and 2 plus 7

In fact, that is my personal initial strategy… how many groups of 10 can I create? Even when adding the 8 and the 9 I would prefer to break down the 9 into 2 plus 7. 

So now I have 10 + 10 + 7 which I can easily and confidently express as 27. 

Multiple Approaches to Simplifying

Since as a math teacher my goal is not for my students to compete with calculators but rather to develop number sense I am all about “what is your strategy?” instead of “what is the first step?” And whenever possible to push students to “do it another way” or “compare and contrast your strategy with your partner.”

The more students see multiple approaches and don’t feel boxed in by the rules of order of operations, the more they develop number sense and a greater sense that they are indeed “a math person.” 

Teaching Math with Google Apps
Available on Amazon: Teaching Math with Google Apps by Alice Keeler

Can You Start With the Exponent?

Join me in my workshop with OTIS to see how you CAN INDEED start with exponents in an expression and why you might want to do that.

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