Nix the Tricks Book Study – Chapter 2: Operations
This post is part of an ongoing book study series on Nix the Tricks by Tina Cardone. Each week, a group of math teachers has been meeting to reflect on one chapter of the book and discuss how we can move away from shortcuts and toward a deeper understanding of mathematics. You can find our reflections from Chapter 1: Introduction in the previous post and follow along as we continue through the book.
Our second week of the Nix the Tricks book study focused on Chapter 2, “Operations.” This chapter took us into some of the earliest habits students develop around computation, key words, order of operations, and the tricks we’ve all seen (and maybe even taught) that make math seem like a list of steps rather than something that makes sense.
As we worked through the examples, one big question kept surfacing: Are students relying on tricks because they lack mathematical understanding, or because they struggle with literacy?
Key Words and Context
The chapter opens with a discussion on “Total means add,” and it hit home for many of us. In the past, several teachers admitted to relying on key words as a way to help students navigate word problems, especially during test prep. It’s easy to see why; it gives struggling readers something tangible to grab onto.
But as one participant pointed out, the problem isn’t just mathematical; it’s often about literacy. Many students struggle to translate context into operations because they have difficulty comprehending longer passages. For them, key words can feel like a lifeline. Still, this chapter reminded us that when we teach key words in isolation, we inadvertently discourage sense-making.
The suggested fix, encouraging students to draw models, felt like a practical and powerful alternative. Visual representations help students see relationships, make sense of the context, and build reading comprehension along the way.
Of course, we also acknowledged the reality of pacing pressures. In Algebra 1, especially under testing demands, it can be hard to give up key word lists when they sometimes “work.” But as this chapter highlights, short-term success can result in long-term confusion.
Rethinking PEMDAS
One of the most passionate parts of our discussion centered on the order of operations. We explored the idea of replacing PEMDAS with GEMA, Grouping, Exponents, Multiplication, Addition. The change may seem small, but it clears up a major misconception: multiplication doesn’t always come before division, and addition doesn’t always come before subtraction.
GEMA also encourages teachers to focus on the power of operations, why exponents come before multiplication, or why grouping symbols override other operations. This framework reinforces reasoning rather than rote memorization and gives students language that scales as they encounter more advanced math concepts (for example, grouping symbols can later include radicals or fraction bars).
Making Sense of Division and Place Value
We also discussed other tricks from this chapter, such as “Ball to the Wall” for dividing decimals and “Does McDonald’s Sell Cheeseburgers” for long division. The consensus was clear: mnemonics might help in the moment, but they rarely lead to lasting understanding.
Several teachers shared success using color-coded division steps or allowing students to take away smaller chunks during long division, helping them see the connection between repeated subtraction and the standard algorithm.
Our group even connected this to grading practices in earlier grades. If elementary students lose points for sign errors or partial understanding, are we unintentionally discouraging them from taking risks and reasoning through problems?
Big Takeaways
Context over key words. Students should make sense of the situation, not match words to operations.
Concepts over mnemonics. Replace PEMDAS with GEMA to emphasize reasoning and relationships.
Visual models matter. Area models, number lines, and place value charts build conceptual understanding.
Math and literacy are linked. Struggles with word problems often stem from reading comprehension, not computation.
Process over product. Students need time and space to value reasoning, not just right answers.
Next time, we’ll dive into Chapter 3: Proportional Reasoning, a topic that is sure to spark strong opinions and thoughtful reflection. We’re eager to unpack how to move beyond “Butterfly Method” and “Flip and Multiply” toward strategies that truly build proportional thinking.
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