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

Dr Esme Voges from Tshwane University of Technology

Live blogging: Note that these are notes I’ve taken live, but will edit this today into a more readable format. I want to put this up straight away though to see if I have any obvious misunderstanding. Equations will also be put into more readable format ASAP.

Talking about Mathematica from a lecturers point of view.

Background: Diploma and B Tech engineers students.

The students are millennials – they can figure things out for themselves.

How do you make maths applicable for engineers?

Coffee cooling problem: Using Manipulate and Animate to create an interactive graphic. Can step through, can see how the different variables change things? Taken from here:

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This is an application of a differential equation.

Can explain many different concepts from a single example – what does T=0 mean? What is a natural log? What are temperature conversions? What can differential equations do for you?

Next example: Second order differential equations: Spring system.

How do you explain  the convention that down is positive when you have a mass on a string, when normally up is positive on a graph?

Free vibrations of a spring-mass-damper system: The student can follow the displacement and the velocity. Why is the velocity negative? What does damping do to a spring system?

Students often can’t think about an answer – if you get the solution of a problem that a fly is 10^6 kg, there’s a problem!

Critical points of z=f(x,y) – what is a “saddle point?” What is a saddle?! Students may never have seen a saddle.

How do you tell students to visualise a 3d graph when they have difficulties already with 2d graphs?

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Properties of a matrix: You can dynamically generate the inverse, trace, determinant, rank.

“Change the elements in the matrix using the sliders on the left”

The students are given the answers, but they must do the calculations themselves.

The code is hidden: Useful so that students aren’t overwhelmed.

Partial fractions: Taken from wolfram demonstrations project

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Issues:

  • Mathematica is expensive
  • Students can download the CDF reader
  • Wolfram demonstrations project: Tracy Craig’s student problem about the scalar product: Find the components of a vector orthogonal and parallel to another vector.

Mathematica is not just for mathematics.

Teaching music.

Web embeddable: Include in your online interactive material

 

 

 

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