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GREENSHAW LEARNING TRUST & FRIENDS MATHS BOOK CLUB

11/5/21

Mathematical Beauty by Dan Pearcy

#GLTBookClub

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@DanielPearcy

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Hosted by:

@Noni_Rainbow

@DaveTushingham

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Takeaway: @atulrana

SlideNotes: @Harry45416494

This session focused on pages 113-121 of Dan’s book which considers a framework for mathematical aesthetics and how this can support us in allowing pupils to appreciate mathematical beauty.

Aesthetic Criterion

  • Enlightenment
  • Elegance
  • Simplicity and complexity
  • Symmetry
  • Surprise
  • Ingenuity

Quotes:

  • “Mathematical beauty lies in the mind of the beholder”
  • “Access to true aesthetic beauty in mathematics necessitates a threshold level of knowledge and understanding”
  • “Any beautiful piece of mathematics almost always contains an ingenious argument”
  • “One beautiful component of our subject is that there continues to be more and more problems to be solved”
  • “The lesson begins once the problem has been solved”
  • “Celebrating students different methods and encouraging to connect methods is integral”
  • “Collaborative tasks can develop a “buzzing excitement” within groups and contribute to process aesthetics”
  • “When separate areas of mathematics connect with each other in a surprising way, we feel a sense of aesthetic pleasure”
  • “Truly beautiful mathematics often applies to universal phenomena”
  • “Mathematical beauty is about generating patterns and forming relationships in creative ways”

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Takeaway:

  • It’s not just doing maths it’s about appreciating the beauty.
  • Mathematicians are curious and enjoy the challenge of a problem.
  • Important to convey beauty and a sense of enlightenment to our pupils.
  • We’re socially wired to respond to stories. Helps pupils engage.
  • A maths problem isn’t about the answer, it’s about what it makes you think in the process.
  • Solving a problem like switching on a light after stumbling around in a dark room.
  • “Look to include an Ah, Aha or Haha in your lessons” – Rob Eastaway

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Reflections and takeaways:

  • Mathematicians are curious and on a quest to find answers (even if they don’t exist). This in itself is beautiful.
  • Developing subject knowledge is crucial to allow pupils to make links between different areas of maths and appreciate this beauty.
  • Maths is an art form. Like music.
  • Surprise and the “wow factor” are powerful ways to engage pupils.
  • We learn through (relevant) stories.
  • Important to carefully prepare script and lesson when looking to introduce story/real-life application (rather than shoehorning into topic).
  • Mathematics is beautiful and enjoyable in it’s own right, even if not applicable in the “real-world”.
  • As teachers we should show our genuine enthusiasm and passion for mathematics to pupils (rather than hiding it).
  • Beauty is personal – expose pupils to a range of ideas to maximise chance of experiencing this beauty.
  • Understanding can be crucial in accessing the deep beauty…but sometimes understanding can ruin “the magic”!
  • Encouraging pupils to use multiple approaches for solving a problem helps to develop a sense of “connectedness”.
  • Pupils can be supported in finding which approach is most powerful (i.e. it translates to most areas of mathematics) and consider which is the most ingenious.

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Resources/ideas

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