The problem was −2(3x/2 − 5) = 16. A high school student I was tutoring distributed the −2 to the first term and stopped, missing the need to multiply the second term, −5, by −2, turning it into positive 10.
We circled the −2, drew two arrows, and the rest followed.
At last, we did the part I love most: we plugged the answer back into the original equation to check ourcalculations.
It held. x = −2. Nothing to argue about.
For nearly two decades, my work has been in literacy, where meaning is layered. An essay can always be reread for edits and revision: more often than not it is only a deadline that puts an end to the tinkering.
Tutoring algebra has given me back something I am realizing I missed: a problem with one, and only one, solution. You work through the equation, check your calculations, and it is right.
My father, an engineer, understands this completely. When I recounted my tutoring sessions, he told me that this was exactly why he had always loved math: there was no disputing the answer. In high school, his teachers gave him a hard time because he skipped steps. His reply: “This is the answer.”
Perhaps he had arrived at it in an unconventional way, mostly through mental math, but if it was right, it was right.
As an academic tutor, I now find myself on the other side of that argument. For a struggling student, the steps are precisely where the learning lives. A dropped sign or a misread word shows me how the student worked through the problem and where the reasoning went astray. Together, we can work backward to identify the errors and recalculate. In doing so, I help the students learn to monitor their own work and check each step for accuracy.
That process feels familiar. As a reading specialist, I have spent years listening closely to students, noticing where they hesitate, what they overlook and how they make sense of what is on the page. In algebra, too, understanding the language matters. A student may know how to calculate but struggle to interpret what a question asks. My years in literacy turn out to be good preparation for helping studentsin mathematics, too, and for this I am grateful.
Across disciplines, we are always seeking that lightbulb moment: when something clicks and the learner thinks, “Aha. Now I see.” There is satisfaction in watching something become clear; something settles.
Recently, I figured out how to solve a double-digit multiplication problem using the Japanese method, and it was indeed satisfying. I am grateful to help students experience incremental moments ofunderstanding — and, through them, develop the independence and confidence to work through challenges with greater resilience and grace.
Amelia Clune is a writer and literacy educator based in the Monadnock region of New Hampshire.