About the Researcher

Noah Heller

Noah Heller is a Lecturer on Education and the master teacher in residence in mathematics for the Harvard Teacher Fellows Program. His research focuses on how and why some students identify as “math persons.” He spent nine years as a high school math teacher before transitioning to training and mentoring math and science teachers. See full bio


Submit a Question
Ask Now

Embrace errors as learning, emphasize reasoning, and relate math to student strengths

By Noah Heller

Erik Gundersen and Mark Russo of Pascack Valley Regional High School District askec, “What techniques can help students gain confidence in mathematics and reconsider their own position in regards to mathematics?”

I think it’s important to think about why students might not feel confident. Unfortunately, math is often treated as a binary: Either you’re good at it or you’re not good at it. And if students have received negative feedback on assessments, if they’ve been placed in lower math tracks, or if they misunderstand the content, then oftentimes, they think they’re bad at math.

One way to change this assumption is to create a classroom culture where errors become learning opportunities. For example, when a student voices a wrong answer, teachers can get excited about that. Rather than moving on from a wrong answer or pivoting directly to a student who has a right answer, find out what is right about that student’s thinking. This can show that student she was on the right track, and provide an opportunity for her to uncover her own mistake or misconception.

It can also be helpful to more generally de-emphasize answers and spend more time on reasoning. Teachers can put a worked example with a wrong answer up on the board and have students find the error. Or they can rethink the way they use class participation. It’s common practice for teachers to ask for volunteers to share out an answer. But they can suspend that, and first say, “I don’t want to hear the answer just yet. I want to hear about the first thing you thought about.” Different students will share different ideas, which can help them all see that there can be multiple ways to solve a problem.

These discussions and practices can make mathematics class more discursive and less about a single answer, which can help students feel confident when they don’t know the answer right away, or get the wrong answer at first.

Another way to build confidence is to help students understand how the ways in which math gets used in the world can relate to their personal strengths. For example, imagine you’re working with percentages, and you have a handful of struggling students who love playing basketball. Teachers can relate percentages to the basketball statistics students often look at, which allows students to feel more confident with the content. Students might not be experts on how to calculate percents, but they could be experts on which NBA players have the highest shooting percentages. When students make that connection, their positionality changes. They’re the ones bringing something to the table that’s valued and important and relevant.  Activating students’ expertise in math contexts gives them power as math learners.

Of course, a final go-to around confidence is promoting a growth mindset. In mathematics in particular, students often think that intelligence is fixed. It’s important to give feedback in ways that values effort and encourages persistence, which can show students that there is always room for them to improve their skills.

This answer was developed in partnership with Usable Knowledge at the Harvard Graduate School of Education.


Resources for Further Learning