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:


  1. Posing a question
  2. Going from the real world to a mathematical model
  3. Performing a calculation.
  4. Going from the model back to the real world, to see if the original question was answered.
"What employers need, is people who can ask good questions, set up models, analyse results, and interpret mathematical answers.  It used to be that employers needed people to calculate; they no longer need this.  What they need is people to think and reason."

"Parents often do not see the need for something that is at the heart of mathematics: the discipline.  Many parents have asked me: What is the point of my child explaining their work if they can get the answer right? My answer is always the same:  Explaining your work is what, in mathematics, we call reasoning, and reasoning is central to the discipline of mathematics.  Scientists prove or disprove theories by producing more cases that do or do not work, but mathematicians prove theories through mathematical reasoning.  They need to produce arguments that convince other mathematicians by carefully reasoning their way from one idea to another, using logical connections.  Mathematics is a very social subject, as proof comes about when mathematicians can convince other mathematicians of logical connections."

"We also want students reasoning in maths classrooms because the act of reasoning through a problem and considering another person's reasoning is interesting for students.  Students and adults are much more engaged when they are given open math problems and allowed to come up with methods and pathways than if they are working on problems that require a calculation and answer."

Laurent Schwartz (2001):
"I was always deeply uncertain about my own intellectual capacity; I thought I was unintelligent.  And it is true that I was, and still am, rather slow.  I need time to seize things because I always need to understand them fully.  Towards the end of the 11th grade, I secretly thought of myself as stupid.  I worried about this for a long time.
I'm still just as slow....At the end of the 11th grade, I took the measure of the situation, and came to the conclusion that rapidity doesn't have a precise relation to intelligence.  What is important is to deeply understand things and their relations to each other.  This is where intelligence lies.  The fact of being quick or slow isn't really relevant."

"The powerful thinkers are those who make connections, think logically, and use space, data and numbers creatively.










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