Why I like Mathematics and why Students should Discover and Create their Own

I gave a presentation yesterday to some Year 11/Grade 10 students about why I like maths. I tried to steer clear of the applications of mathematics in technology and science and wanted to give a presentation that made sense from their reference frame – hence if I was giving a presentation to younger students, older students or parents I’d probably choose different things to talk about.

Whilst I think that technical skill and learning content is important in everything we do and aids discovery and creativity, I do think that we don’t do enough in school mathematics to expose students to discovering and creating their own stuff. That’s the fundamental aspect of the talk.

At the start of the presentation, I showed two clips (Clip 1 – if you’re stretched for time watch from 1:50 onwards and Clip 2) about the new Karate Kid film and asked them for their opinions on why he became so frustrated and why he didn’t enjoy learning Kung Fu. The answers are obvious:

1) He didn’t have a clue why he was putting a coat up on a peg and couldn’t see how this would help in his life.

2) Continuous drills of doing the same thing over and over again is not Kung Fu – it’s practice!

In the second clip, even though he knew he’d continue to get bullied, he decided that it wasn’t worth the effort and nearly quit. It was only when he was able to apply skills to a scenario and “Do Kung Fu” that he began to understand and was genuinely shocked at what he’d been able to achieve – he obviously had no idea that he was able to do that and just needed Mr.Hang to provide the right opportunity for him to be creative.

After that, I asked them to read the second page from A Mathematician’s Lament by Paul Lockhart. It’s the part where an Art teacher has a nightmare about observing a class that is solely based on rote learning, drills and no creativity. I said that I felt that my own maths Education was quite similar to that and a student said that this is a common perception about how maths is taught in schools.

After that I started talking about a few examples which I felt would illustrate the playful and creative side of mathematics to a class of 15-16 year old students. Unfortunately we only had 45 minutes so we couldn’t explore things together, it was more about my explorations. It’s highly edited due to the 500MB capacity of vimeo. [By the way, I don’t have a clue where I plucked out the 90% statistic towards the end – extra planning was needed here I think!]

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3 Responses to Why I like Mathematics and why Students should Discover and Create their Own

  1. Cristina says:

    Dan, I am on my own journey of preparation to teach Math, eventually, so I would like to thank you for this blog post: it’s blowing me away! It’s giving me so much food for thought- I’m overwhelmed! I showed the movie clips to my family during breakfast this morning and read some of Paul Lockhart’s critique emphatically gesturing and nodding as I read it because he put into words some of my very own thoughts. I also appreciate his dialogue between Salviati and Simplicio, which seems to be referencing Plato’s dialogues. Thanks for posting a link for that text, by the way- I had never read it before. So much of it resonated with my own thoughts on my own Math education and reinforced the idea that I have to create meaningful ways to teach my future Math students. I realize I may sound very idealistic: I understand that education systems claim to give teachers autonomy but tend to not allow that in practice. Nonetheless, thank you for inspiring and demonstrating how teachers can (and should) be leading and encouraging students to conjecture in the Math classroom.
    Best regards to you,
    Cristina

    • Hi Cristina,

      I’m really glad you got something from the post – I also loved reading a Mathematician’s Lament. I found it so interesting that I was in stitches of laughter but at the same time didn’t really want to be laughing at it if you know what I mean. As you mentioned it can be difficult, especially with external assessment pressures, to always promote investigation and discovery but I think the teaching profession needs as many idealistic people as we can get!

      Good luck with your preparation to go into the teaching profession,

      Dan

  2. Phil May says:

    I really enjoyed reading this post and watching the clips from your lesson. What a great way to introduce a class to what mathematics is all about. I’m hoping (if you don’t mind) to use some of these ideas when I start with some of my classes next year… The mathematician’s lament illustrates the idea really well. I’ve only read the short segment, I’ll have to read the rest over the Summer!

    Thanks for putting this on a post!

    Phil

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