800+ Hours of Mathematics tutoring for Years 5-12 and Undergraduate Maths. Third-year student at the University of Melbourne, majoring in Statistics. Received a 96.05 ATAR, Multiple First Class Honors

Learn more about Luke

• 1) When did you develop an interest in your chosen field and in private tutoring?

  I have loved mathematics for as long as I can remember. In primary school, I was drawn to the absoluteness of the subject, the idea that there is a correct answer and a logical way to reach it. My interest in private tutoring came later. By the time I reached Year 11, I was one of the highest‑performing students in both Mathematical Methods and Specialist Mathematics. My mates frequently asked me to explain concepts and work through problems, and I realised I enjoyed the challenge of breaking down ideas and watching the light bulb go on for someone else. That experience led me to start tutoring privately.

• 2) Tell us more about the subject you teach, the topics you like to discuss with students (and possibly those you like a little less).

  I mainly teach Mathematical Methods and Specialist Mathematics, though I’m also comfortable teaching General Mathematics. My favourite topics are almost always algebraic. Mastery of algebra simplifies many other areas of mathematics, because it allows you to model questions as algebraic equations. On the other hand, I am less enthusiastic about General Mathematics. It covers a broad range of topics that can rely on memorisation of techniques rather than deep reasoning. I believe mathematics should be about understanding and critical thought, not rote learning.

• 3) Did you have any role models; a teacher that inspired you?

  During my early high‑school years(year 7 - 9), my grades slipped because I lost interest; the topics felt uninspiring, and I didn’t put in effort. In Year 10, I had a teacher named Ivan Kummerle who completely changed my perspective. He taught mathematics as a form of problem‑solving rather than a list of procedures. His approach reignited my love of the subject and set me on a path that continues today—I’m now studying statistics and pure mathematics at Melbourne University.

• 4) What do you think are the qualities required to be a good tutor?

  Proficiency: One requires a deep understanding of the material they are teaching. It’s fine to make occasional mistakes, but you must be able to answer almost any question about the topic.
  
  Adaptability: An effective tutor adjusts explanations, pacing and examples to fit one's individual needs, learning styles and personalities.
  
  Passion: Passion carries you through the days when tutoring isn’t your top priority and inspires students to engage more deeply, elevating your lessons to the next level.

• 5) Provide a valuable anecdote related to your subject or your days at school.

  At the start of Year 9, I scored 31 % on an indices test(yes I still remember it was in fact that bad)—the lowest grade in the class. I hadn’t been working consistently, and gaps in my understanding had grown from previous years. By the end of Year 10, after deliberately addressing those gaps and putting in steady effort, I scored 97 % on my final exam. That transformation taught me that mathematics rewards consistent effort. Learning the subject is like stacking bricks; each concept builds on the last, and a solid foundation makes the higher levels stable.

• 6) What were the difficulties or challenges you faced or are still facing in your subject?

  My early struggles began because primary‑school maths was too easy; I became bored and stopped trying. Those bad habits carried into Year 7 and created gaps—basic things like adding and subtracting negatives—that I didn’t fully understand. In Year 10, I had to make a concerted effort to patch up those gaps. Ironically, teaching myself and working through difficult problems built the skills that now make me a better tutor. Even today, as a third‑year university student, mathematics remains challenging—especially advanced analysis courses—but my love for the subject keeps me going.

• 7) Do you have a particular passion? Is it teaching in general or an element of the subject or something completely different?

  Mathematics has always been my main passion. The subject’s absoluteness appeals to me: there is usually a concrete answer or way of doing things, even if it’s hard to find. Mathematics also embodies the pursuit of perfection in two senses. First, to perform well on assessments, you need to be precise and disciplined. Second, mathematics as a field strives to model the real world as perfectly as possible. However, Gödel’s incompleteness theorems show that any consistent formal system capable of basic arithmetic cannot prove every true statement within that system, yet mathematicians continue to work on the subject. The art of trying to model reality while knowing absolute perfection is unattainable makes mathematics fascinating to me. Teaching adds another layer of fulfilment. Helping someone understand a concept and sharing my love for the field is a special feeling that goes beyond solving problems myself.

• 8) What makes you a Superprof (besides answering these interview questions)?

  What makes me a good tutor is the combination of strong subject knowledge, personal experience overcoming challenges in mathematics, and a genuine passion for helping students understand the subject. However, what truly shapes my approach is the path I took to get here. Early in high school, I developed gaps in my knowledge because I lost interest and stopped putting in effort. Rebuilding that foundation in Year 10 taught me exactly how misunderstandings form and how to fix them. Because I’ve gone through that process myself, I’m very good at identifying where students are getting stuck and explaining concepts in a way that makes sense to them. This makes me an invaluable asset to the students I teach, as I can often spot what they’re trying to do and correct their line of thinking.