Blogging from The Tenth Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics

Dr Claire Cornock from Sheffield Hallam University.

Based on Teaching group theory using Rubik’s cubes.

See presentation here.

Backgrounds: Maths at Sheffield, Hallam University:

  • Real, practical, development of employability skills – in a very applied degree program
  • Students struggle with abstract concepts

Pure maths modules:

  • Knot theory, linear and discrete maths, number and structure, abstract algebra.
  • Abstract Algebra: roughly 75% of students taking the module took the questionnaire.

Teaching methods:

  • Groups of 30 students
  • 2 hour workshops
  • Support groups
  • Partially printed notes
  • All given a Rubik’s cube

They don’t have to be able to solve a Rubik’s cube!! They can always swap theirs for a new one.

Taken from http://www.sigma-network.ac.uk/wp-content/uploads/2013/10/Cornock_CETLMSOR_2013_Presentation.pdf

Taken from http://www.sigma-network.ac.uk/wp-content/uploads/2013/10/Cornock_CETLMSOR_2013_Presentation.pdf. Original paper here: http://sporadic.stanford.edu/bump/match/rubik.pdf

 

Name different moves: ie. move front face 90 degrees clockwise. See here:

Can talk about

  • subgroups
  • generators
  • homomorphisms
  • equivalence relations
  • permutations

Let G be a group and let g, h\in G. Then:

 

(gh)^{-1}=h^{-1}g^{-1}

 

How would you undo FR (front, right each moved 90 degrees)?

Homomorphisms: see how a move acts as a permutation.

Students are discovering, then you can introduce the formal definition.

  • “Seeing a demonstration in anything immediately clarifies any misunderstanding”
  • “I could visually see why something worked”
  • “More than one approach was extremely better especially if it’s a hands on approach”

Reasons for not liking the cubes:

  • Frustrating when they messed the cube up
  • Distraction
  • Confusing

Assessment:

  • 50% coursework (1 group task, 2 individual), 50% exam.
  • Gives them space to experiment with ideas
  • Provide their own examples
  • The rubik’s cubes DO feature in the exam!
  • “It’s easy to remember concepts when visual examples are in mind” – having the cube on the table helps!

Evaluation

Attendance is very very high – from 80%-95% – those absent were ill, or at interviews:

  • Not wanting to fall behind
  • Enjoy the module
  • Personal motivation
  • Group work
  • Content difficult without taught lesson
  • On average, on the group theory assignment, the mark was 71.4%
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