UoM 2nd year undergrad studying maths here.

To be honest, I'm not sure one could easily give a "concise" answer to the question of why we study maths, but I'll do my best in a short paragraph.

Mathematics provides the framework for which we can **objectively** understand the world around us. A good question to ask yourself might be: what would we be capable of *without* mathematics? And to be honest, my answer is *probably not much*. This isn't a good answer, but it's the best one I've got. I'm not sure there's anything that doesn't involve mathematics in some form.

There's only one type of person who says that mathematics is easy. And they are those who are too naive, and don't respect the discipline enough to realise their own incompetence. *Mathematics is difficult because it is logical and humans aren't logical*. Anyone who says otherwise just needs their ego shot by being presented something more. I'm not ashamed to say that I used to be this type of person. In fact, that version of me sometimes creeps back, and it takes a lot of maturity to stay disciplined, remain critical about your thinking, and not take things for granted.

My students often ask me why I decided to continue studying maths at university, and I usually answer with *"because I enjoy how difficult mathematics is"*. To which, I usually receive a confused look. Then, I tell them to *"think about it"*.

At this point, you're probably wondering what this has to do with whether teachers should focus more on the 'why'. My answer to this question is **YES**, and I think students will be much better off. I truly believe that high school doesn't foster an environment where both critical and creative thinking in mathematics is allowed. As you said, a lot of it (which is too much of it) is about rote-learning processes without learning the motivations behind it. In saying this though, I'm not sure this will change. There comes a point where you do have to just learn those processes. This is especially true for VCE since investing time into discovering the formation/motivation behind concepts is often more costly than it is useful.

I believe I've been extremely lucky in life - the teachers I had in high school and my parents went to great lengths to ensure I understood and appreciated the bigger picture - the 'why', if you will. It saddens me that there are many people who believe mathematics has been designed to be confusing (or something like that of a beast), and this is why I became a tutor after I graduated - so I could share my passion and try to inspire those who give mathematics a chance.

Last year, one of my students nearing exams said to me *"I think I get it... I think I understand why you love maths"* - something I'm still very proud of.

So, I ask that you give mathematics a chance. Ask the difficult questions, and put in the effort to pursue the 'why', and I **promise** you that the inner beauties of mathematics will be revealed. The above example about my student proves that it is possible to "get it".