At the core of productive struggle is a practice in which the mind accommodates new experiences and ideas by first allowing room for the questioning, and if necessary, loss of pre-existing notions. This practice is simply represented in the following elementary math students experience:
Kriya learns about squares one day in math class – an intangible four-sided enclosed shape, with congruent sides that come together to form four right angles. All class, students tackle square-related problems. Then, the teacher presents a challenge problem in which there is a diamond-shaped figure. Kriya’s peers observe the drawing…they all begin to assert how it must be a “weird square” but a square nevertheless. Kriya begins to wonder, “Is a square the only four sided enclosed shape in the world?” She looks around the classroom – the ceiling didn’t have four congruent sides and the textbook on her desk was not quite like squares either. “Then, perhaps, not all four sided shapes in the world are square,” Kriya wonders.
What was it about Kriya’s mental habits that allowed her to engage and grow as a math student? Unlike her classmates, who began to classify all four-sided figures as squares, Kriya questioned the belief that “everything presented to the class will be some sort of square.” She left room in her mind for the possibility of the loss of beliefs and the arrival of new notions and learning. This space for letting go and accepting the loss of thought processes when old ideas fail to provide a clear view of reality is the cornerstone of productive struggle.
Let’s fast forward 7 years – Kriya is now in 12th grade and, with her flexible mind and habits, she has thus far experienced success in high school mathematics. She is now taking College Calculus. One day, the teacher presents a graph and asks the students to work together to find one method that accurately approximates the area under the curve between two bounds. Kriya talks to classmates – initially befuddled, they put their heads together to come up with some idea. For the first time, Kriya feels like she just can’t do math, “Perhaps, I’m actually not cut out for this? Maybe real math is too hard for me. I can’t even come up with a simple method.” Dismayed, Kriya doubts her abilities…as the teacher comes by to give hints to the group she is still lost in thought and misses the guidance.
While Kriya had practice in leaving room for new content in her mind, she now faced a very different aspect of the practice: leaving room for new insights that impact one’s psychology. Kriya had trouble fitting two ideas, failure and mathematical success, in her mind. There was no space or flexibility for the two notions to co-exist. However, to make room for the notion that failure is part of learning math, Kriya needs to modify the second belief. Instead of just believing “I am successful in mathematics”, she can more accurately accommodate the belief, “Success in mathematics entails failure, frustration, and perseverance.” This belief leaves room for failing, trying again, failing, and trying again…building immense capacity for perseverance.
What have these examples shown us? In order to learn, we must practice letting go of and accepting the loss of beliefs that no longer align with reality or lead to growth. This practice is not confined to learning content (subject-specific material). It encompasses our psychology and we must choose between being static or embracing the evolving mind. The mind evolves with loss and renewal, allowing all of us to engage in productive struggles. As I wrote in On Struggle (Part 1): Befriending Struggle, struggle is our toughest teacher – it helps us question our beliefs so we can evolve into more resilient individuals ready to absorb and assimilate knowledge about the world around us and within us. In my next post “On Struggle (Part 3),” I will post a meditation on Embracing the Evolving Mind.
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