IntroductionAll my courses, from first year to graduate level, make extensive use of Mathematica, which has broad application to physics, engineering, mathematics, mathematical modelling, and simulation, and for which UWA has a site license. This general and very powerful software enhances existing mathematical skills, teaches new skills, increases confidence, and inspires students to learn more through tackling real-world computational problems. In my courses:
- At first year, Mathematica is primarily used as an interactive presentation tool through the use of Computable Document Format (CDF) documents
- At second year, students learn the basics of Mathematica and use it to solve non-trivial problems in Applied Mathematics and Electromagnetism
- By third year, students now have considerable expertise in the use of Mathematica and start applying it to research-level problems
Approaches to learning and teaching that influence, motivate and inspire students to learnQ: What innovative methods do you use in your teaching to engage students?
A: I use tightly integrated and immersive use of the best technology for teaching and learning in science and engineering. Many courses integrate current research problems; my courses analyse and investigate research problems in a way that is immediately accessible to students, evidenced by the following student quotes:
The effective use of Mathematica in assisting teaching. The graphs, pictures, formulas, etc. were highly accessible in this form.
He uses Mathematica which allows him to visualise abstract concepts. Powerpoint should be banned in physics for all topics because Mathematica is so much more effective and functional.
Really like the use of the software in the lectures, Mathematica. Explain concepts that reach ahead and makes one think.
Paul is very enthusiastic and knowledgeable! He has a great love for his subject and this was quite infectious. The use of Mathematica was excellent!”Q: How do you develop students' critical thinking skills?
A: It is impossible to solve Physics problems without excellent critical thinking skills. Most students already arrive in first year with well-developed skills. My goal is to leverage these existing skills, and to further develop them. The problems I ask are non-trivial; by combining numerical, symbolic (analytic), and graphical approaches, the students find that they can tackle them and, at the same time, enhance their critical thinking skills, as evidenced by the following student quotes:
Paul’s lectures are very inspiring. I have always been enlightened by his way of logic and thinking.
I found he really explains key concepts well, and makes lectures interesting, I liked how he related what we were learning to real life examples.
Q: How do you motivate students through your teaching?
A: Best answered by student quotes:
You often gave indications of how deep concepts have profound applications generally (and also for more advanced studies) while providing enough information regarding where to hunt down more information.
Paul Abbott is an enthusiastic lecturer whose passion for the subject encourages all students to commit their fullest. His in-depth knowledge of the subject material allows him to answer all student queries.
Often relates concepts we’re learning to current research in other areas of physics; helps [us] see the use of seemingly strange concepts.
Paul Abbott goes above and beyond what is required for a lecturer. Students respond positively to his enthusiasm.
I really enjoy his lectures because he always tells us why. I constantly ask why we want to know, or what application various physics concepts have, but Paul is always telling us and it is very refreshing to learn from him.
He explains concepts in a really interesting and easy to understand manner. I think he has been the best physics lecturer yet, as he keeps my interest, and I come out of the lecture understanding what has been said.
Q: Is there any other information related to this heading that you would like to supply in support of your application?
One more student quote:
The methodical way in which we worked through the material and linked it all to the aspects e.g. linking resonance in electrical and mechanical systems. Mathematica was a good tool and all of the demonstrations were helpful. I like the way we worked through the material as it was on the screen, rather than discussing material unrelated to the screen.Of course, one cannot always be successful in motivating students to enjoy the topic at hand:
He was a brilliant teacher. I’m just not interested in the topic
Development of curricula and resources that reflect a command of the fieldOver the last 10 years, I have been responsible for developing novel and contemporary curriculum materials for the following courses, or parts of courses, all using Mathematica:
- PHYS1001 (Electricity)
- PHYS1002 (Magnetism and Resonance)
- PHYS2001 (Electromagnetism)
- CITS2401 (CS Course on Matlab and Excel, including 6 lectures on Mathematica)
- PHYS3011 (Computational laboratory projects)
- MATH2200 (level 2 Applied Mathematics course)
Q: What innovative teaching resources have you developed?
A: My lecture notes for PHYS1001, PHYS1002, MATH2200 and PHYS2001, and the lab classes for PHYS3011 have all been developed (or updated) in the last 3 years, e.g.,
- A PHYS2001 assignment solution
- MATH2200 lecture notes, assignment solution, and student exam solution
- PHYS3011 assignments
Q: Have you undertaken formal evaluation of your teaching innovations?
A: My teaching innovations have been recognised internationally by an Undergraduate Computational Science Award (UGCSA) from the Undergraduate Computational Engineering and Science (UCES) Project (Ames Laboratory, Ames, Iowa, USA).
Approaches to assessment and feedback that foster independent learning
Q: How do you foster student's independence in learning?
A: My goal is to make each student capable of solving real-world and non-trivial problems. In the two hour computational laboratory sessions, students get immediate feedback from Mathematica, and are encouraged to do a wide range of self-consistency checks; numerically, symbolically, and graphically.
Independent learning is fostered by research-based questions using a research tool, which is widely used by scientists. See the student exam solution to the MATH2200 exam.
Q: How do you outline the objectives and anticipated student learning outcomes of the unit and expectations of students?
A: The objectives and required learning outcomes of my units are embedded in the interactive lecture notes, and emphasised during the associated laboratory sessions. Student comments show that the objectives and outcomes are clear to students:
Everything was well explained. Lecture notes were very helpful. Assignments were helpful for better understanding the material. Lecturer was enthusiastic.
He explains concepts in chronological order so that learning one concept helps to understand the next concept.
Explains important concepts well. Does not assume knowledge. Uses demonstrations as an aid for teaching.
Great slides and lecture notes, very easy to follow and you actually understand and learn as you go, not always the case for other topics. Good presenter–explains well, interesting, easy to understand and follow.Q: How do you provide feedback to students?
A: Mathematica encourages the addition of comments—including interactive comments—on student solutions. During lab sessions I work with students, commenting on their progress, questioning their understanding, and giving them hints to get them back on track if they are struggling—but never just giving the answer. Full worked interactive solutions are also provided.
Scholarly activities and innovations that have influenced and enhanced learning and teachingQ: Have you published in respect to your teaching or presented at science education conferences?
A: At the 2010 Australian Conference on Science and Mathematics Education: Creating ACTIVE Minds in our Science and Mathematics students, I presented a talk entitled Reflections on Teaching Computational Physics and Applied Mathematics.
I gave an invited plenary speech at the 2013 Asian Technology Conference in Mathematics: Addressing Challenges of New Technology in Mathematics Instruction, held at the Korea National University of Education, on Sums, Products, and the Zeta Function: Visualizing a $1,000,000 Problem.