The text popped up on my phone late in the afternoon, “Any chance you’re still in your office??”
My answer, “No – at home.”
Her response, “Ok. I have to come show you some papers
tomorrow.”
More from her, “Here’s a preview. This is a quiz…after two
weeks of instruction.”
The teacher did come by the next day, and she brought the quiz
papers. She was frustrated that her 11th grade students couldn't solve equations. She was looking for ideas on how to help her students.
She’s a great teacher. She develops good relationships with
her students, she's not afraid to take risks, and she's always seeking ways to help
her students. So when her students struggled on this quiz, she didn't say, “I
can’t teach them,” or blame the teachers before her on their lack of
preparedness.
All she focused on was how to help them.
In 2025, this situation is not unusual. With years of unfinished learning, students’ math foundations can be uneven. And with AI tools giving instant answers, it’s even more important that students know why steps work and not just what buttons to push.
So we talked through next steps, and here’s the strategy that changed everything.
Using Errors as Opportunities
I suggested she take several real student errors, copy them exactly as written, and project or print them for the class.
But here’s the twist:
Students wouldn’t solve the problems.They would only diagnose the mistakes.
In small groups, students would:
- identify where the error occurred
- describe why it was wrong
- rewrite the correct mathematical thinking
- compare their explanations with another group’s
This is called error analysis, and it’s one of the most powerful strategies in math instruction today, especially in an AI-saturated world. When students must explain why something is wrong, they engage in deeper thinking than when simply repeating steps.
She also wanted to allow the students to retake the quiz. I supported that, but only with a plan.
I
suggested that she create a “study contract” that they complete in order to retake
the quiz. The students would have to attend a certain number of our “Math ER” help
sessions we offer during students' lunch/advisory period and complete a study
guide containing extra problems just like the ones on the quiz but with
different numbers and variables.
👉 Download a printable version of this Study Contract
(Perfect for math teams, PLCs, and classroom use.)
The Surprising Results
The next day she found me again... with a smile.
She said the activity was eye-opening.
Some students who could solve problems correctly had trouble identifying mistakes.
Others who scored poorly could immediately find the errors—and explaining them helped correct misconceptions.
It separated those who were following memorized steps from those who could truly think.
It also highlighted who needed foundational support versus who needed conceptual stretching.
Most importantly, she now had clarity on how to target her instruction.
A Culture That Chooses Solutions Over Blame
Every school has moments like this, when students struggle with what seems like basic content. What matters is how teachers respond.
This teacher chose curiosity instead of blame.
She chose problem-solving over frustration.
She chose growth over excuses.
And students benefited.
As leaders, we can build cultures where those choices are normal: where struggle is met with support, and where mistakes become stepping stones instead of stumbling blocks.
I can’t wait to see how her students do on the retake.
Hopefully she won’t get any more answers like this…
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