Exit Slip: Six controversial statements about mathematics learning from Rafaella Borasi

In a segment of today's class we explored "six controversial statements about (mathematics) education." My group specifically investigated the statement "you cannot learn from your mistakes." My take on this statement is that I very much disagree with it. I believe that making mistakes is one of the most valuable and enriching ways to learn. Psychological neuroscience has shown us that when we do something correctly (or rewardingly) our brain fires stronger and faster neural signals for doing this action; conversely when we do something the wrong our brain keeps memory of the way these neural signals were fired, and remembers not to do it again. Memory, therefore, is one of the strongest reasons I believe that you can and should learn from your mistakes.

Although my group and I unanimously disagreed with the statement, we attempted to find reasoning backing the statement. I thought that making mistakes again and again may wear on the confidence of the student, proving it a emotionally harmful way to learn (but only if the mistakes are overwhelmingly frequent). Furthermore, if the student keeps all their mistakes in their head they may get confused between what was a mistake and what was the correct solution.

Overall, I still disagree with the statement and believe that it may have been made in past generations when knowledge about education and its nuances were not as well-explored. Intelligence is not pre-determined, it is malleable, and so making mistakes, in my opinion, is a valuable way to learn.

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