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Jo Boaler: Mathematical Mindsets

Chapter 3: The Creativity & Beauty in Mathematics

This chapter has really challenged me to think about what maths is really all about...

Mathematicians "will say it is the study of patterns; that it is an aesthetic, creative, and beautiful subject (Devlin, 1997)."

"Mathematics is a cultural phenomenon; a set of ideas, connections, and relationships that we can use to make sense of the world.  At its core, mathematics is about patterns .  We can lay a mathematical lens upon the world, and when we do, we see patterns everywhere; and it is through our understanding of the patterns, developed through mathematical study, that new and pwerful knowledge is created."

"When we do not show the breadth of mathematics to students, we deny them the chance to experience the wonder of mathematics."

Wolfram (2010) proposes that working on mathematics has four stages:


Posing a questionGoing from the real world to a mathematical modelPerforming a calculation.Going from …

Jo Boaler: Mathematical Mindsets

Chapter 2: The Power of Mistakes and Struggle

"Every time a student makes a mistake in math, they grow a synapse." (p.11)

The ramifications of this are HUGE! So, if students are not making mistakes (Often the best and brightest), synapses are not developing.

"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, with the more successful people making more mistakes." (p.13)

"Imperfection is a part of any creative process and of life, yet for some reason we live in a culture that has a paralysing 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." (Sims, P. (2011, August 6). Daring to stumble on the road to discovery. New York Times. Retrieved from http://www.nytimes.com/2011/08/07/jobs/07pre.html?_r=0) (p.…

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, …

Carol Dweck: Mindset

Adult Enablers: What am I/my colleagues doing to enable my students to do?

Are we enabling students to succeed or fail? What messages are we sending? "When people think that some kids just can't do math, that success in math is reserved for only certain kids, thought of as "smart," or that it's just too late for kids who haven't had the right background, then they can easily accept that many students fail math and hate math.  In fact, we have found that many teachers actually console their students by telling them not to worry about doing poorly in math because not everyone can excel in it." 
Dweck, C.S. (2006b). Mindset: The new psychology of success. New York: Ballentine Books.