How to Tell If You're Overusing Process Words in Math Explanations

Process words are transitions: "then," "next," "so," "therefore," "after that," and similar phrases. They’re common in everyday writing and in step-by-step instructions, so it’s natural to use them when asked to explain your math work.

But in math, the goal is not to narrate every move. Instead, you want your reasoning and logic to be visible—why you did each step, not just the order you did them in. Overusing process words can mask gaps in understanding or make your work harder to follow.

A well-placed "therefore" or "so" can signal a conclusion or a key step. For example:

• "We have x = 3, so y = 2x = 6."
• "The function is continuous, therefore the Intermediate Value Theorem applies."

But if every line starts with "then," it’s a sign you’re writing a sequence, not an argument. For example:

• "First, subtract 2 from both sides. Then, divide by 3. Next, write the answer."

This tells the reader what you did, but not why. In longer problems, it can make your solution feel like a recipe instead of a demonstration of understanding.

Two Signs You’re Overusing Process Words

1. Every line starts with a transition: If you can fold the page and every line says "then," "next," or "so," you’re likely overusing them.
2. Your solution reads like a story, not an argument: If it sounds like you’re narrating a cooking show, it’s time to revise.

Teachers and graders want to see your logic. That means:

• What property or rule lets you move from one line to the next?
• Why did you choose that method?
• Are you connecting ideas, or just listing actions?

Focusing only on process words can hide the actual math. For example:

> "Then, I factor. Next, I set each factor to zero. So, I solve for x."

Instead, you could write:

> "Factoring gives (x-2)(x+3)=0. Setting each factor to zero (Zero Product Property), we get x=2 or x=-3."

Notice the difference: the second version names the property and shows the logic.

1. The Highlighter Test

Take a colored pen or highlighter and mark every process word in your solution: "then," "next," "so," "after that," "therefore." If you see a streak of color down the left margin, it’s a sign you’re using them as a crutch.

Try removing some and see if the logic of your solution still holds. If it does, you probably didn’t need them.

2. The "Why" Swap

For each process word, ask yourself: "Could I replace this with a reason or a property?" For example:

• Instead of: "Then, I multiply both sides by 2."
• Try: "Multiplying both sides by 2 (to isolate x), we get..."

Or:

• Instead of: "So, the answer is 5."
• Try: "Therefore, the solution is 5 by substitution."

This doesn’t mean you can’t ever use "then" or "so"—just that you should use them to clarify, not to fill space.

On assignments and especially on exams, graders look for understanding. If your work is a chain of process words with no mention of mathematical principles or properties, you risk losing marks for not showing reasoning—even if your answer is correct.

Conversely, if you use a few well-placed transitions to signal a big step or a conclusion, that’s helpful. The difference is intention: are you guiding the reader through your logic, or just narrating what you did?

Sometimes, overusing process words can actually hide errors. For example, you might write:

> "Then, I divide by zero. Next, I get x = 3."

But dividing by zero isn’t valid. If you’re always narrating, you might not pause to check if the step is allowed. Instead, writing out the property ("Division by zero is undefined") forces you to notice mistakes.

• Name the property, theorem, or rule each time you use one (e.g., Distributive Law, Zero Product Property, Chain Rule).
• Use process words sparingly, only to signal a shift or a conclusion.
• If you’re explaining why you chose a method, say so directly (e.g., "Since the equation is quadratic, factoring is possible.")
• Reread your solution: does it show why each step is justified?

Pick a problem you’ve already solved, especially one with lots of "then" or "next." Rewrite it, aiming to:

• Remove half the process words.
• Add at least one property, rule, or justification per major step.

Read both versions side by side. Which one actually shows your understanding?

There are moments when transitions help:

• At the start of a new section: "Next, consider the case when x < 0."
• When summarizing: "Therefore, the solution for all cases is..."
• To signal a big logical leap, not just routine steps.

But if you’re using them on every line, it’s a sign to pause and refocus.

If you notice your math solutions are full of "then," "next," and "so," you’re not alone—but it’s worth practicing a different habit. Instead of narrating each action, aim to show your logic and the mathematical principles at work. Your solutions will be clearer, more concise, and more likely to earn full credit.

If you want feedback on your explanations, you can always ask a peer, teacher, or even a tutor—Learn4Less is here if you want a second set of eyes. But with these checks, you can start improving your own writing today. You’re more capable than you think.