How to Spot When You're Overusing Process Words in Math Explanations

Process words exist for a reason. They help signal the flow of your argument. But unlike in essays, in math, each step should be justified by a rule, property, or calculation—not just by a transition word.

If every line starts with “then”, “so”, or “therefore”, it can: - Mask weak reasoning (the step happens, but why?) - Make it look like steps are connected simply by order, not by logic - Confuse the reader about what’s being assumed versus what’s proven

For example:

> "First, x = 2. Then, x^2 = 4. So, 2x = 4. Therefore, x = 2."

This is a chain of steps, but it’s not clear why each move is valid. Are you using a property? Substituting? Assuming something? The process words string the lines together, but don’t explain the math.

It’s easy to slip into a rhythm: write a step, add “then”, write the next, and so on. But how do you know when you’re overdoing it?

Signs you’re overusing process words: - Nearly every line starts with a connector: “then”, “so”, “therefore”, “thus”, “next”, “after that”, etc. - You use process words even when the step is just copying the previous line or restating a result - Your solution reads like a list of steps with little math language (no mention of properties, theorems, or operations) - You notice your explanations are long but not actually more informative

Try reading your solution out loud. If it sounds like a sequence of “then… so… then…”, you’re likely relying on process words as a crutch instead of making your reasoning explicit.

In math, the point of an explanation is to show your reasoning—not just the sequence of steps, but the justification for each move. Process words should clarify, not obscure.

If your writing is full of connectors but light on justification, graders can’t see your understanding. They may not know if you applied a rule correctly, or just copied steps from memory. Worse, it can make your solution look circular or incomplete, especially if you’re missing key reasons for each step.

1. Process Words vs. Mathematical Justification

A process word tells the reader you’re moving to a new step. A justification tells them why that step is correct. For example:

• Process: “Then, x = 3.”
• Justification: “By substituting into the original equation, x = 3.”

The difference is subtle but important. The process word only signals order; the justification gives a reason. If your solution only uses process words, you’re not showing the why.

2. “Therefore” vs. “Because”

“Therefore” means you are drawing a conclusion from previous results. “Because” means you’re giving a reason for a step. Overusing “therefore” can make it look like you’re concluding too often, or skipping the reasons behind your steps.

Example:

• Weak: “x = 5, therefore x^2 = 25.”
• Stronger: “Because x = 5, we have x^2 = 25 by squaring both sides.”

Notice how the second version makes the operation and the logic clear.

You don’t have to eliminate process words entirely. Used well, they help the reader follow your solution. The goal is to balance them with real explanations.

Try this approach:

1. Replace some process words with explicit math language. - Instead of “then”, try “by the quadratic formula”, “by factoring”, “substituting into the equation”, or “since x > 0”.

2. Use process words only when you’re making a logical leap or conclusion. - “Therefore” should come before a conclusion, not every step.

3. Ask yourself: what is the reason for this step? - If you can’t name the property, rule, or operation, your explanation might be missing something.

4. Limit consecutive process words. - If you use “then” or “so” more than twice in a row, try rewriting at least one step to include justification.

Let’s take a typical over-processed solution:

> "Let’s solve x^2 - 4 = 0. First, x^2 = 4. Then, x = 2 or x = -2. So, the answers are x = 2 and x = -2."

Now, let’s add real justification:

> "To solve x^2 - 4 = 0, add 4 to both sides to get x^2 = 4. Taking the square root of both sides, x = 2 or x = -2. Thus, the solutions are x = 2 and x = -2."

Notice how the second version uses process words (“thus”) only for the final conclusion, and each step explains the operation being performed.

After each step, ask yourself: If someone asked “why is this true?”, could you answer with a property or rule? If not, your solution might be too heavy on process words and too light on math reasoning.

For example:

• “Then, x = 3.” → Why? (Missing justification)
• “By dividing both sides by 2, x = 3.” → The reason is clear.

Process words are not forbidden. They help signal progress, especially in multi-step arguments or proofs. The key is to use them to connect ideas, not to replace explanation.

Use process words: - To summarize a chain of reasoning (“Therefore, x = 2.”) - To indicate a logical conclusion (“Thus, the equation has no real solutions.”) - To guide the reader through a longer argument, as long as each major step is justified

Avoid using them: - As the only explanation for a step - In place of naming the operation, property, or theorem you’re using

Try this exercise on your next assignment: - Write your solution as you normally would. - Mark every process word (“then”, “so”, “therefore”, etc.). - For each, ask: Can I replace this with a reason, or add a justification? - Revise at least two steps to include explicit math reasoning.

Over time, your explanations will become clearer and more convincing—not just to your teacher, but to yourself when you review them later.

Getting used to writing clear, justified math explanations takes practice. If you find yourself leaning on process words, you’re not alone—it’s a common habit. But with a few adjustments, you can make your solutions clearer, more logical, and easier to follow. If you want more feedback on your explanations, Learn4Less can offer guidance—but you can start improving your writing right now, on your own.