It took being laughed at during class for Daniel Mansfield to set his mind to improve his maths skills. Starting out as a good student, he became an excellent one to prove his teacher wrong. Mansfield went on to achieve a PhD in mathematics and to be named ‘Most Inspiring Lecturer in First Year’.
- Can you please tell us a little bit about yourself?
My name is Dr. Daniel F. Mansfield, and I am a lecturer in the UNSW School of Mathematics and Statistics.
- When did you first become interested in maths?
I was always good at maths, but I didn’t become very good until Year 11 of high school when my teacher laughed at me in front of the class and told me that I couldn’t do advanced mathematics. Spurred on by a burning desire for revenge I became excellent at mathematics, and went on to study mathematics at university.
- What kind of school student were you and can you remember any particularly inspiring teachers?
I was a quiet student, I remember spending my lunchtimes in the school library reading books. I would occasionally go outside and play, but I preferred the books. I had one particularly inspiring teacher, Brian Sheedy, who was both caring and terrifying. We were all afraid of Mr. Sheedy, but he cared deeply for the well-being of his students. He was a great role model for young boys who were beginning the transition into young men.
- What made you decide to pursue a PhD in mathematics?
I completed my university degree and fell into a job writing computer code. After a while I realised that this was never my intended career so I rang up my old professor Tony Dooley and asked if he would like to have me as a PhD student, and he agreed. But it was never my intention to become an academic – I wanted to go back into industry, or somewhere ‘sciency’ like the CSRIO, but UNSW liked my teaching so much that they offered me a position.
- You’ve been voted ‘Most Inspiring Lecturer in First Year’ by your students. How do you keep your students engaged?
By combining my research with my passion for teaching. My research involves ancient Mesopotamian mathematics and students love hearing about how that ancient culture approached mathematics, which is so very different to the way we approach mathematics today. For example, they used base 60 to represent numbers instead of our decimal system, or the way they related the area of a circle to the circumference instead using pi times the radius squared. Its a nice way to refresh the students and keep them interested during a two-hour lecture.
- How did you get involved with secondary school mathematics?
I love teaching, and so it’s natural for me to be involved with secondary school mathematics because there is a lot of demand for teaching in that area, especially with the new syllabus changes coming in 2019/2020.
- Why do you think the subject, Networks, has been introduced to the Mathematics Standard syllabus?
Networks offers students a genuine fresh start in mathematics. As a student, at the start of every year, I can remember the teacher saying “it’s a new year, so you can make a fresh start” and that is not entirely true because if you don’t know fractions then you are not going to be able to understand trigonometric functions, and if you don’t know trig functions then you are not going to be able to do calculus. So if you missed something early on, that can really hold you back in mathematics. But in networks you really do get a fresh start – the only skill that is required is an ability to count. All the definitions and concepts are provided. So it’s a chance for people who may have previously struggled in mathematics to get stuck into a subject and do well.
- What interests you about Networks?
This is a subject about logic and counting, I like it because it is full of reason, algorithms and real things. I think that the Babylonians would really have liked the subject. But I also like it because when I was a student this subject was taught to me by a really brilliant teacher. So for me there is a fair bit of nostalgia too.
- Do you have any tips for those teaching Networks for the first time?
Use it to answer real questions. Personally I like the question about how to cook al-dente pasta using the “Latest Starting Time”, but there are lots of great examples in the book. Also, give it plenty of time – it is different (in a good way) to what the students have seen before, and the syllabus is quite full, which means that there is a lot of new material to be covered.
- Is there anything else you’d like to see in the Mathematics Standard syllabus?
I think the syllabus is pretty full at the moment, and so I’m hesitant to suggest that more should go in. I was really glad to see the maximum flow-minimum cut theorem in the standard syllabus. This is a real theorem that students will appreciate, and I think it is the best of all the additions to the Standard syllabus.
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