Jo Boaler: Mathematical Mindsets
Chapter 1: The Brain and Mathematics Learning
Scientists are able to look at brain growth and brain degeneration and can see the impact of different emotional conditions upon brain activity! Wow!
"When we learn a new idea, an electric current fires in our brains, crossing synapses and connecting different areas of the brain." (P.1)
"If you learn something deeply, the synaptic activity will create lasting connections in your brain, forming structural pathways, but if you visit an idea only once or in a superficial way, the synaptic connections can "wash away" like pathways made in the sand. Synapses fire when learning happens, ... synapses fire when we have conversations, play games, or build with toys etc." (p.1)
Example of London Black Cab drivers who have to learn 25, 000 streets and 20,000 landmarks within London, taking two to four years of study to complete. The hippocampus in the taxi drivers' brains had grown significantly! After retirement, their hippocampus began to shrink again.
Brain ability is not fixed!
"The new evidence from brain research tells us that everyone, with the right teaching and messages, can be successful in math, and everyone can achieve at the highest levels in school." (p.4)
"Einstein...spoke often about his achievements coming from the number of mistakes he had made and the persistence he had shown. He tried hard, and when he made mistakes he tried harder." (p.5)
"A lot of scientific evidence suggests that the difference between those who succeed and those who don't is not the brains they were born with, but their approach to life, the messages they receive about their potential, and the opportunities they have to learn." (p.5)
"Students with a fixed mindset are more likely to give up easily, whereas students with a growth mindset keep going even when work is hard and are persistent, displaying what Angela Duckworth has termed 'grit.'" (Duckworth, A., & Quinn, P. (2009). Development and validation of the short grit scale. Journal of Personality Assessment, 91 (2), 166-174.) (p.6)
"When students are given fixed praise - for example, being told they are smart when they do something well - they may feel good at first, but when they fail later (and everyone does) they think that means they are not so smart at all." (p.7)
There are huge implications in this chapter for our community at RSS and our staff. Do staff and parents really believe that anyone is capable of high level maths? What about the kids? Do they think that? What do our groups tell our learners?
Scientists are able to look at brain growth and brain degeneration and can see the impact of different emotional conditions upon brain activity! Wow!
"When we learn a new idea, an electric current fires in our brains, crossing synapses and connecting different areas of the brain." (P.1)
"If you learn something deeply, the synaptic activity will create lasting connections in your brain, forming structural pathways, but if you visit an idea only once or in a superficial way, the synaptic connections can "wash away" like pathways made in the sand. Synapses fire when learning happens, ... synapses fire when we have conversations, play games, or build with toys etc." (p.1)
Example of London Black Cab drivers who have to learn 25, 000 streets and 20,000 landmarks within London, taking two to four years of study to complete. The hippocampus in the taxi drivers' brains had grown significantly! After retirement, their hippocampus began to shrink again.
Brain ability is not fixed!
"The new evidence from brain research tells us that everyone, with the right teaching and messages, can be successful in math, and everyone can achieve at the highest levels in school." (p.4)
"Einstein...spoke often about his achievements coming from the number of mistakes he had made and the persistence he had shown. He tried hard, and when he made mistakes he tried harder." (p.5)
"A lot of scientific evidence suggests that the difference between those who succeed and those who don't is not the brains they were born with, but their approach to life, the messages they receive about their potential, and the opportunities they have to learn." (p.5)
"Students with a fixed mindset are more likely to give up easily, whereas students with a growth mindset keep going even when work is hard and are persistent, displaying what Angela Duckworth has termed 'grit.'" (Duckworth, A., & Quinn, P. (2009). Development and validation of the short grit scale. Journal of Personality Assessment, 91 (2), 166-174.) (p.6)
"When students are given fixed praise - for example, being told they are smart when they do something well - they may feel good at first, but when they fail later (and everyone does) they think that means they are not so smart at all." (p.7)
- I can think of many kids who fall into this category! Children who fall on either end of the 'I'm good at maths spectrum' - kids who don't see themselves as good at maths, who won't even try because they are worried they can't do it, to kids who see themselves as very good at maths, who, if they don't think they can do it, won't try so they don't make themselves look bad! How do children learn these things? What are we doing at school to magnify these problems? What messages do we/our parents give our students?
"Praise feels good, but when people are praised for who they are as a person("You are so smart") rather than what they did ("That is an amazing piece of work"), they get the idea that they have a fixed amount of ability. Telling students they are smart sets them up for problems later. As students go through school and life, failing at many tasks - which, again, is perfectly natural - they evaluate themselves, deciding how smart or not smart this means they really are. Instead of praising students for being smart, or any other personal attribute, it's better to say things like: "It is great that you have learned that," and "You have thought really deeply about this." (p.8)
"Many people believe there is a developmental stage students must go through before they are ready for certain mathematics topics. But these ideas are also outdated, as students are as ready as the experiences they have had, and if students are not ready, they can easily become so with the right experiences, high expectations from others, and a growth mindset. ...When students need new connections, they can learn them." (p.8)
There are huge implications in this chapter for our community at RSS and our staff. Do staff and parents really believe that anyone is capable of high level maths? What about the kids? Do they think that? What do our groups tell our learners?
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