# Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching by Jo Boaler

### Chapter 1 Sketchnote Summary

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### A Few Quotes I Like:

“If we believe that we can learn, and that mistakes are valuable, our brains grow to a greater extent when we make a mistake.”

– Jo Boaler

“The game is played by partners. Each child has a blank 100 grid. The first partner rolls two number dice. The numbers that come up are the numbers the child uses to make an array on their 100 grid. They can put the array anywhere on the grid, but the goal is to fill up the grid to get it as full as possible. After the player draws the array on their grid, she writes in the number sentence that describes the grid. The game ends when both players have rolled the dice and cannot put any more arrays on the grid”
― Jo Boaler, Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching

## A Few More Popular Quotes from the book:

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. — Jo Boaler
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. — Jo Boaler
The powerful thinkers are those who make connections, think logically, and use space, data, and numbers creatively. — Jo Boaler
The vast majority of all math apps and games are unhelpful, encouraging drill and rote memorization. In this section I highlight four apps and games that I regard as valuable, as they visually engage students in conceptual mathematics. I am an advisor to three of the four companies (Wuzzit Trouble, Mathbreakers, and Motion Math). — Jo Boaler
“Every time a student makes a mistake in math, they grow a synapse.” — Jo Boaler
In the 1930s the Swiss psychologist Jean Piaget, one of the world’s leading psychologists, rejected the idea that learning was about memorizing procedures; he pointed out that true learning depends on an understanding of how ideas fit together. — Jo Boaler
The most powerful learners are those who are reflective, who engage in metacognition—thinking about what they know—and who take control of their own learning (White & Frederiksen, 1998). — Jo Boaler
If we believe that we can learn, and that mistakes are valuable, our brains grow to a greater extent when we make a mistake. — Jo Boaler
With conceptual, investigative math teaching and mindset encouragement, students will learn to shed harmful ideas that math is about speed and memory, and that they either get it or they don’t. — Jo Boaler
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