When mistakes are normalized in the classroom, students develop a stronger connection to mathematics and become more engaged and motivated. Removing the pressure of grades and replacing them with meaningful feedback allows students to take intellectual risks, fostering deeper learning. Students who previously felt discouraged by low grades report feeling freer, more confident, and more willing to engage with challenging material when assessments focus on growth rather than performance.

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Mistakes as a learning tool

Peter (2012) emphasizes that critical thinking is a learned skill that requires instruction and practice. This aligns with the idea that students need to be given space to struggle productively and learn from their errors rather than being penalized for them.

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Luzano’s (2024) study,  exploreshow fear of failure and the stigma around mistakes can hold students back in math but also how the right classroom environment that embraces mistakes can lead to deeper learning. Luzano interviewed college-level math students and found five major themes: (1) Fear of Failure, (2) Stigma of Mistakes, (3) Importance of a Growth Mindset, (4) Role of Teacher Support, and (5) Transformational Learning Experiences. His research highlights that students build resilience and confidence when they see mistakes as learning opportunities rather than failures. He also introduces the Unlocked Power Funnel Model of Productive Failure, which emphasizes how shifting students’ perspectives on mistakes and strong teacher support can lead to better engagement and understanding in math.​​​​​​

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Fear of Judgement from Peers

Many students avoid participating in math discussions due to the fear of embarrassment when making mistakes publicly (Luzano, 2024). This stigma of mistakes prevents students from fully engaging in mathematical discourse and problem-solving.  “In math class, I always feel like there’s no room for mistakes. If you get something wrong, people look at you differently, or the teacher just moves on without really helping.” Luzano, 2024, p.1736)

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In classrooms that focus heavily on grades and right answers, students often fear judgment from peers or feel trapped by labels. Boaler (2015) notes, “Students describe themselves as A or D students because they have grown up in a performance culture that valued frequent testing and grading, rather than persistence, courage, or problem solving” (p. 2). She also warns, “When students are given scores that tell them they rank below other students, they often give up on school... and take on the identity of an underperforming student” (p. 4). These examples show how important it is to shift away from grading cultures and toward environments that support all learners in their growth.

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Teacher’s Reaction Matters

Students thrive when mistakes are treated as a natural and valuable part of learning. When students feel safe enough to take risks without fear of judgment, they engage more deeply, challenge their own thinking, and grow both academically and personally. On the other hand, when mistakes are met with criticism or dismissal, students tend to shut down, avoid participation, and miss out on meaningful learning experiences.

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One of the most powerful takeaways from this study is that teachers set the tone for whether students feel comfortable making mistakes. When instructors are open, nonjudgmental, and encourage discussion, students feel free to explore new ideas and push themselves further. But in classrooms where criticism is the norm, students hold back, afraid of being wrong.  Holley and Steiner (2005)  "A classroom in which safe means no conflict, and that no one is ever feeling challenged or uncomfortable is likely to be a classroom in which little learning and growth are occurring" (p.52).  This means a truly supportive classroom isn’t about avoiding discomfort, it’s about creating a space where students feel safe enough to struggle, ask questions, and learn from their mistakes. If we want students to take risks and push their thinking, we have to show them that mistakes aren’t failures, but they’re stepping stones to real understanding.

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Growth Mindset Takes Time

Boaler’s research makes an important point that mistakes aren’t setbacks; they’re essential to learning. When students feel safe to make mistakes without fear of failure, they engage more, take risks, and develop a stronger understanding of mathematics. Rather than seeing mistakes as something to avoid, students begin to recognize them as opportunities to grow. As Boaler (2015) states, “Well-crafted tasks and questions accompanied by clear feedback offer students a growth mindset pathway that helps them to know that they can learn to high levels, and, critically, how they can get there.” A classroom that normalizes mistakes fosters confidence, resilience, and curiosity. If we want students to truly succeed, we need to create an environment where mistakes aren’t just accepted, but valued as part of the learning process.

 

Boaler’s insights really support the idea that the way mistakes are handled in the classroom can shape how students feel about learning math. When teachers create an environment where errors are welcomed and used as learning opportunities, students begin to see that struggling with a concept doesn’t mean they’re bad at math, but it means they’re growing. As Boaler (2019) puts it, “When students are in math classes that value their thinking, include opportunities for growth, and celebrate mistakes and struggle, they develop the most important attitudes and behaviors for success” (p. 30). This really speaks to my research focus because it shows that normalizing mistakes doesn’t just help students understand math better, but it can also make them feel more confident, resilient, and willing to participate in class without fear of being wrong.​​​​​​

 

Increased Confidence Over Time

Luzano (2024) found that teacher support plays a crucial role in how students perceive and react to mistakes. When teachers encourage risk-taking, provide constructive feedback, and avoid shaming mistakes, students feel safer and more willing to engage in problem-solving. 

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Normalizing mistakes doesn’t just improve understanding but it also boosts student confidence and motivation. In supportive classrooms, students feel more capable and willing to engage in challenging tasks. Boaler (2015) observed this shift firsthand: “Math anxiety, formerly commonplace among students, disappeared and was replaced by student self-confidence, which led to higher levels of motivation, engagement and achievement” (p. 3). This shows that the emotional tone of a classroom, especially how it handles errors and can change students’ relationship with math for the better.

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