This is how I teach
This month we spoke to Dr Stuart Johnson, Lecturer with the School of Mathematical Sciences and recent recipient of a Tony McMurtrie Practitioner Award for Academic Integrity (Special Commendation), for his work on reducing contract cheating in mathematical assessments. Stuart, an Affiliate member of the Adelaide Education Academy, speaks about the importance of active learning and how he has harnessed technology to engage and support his students.
What do you like most about teaching in your discipline?
Maths is a discipline that students have already seen a lot at school, but there is so much more to it and it's great to be able to open up a much wider world of maths for the students to experience. Many of the students I teach aren't here to study maths specifically, but rather need it to support their studies in other areas, so the challenge is to show why it is interesting and relevant to them.
I also really like giving context to the history of the discipline in my teaching. For example, I enjoy teaching the proof by Euclid that there are infinitely many primes, and pointing out that this was done over two thousand years ago. The result will still be true in another two thousand years, and forever, because we can prove it.
There probably aren't too many things that can be taught in essentially the same way now, as two thousand years ago! This example is not only of historical interest. It is at the very foundation of the theory behind many modern applications - such as cryptography.
How would you describe your approach to teaching/your teaching philosophy?
Learning maths is like learning anything else in that you need to actually do it to learn it, so active learning is essential. I've asked students how many YouTube videos on juggling you need to watch to be able to juggle well. The answer is, obviously, that you can't learn only by watching videos, but sometimes this seems less obvious to students when it comes to learning maths.
You need not only to try things, but you need space to make mistakes. I make this space through interactive quizzes in class, encouraging students to have a go and making sure that they understand it is OK to get it wrong, and also through tutorials centred on students working through problems in groups. When something is done incorrectly it is always an excellent learning opportunity - and I make sure that I react in a way that shows this.
I point out to students that I didn't get everything right the first time, and neither did anyone else. This is important, as they can feel that some people just instantly "get" maths and others don't, which is not a helpful perspective.
What is your favourite way to use technology to enhance learning?
Mathematics is naturally amenable to computer aided assessment, and it is something that I have worked on a lot. Its origins, many years ago, may have been about saving on the amount of marking to be done, but the first year maths team (Adrian Koerber, Raymond Vozzo and myself) have worked to utilise the pedagogical benefits of this approach. In particular, an aspect which is popular with students is to use computer assessment to be able to give instantaneous feedback to allow them to practice and master certain skills. Also it can be used to create questions which are easily marked by computer, but not by a human, which opens up new types of questions which may not have been asked before, and which can be excellent for testing deeper understanding. We have developed many novel techniques for creating questions which can be heavily randomised and reused, and I enjoy the challenge of designing and coding new types of questions that might not always be the traditional way that we test things.
How does you teaching help prepare students for their future?
The course material gives students the basic mathematical tools they'll need for a variety of applications in a wide range of fields, but the value to them should go well beyond that.
I want them to develop highly transferrable skills in thinking logically, solving problems, handling abstract concepts, practical aspects of using technology and being able to clearly communicate technical ideas using appropriate language. Whilst some of the theory I teach is very old with interesting historical contexts, the skills developed in learning and working with this theory prepares students to handle the new technologies that will develop throughout their future working lives.