The philosophy of failure: why struggling in math can lead to success
30 September, 2024
The hidden key to learning
In education, failing in subjects—especially math—has long carried a negative stigma. However, research now demonstrates that struggling and learning from mistakes are essential for developing the skills, knowledge, and understanding needed to tackle challenging concepts. Mistakes should not be viewed as failures but as integral steps in the journey to success. This perspective, rooted in anthropology, highlights the importance of failure as a necessary part of progress.
Fostering development through
learning from failure in life
learning from failure in life
Among the key developments driving the growth of modern education is the concept of a growth mindset, a notion explored by educational psychologist Carol Dweck and embraced by researchers like Russell, Salgado, and Fair, as well as students themselves. A 2019 study demonstrated that students with a growth mindset were 3% more likely to improve their mathematics grades than those who viewed failure as a sign of inadequacy. These students are more willing to take on challenges, persist through difficulties, and ultimately achieve more in the long run.
Angela Duckworth’s research on grit—a specific form of persistence that involves overcoming obstacles—also underscores the importance of resilience in academic success. In a sample of over 2,000 students, those with higher levels of grit scored about 8% higher than their peers on standardized math tests, suggesting that persistence, rather than ability alone, is a key determinant of academic achievement.
Cognitive growth
Cognitive development is inspired by children’s mistakes, particularly in mathematical contexts where certain mistakes can be useful. A Psychological Science study published in 2021 revealed that students who worked with their mistakes did 23% better in the tests later on. The tendency to cope with mistakes and to enhance one’s abilities in problem-solving and long-term cognitive adaptability, which is fundamental for memory encodings, are emphasized. In addition, this is emphasized in the findings of the National Bureau of Economic Research where productive failure, a model that recommends straining students before solving a problem, when applied increased students’ understanding of mathematics by 6.6%. Productive failure achieves this by encouraging deeper thinking and not just helping students understand the mechanics of solving the question but also its internal logic.
The role of Calcularis in supporting learning through failure: with each session, learners make incremental progress, and over time, they gain mastery in areas they once found challenging. Parents and teachers have praised the program for helping children who have struggled for years to finally overcome their fear and frustration with math.
Failure in math should not be feared but embraced as a crucial learning tool. Research shows that those who engage with their mistakes, persevere through challenges, and adopt a growth mindset achieve greater academic success. Tools like Calcularis are invaluable in this process, supporting students as they learn to transform failure into an opportunity for growth and mastery. The next time you or a student struggles with math, remember that each mistake is a step closer to success. Embracing failure can unlock new potential and set the stage for long-term achievement.
