Chapter 2 Notes Jan 29 - Summary Mathematical Mindsets PDF

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Notes for chapter 2 from the textbook (growth mindsets)...

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The Power of Mistakes and Struggle  

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January 29, 2018

It is really important to believe in yourself, to believe you can do anything. Those beliefs can change everything. Common misconception: if I make a mistake, I am bad at math. o Research has shown that mistakes don’t only help us learn, but cause our brains to constantly grow and improve, even if you’re unaware of the mistake or that it’s happening. o We are brought up in a performance based culture  Mistakes are not valued, in fact were punished for it  Compared to Japan/China which a process based culture that focuses on hard work. *see further down in notes* “Every time a student makes a mistake in math they grow a synapse.” o Significance of this statement:  Speaks to the significant power and value mistakes  Mistakes cause your brain to spark and grow even when you’re unaware you’ve made an error.  The brain is being challenged, so it grows Psychologist Jason Moser studied the neural mechanisms that operate in people’s brains when they make mistakes (Moser et al., 2011) o When we mistakes, there are two potential responses:  1. ERN - increased electrical activity when the brain experiences conflict between a correct response and an error.  **Occurs whether or not the person is aware they made an error  2. Pe – brain signal reflecting conscious attention to mistakes. This happens where there is awareness of an error. o The researchers looked at people’s mindsets and compared it to their ERN and Pe responses when they made mistakes. Important results:  1. Greater ERN and Pe responses – electrical activity – when students made mistakes compared to when they answered correctly.  2. Brain activity was greater following mistakes with individuals with a growth mindset compared to those with a fixed mindset.  3. Individuals with a growth mindset had a greater awareness of errors than those with a fixed mindset  Therefore they were more likely to go back and correct answers.  All students react with a brain spark – synapse – when they make mistakes, but having a growth mindset means that the brain was more likely to spark again. We want students to make mistakes in the classroom.

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China o Leads world in math advancement o Deals with mistakes differently. o The author sat in during a math lesson in a second grade classroom in Shanghai  Teacher gave the students deep conceptual problems to work on and then called on students individually  The teacher purposely chose students who had made mistakes to share their work with the class  Which students were more than happy to do o Proud  Teacher views value in mistakes “Individuals with a growth mindset have more brain activity when they make mistakes than those with a fixed mindset” o These mindsets can tell us the ideas we hold about ourselves.  Where we believe in ourselves or not. o If we believe that we can learn, and that mistakes are valuable, our brains grow to a greater extent when we make mistakes o It is important for students to believe in themselves

Mistakes in Life 

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What separates the more successful people from the less successful people is not the number of their successes but the number of mistakes they make. o More successful make more mistakes. Mistakes enhance creative and entrepreneurial thinking “Imperfection is a part of any creative process and of life, yet for some reason we live in a culture that has a paralyzing fear of failure, which prevents action and hardens a rigid perfectionism. It’s the single most disempowering state of mind you can have if you’d like to be more creative, inventive, or entrepreneurial.” Habits of successful people: o Feel comfortable being wrong o Try seemingly wild ideas o Are open to different experiences o Play with ideas without judging them o Are willing to go against traditional ideas o Keep going through difficulties https://www.youcubed.org/online-teacher-courses/ o Teaches growth mindset through math activities

How can we change the ways students view mistakes?    

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Teachers and parents can change the messages they give about mistakes and wrong answers in mathematics. When we teach students that mistakes are positive, it has an incredibly liberating effect on them. Page 15-16 of textbook has fantastic example of how to physically represent the brain growth that occurs from mistakes. Teachers should highlight their “favorite mistakes” o Conceptual mistake, not numerical error o Where the mistake occurred and why it was a mistake o “They were in a state of cognitive struggle and their brain was sparking and growing. o If one student is making mistakes, others are too so it’s important to address them. Abandon the idea of taking points off of assignments for making mistakes.

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Disequilibrium o Jean Piaget

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We need to give students more challenging work, so they’re more likely to make mistakes. o These difficulties prompt disequilibrium...