This is how I teach
This month we spoke with Dr Raymond Vozzo from the School of Computer and Mathematical Sciences, Faculty of Sciences, Engineering and Technology. Raymond is a member of the Adelaide Education Academy and the Adelaide College of Reviewers. Here Raymond explains the benefits of active learning as a way of enhancing student engagement.
How would you describe your approach to teaching/your teaching philosophy?
My teaching philosophy is based heavily around bringing active learning techniques to undergraduate classes, increasing student enthusiasm and engagement.
When I was an undergraduate—and when I began teaching at university—the dominant form of instruction in mathematics was certainly quite passive: blackboard and chalk, with the only activity being notetaking. It is probably safe to say that this has been the standard for mathematics education for the last 2000 years!
However, as educators and scientists, we should always be looking for evidence-based approaches to our teaching and I was strongly influenced by some of the papers in science education that showed the benefits of active learning.
Of course, every mathematician knows that maths is not a spectator sport: the only way to learn is by doing! At the beginning of every semester I tell students they should keep a notebook (which, inspired by my daughter's reception teacher, I call their "have-a-go book") and just write down their attempt to every problem. Fear of being wrong is a huge obstruction to getting enough practice. I try to impress upon them how much of what I write down I end up throwing out!
At the same time, I also tell them to take a pad and write "Questions about maths" at the top. Every time they have a question about anything in the course, write it down. Then talk to their friends about it, talk to me about it, and one-by-one cross of all the things they initially did not understand in the course.
What do you like most about teaching in your discipline?
Mathematics has many different facets and therefore many reasons for people to enjoy it (or otherwise). Through one lens, it underpins all of science and engineering (and is therefore indispensable, of course!); through another, it gives us ways of dealing with the enormous amounts of data that the modern world generates every second of every day.
Yet, I feel that the most powerful reason to love mathematics is that it possesses beauty beyond what most people recognise, and beyond almost anything else I can think of.
Students coming into university have a very limited experience of mathematics (in the scheme of things) and sharing and helping students to understand this beauty is the most rewarding part of teaching it.Raymond Vozzo
Following students through the few years they spend with us, from knowing only the rudiments of calculus, to being conversant in the rich ideas present in differential geometry or algebraic topology is really remarkable.
It never fails to surprise me how much they mature over such a short period of time.
How does your teaching help prepare students for their future?
The students in my courses are sometimes mathematics students but more often than not they are from other disciplines, such as science, engineering, teaching, finance, and others that you might not typically associate with mathematics. All these students have their own reasons for studying maths and their own ideas of what they should take away from the course and how they expect to use maths in their future.
From my point of view, I am always aiming to help students to obtain a deep understanding of the material and the analytical problem solving and critical thinking skills to apply this knowledge in the future.
In fact, many mathematics courses do not claim to be immediately relevant to tasks that students are likely to be faced in the future (Real Analysis, I am looking at you) but I always view teaching these courses as a privilege, since it allows me to challenge the students to understand and internalise incredibly complex ideas and reasoning, and these skills are exactly what I am hoping students take with them into their lives in the future.
What is your favourite way to use technology to enhance learning?
I am a strong proponent of active learning and student participation in classes. The problem with many active learning methods is scalability and some of our first year subjects have upwards of 700 enrolments and classes with over 500 students. I like to challenge students with questions in class, which they can submit answers to using their phones or laptops (for example, using Mentimeter). Technology here allows us to have a live channel of feedback and communication with the students that would otherwise be impossible in such a large classroom.
Another example that I am particularly fond of, is the use of web apps to illustrate typically tricky concepts in a clear, visual and interactive way. Geogebra is an online graphing and computational tool with which I have built a collection of these apps focused on various concepts that appear throughout different levels of undergraduate mathematics.