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.

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

• 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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