Online tutorials for first year mathematics

The first teaching semester of 2015 has just finished here at UNSW. It has been very busy for me, which is a convenient excuse for not having blogged much lately. What’s been happening?

Teaching-wise I got a Learning and Teaching Grant from the University to put together new Online Tutorials for our Higher First Year Maths course MATH1141, which combines Algebra and Calculus. With the fantastic help of Daniel Mansfield, and also Jonathan Kress, we have been busily designing interesting questions that our best first year students can attempt on-line using Maple TA. That is a system devised by the clever people at Maple, based in Waterloo, Canada, which allows mathematical computation in the context of online delivery of course questions.

This means we can coerce, I mean motivate, students to actually do homework! How good is that? Up till now we, along with fellow educators around the world, plead and cajole our students to work on their own going over suggested exercises to practise the skills we are teaching them. But not altogether surprisingly, self-interest intrudes, and students often find themselves with something better to do, in other words something for which marks are assigned.

Our Online tutorials are based on videos to problem solutions that we made that show students how to solve questions from our Problem Notes.

Hopefully they watch the videos, and then answer a suite of five questions, ranging in difficulty from easy to more challenging, on that general topic. With the possibility of adding images, diagrams, lots of good looking and well-laid out mathematics, we can make our questions rather nifty. Here is an example of a typical question, which prompts students to discover the rational parametrization of the hyperbola x^2-y^2=1.

Hyperbola

One of the exciting aspects of this is that we have realized we can get our students reading through proofs, and filling in blanks to complete them. This way they get the benefit of walking through a well presented argument and following that logical development—surely a key preliminary to getting them to create coherent proofs themselves.

And of course, there is the flexibility of the online platform that works in their favour, so they can choose the optimal time to do the assignments, which curiously seems to be an hour before Sunday midnight, just before the tutorials close.:)

Next session we are motoring on with more of the same in MATH1241, and next year we hope to roll this out for our big first year course (over 2000 students). Exciting, brave new times for teaching.

 

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