Teaching

The breadth of my mathematical research has made me familiar with most concepts and techniques taught in first and second year mathematics and statistics, including areas such as linear algebra, multivariable calculus, discrete mathematics and elementary statistics. My graduate and postgraduate qualifications and my experience in computer science and information technology also help me to teach subjects that include computer algebra, programming, algorithms and data structures. I have also had exposure to application areas including commerce, physical sciences, biological sciences and earth sciences. This helps me to answer the question “When would I ever use this?”

Mathematics is a subject which is best learnt through doing, but if a student has had inadequate training or negative experiences in high school, it is difficult to develop the courage, patience and perseverance needed to approach learning mathematics at first year university level. The small group workshop approach is part of the solution, but more needs to be done to encourage persistence in the face of confusion and failure during solo work. Perhaps Mastery Learning in conjunction with well-designed computer-based formative assessment can be used to address this difficulty. This is similar to the Maple-based computer laboratories run by Rod James, John Steele and others at UNSW while I was a laboratory tutor there in 2002-2005. The recent introduction of Digital Technology in the Australian Curriculum presents an opportunity for the integrated teaching and learning of STEM, including mathematics, statistics and computing, at high school level, that Australia has yet to adequately take up.

My approach to third year and masters level teaching is to challenge the students to think during lectures. I aim not to merely to put methods and results onto a blackboard, but to ask questions, to assert that there may be more than one legitimate method to approach a problem, to provoke students into making an effort to understand the material at a deeper level. This philosophy guides my approach to assessment, which probes for a flexible understanding of the material rather than just a repetition of methods given in lectures.

Through my participation in the research groups of Richard Brent and Markus Hegland at ANU I have some exposure to Honours, Masters and PhD supervision. In particular, I helped to supervise the PhD project of Yuan Fang (2011). I also graded Advanced Studies Course reports (from students in the ANU PhB program) and Honours theses.

My most formative university teaching experience was during the years 2009 to 2011 at the Australian National University, where I was course convenor of the third year MATH3512 / masters level MATH6112 course on numerical linear algebra. The course included a substantial programming component, which was originally taught using Scilab, and then ported to Python for 2011. For 2009 and 2010, the course also included a substantial component in optimization methods. In 2011, MATH6112 included a project component. 

During 2010-2012 I also studied for the Graduate Certificate in Higher Education (GCHE), where I examined my own teaching and strove to better understand my students' learning, including studying the effect of dropping the optimization component of MATH3512 / MATH6112 from the curriculum. 

In 2010 and 2011, I also attended the ALTC Workshops on Effective Learning, Effective Teaching in the Quantitative Disciplines. The GCHE and the ALTC workshops led me to study the literature on higher education in mathematics, especially linear algebra.

During 2012-2014 I was in a research-only position, but still conducted small reading courses and seminars, as well as assisting Conrad Burden in the teaching of Bioinformatics.

During 2014 I applied for Fellowship of the Higher Education Academy, and became an Associate Fellow in 2015. 

During 2015 I was a casual academic at the University of Newcastle, Australia. In first semester, my teaching roles consisted of course coordination of MATH3510 Combinatorics and Graph Theory, and tutoring for MATH1001 Preparatory Studies in Mathematics. In second semester, with Thomas Kalinowski, I was one of two lecturers for the first year subject MATH1510 Discrete Mathematics, and also was a demonstrator for this subject. During second semester of 2015, I also undertook and was awarded the Fundamentals of University Teaching Certificate.

In 2015, as the casual course coordinator of the MATH3510 course on combinatorics and graph theory at the University of Newcastle, I used the course outline, notes and assessment tasks that were used in 2014 and previously, and adapted them as I went, to correct errors and to more closely fit my approach to the teaching and learning of higher-level university mathematics courses.

As one of the tutors for MATH1001, I supervised group work on whiteboards, where the emphasis was on learning and repeating procedures to solve specific problems, for example, area and volume, speed, time and distance calculations. My role in MATH1001 gave me a better understanding of the effect that the current level of under-preparation for mathematics in high school is having on the transition to first year university, especially on students enrolled in non-STEM programs 

In second semester 2015, the Department of Mathematics and Physics at the University of Newcastle trialled the use of whiteboard workshops, with demonstrators rather than tutors, led by Judy-anne Osborn. As a demonstrator for the first year subject MATH1510 Discrete Mathematics, I supervised group work on whiteboards, where this time the aim was to apply the procedures covered in the lectures to solve combinatorial problems, and the methods were meant to encourage full participation and engagement of each member of each group. These workshops were similar to those described by Shearman, Rylands and Coady.

As a lecturer for MATH1510 I introduced the students to set theory, logic, and some topics in combinatorics. These were large format lectures, in a service-oriented first year course, which covered a fair amount of material as prescribed by the curriculum, the textbook, and the previous year’s slides. I aimed to be as engaging as I could, and to model mathematical thinking, providing extra illustrations and explanations of concepts and methods, and asking questions.

While course coordinator and lecturer for the courses that I taught at ANU and at the University of Newcastle, I used Moodle (Wattle) and Blackboard for course administration, organization and access to course notes, and organization of assessment items. I also used audio recordings at ANU and the University of Newcastle, as well as video recordings, especially for the benefit of students at the Ourimbah campus.

Teaching history