Riding the wave: why I started a new Youtube channel

I really admire intentional people. I mean the kinds of people who think about what they want to achieve, set goals to get them on the right path, and then go out to strategically accomplish their objectives. Those people inspire me: they show me what’s possible when you set your mind on something and then pursue it with all your strength and discipline.

But I’m not one of them. At least, I definitely don’t feel like one. Many of the things I would consider my greatest achievements have arisen from things that took place accidentally or out of my control. I feel like a surfer who just happened to be at the right spot at the right time to ride a wave into the shore.

For instance, my Youtube channel – which is what I’m most well known for at the moment – was never intended for wide public consumption. I started shooting and uploading videos for just one boy I taught two years ago. He was very unwell and missed huge amounts of school due to hospital visits, so I put things up on the channel so he could keep up with us when he was away. This is a little embarrassing now, but I initially made the videos public simply because I didn’t want to deal with the headache of adjusting privacy settings on every single thing I uploaded!

Since the videos were freely available, others started asking if they were allowed to watch too. It started with the other students in my class – no one else knew I was doing this, and they only knew because they saw me setting up my recording equipment each lesson. From there, it spread to students in other classes, mainly Extension 2 students who had glossed over the 2-Unit topics in class and wanted an actual explanation of things like Series and Sequences. And before I knew it, students from other schools – and even other countries! – were watching along.

All of this blew me away. As I said, none of it had been intentional. I never set out to have a popular Youtube channel; it just kind of happened by itself. But at the same time, it wasn’t all that surprising. Mathematics is, at its essence, the same everywhere – and in fact for most of school across the world, it’s compulsory – so it wasn’t that unusual that I found a wider audience of students. What surprised me most, though, was when the people who commented and emailed me weren’t students. They were teachers.

Why would teachers be watching my videos? The videos are aimed at students, not educators. But then I realised why it made sense. In mathematics – not to mention a hundred other areas of human endeavour – one of the key ways to learn is by example. Yes, you can explain the concepts or principles as much as you like – but what does it look like when you _use_ those principles? What do those concepts look like in action? This is why observations form such a helpful part of initial (and continued!) teacher education: there’s nothing quite like seeing someone else actually do something to help you wrap your head around how you might do it.

And that’s what my videos were helping to provide. Just one example of how to go about explaining things. Not the only way, nor the best way – just one way. And apparently there’s a need out there for this kind of thing. Then I thought to myself – are there things I would say to or upload for teachers if I had a channel just for them? And I realised the answer was yes.

So, in light of the opportunity that’s standing right there – to offer practical and thought-provoking content to hundreds of pre-service, early career and even experienced mathematics teachers out there, for free – I’m starting Wootube²: videos for anyone and everyone interested in mathematics education. I’d be lying if I said I have a huge amount of time to invest in the channel – this is most definitely a side project – but I already have tons of ideas for material to post that I hope will be helpful in developing teachers and cultivating constructive discussion around teaching and learning mathematics. If you are a maths teacher and you have ideas or requests for things you’d like me to do on the channel, please contact me and let me know. Otherwise, subscribe and stay tuned!

Number Systems

We have spent so many years doing maths with the same set of numbers that we often forget that our way of writing numbers is just one way among many. We use the Arabic numerals in Base 10, but there are many alternatives each with their own story. For two other number systems, research the following:

  1. What is the purpose of this number system, and what are its distinctive features?
  2. Explain where and how this number system is used today.
  3. What are the advantages and disadvantages of this number system?

Put these into your own post and submit them by the end of the lesson!

A response to: the transcience of sharing

Last week, Simon Job – the creator of MathsLinks and its attendant sites – wrote a post called The transcience of sharing.

Simon is a sharer par excellence, not to mention a generally thoughtful and down-to-earth guy. So when he talks (types), I listen (read). Essentially, in his post he is posing this very valid question:

Why is sharing happening on social media (where it is transient) rather than on platforms that are clearly built for it and superior to it in almost every way (e.g. MathsLinks)?

This is a question I’ve thought about too – and it’s bugged me. Over the last few months, these have been the thoughts percolating around my head.

  1. (a) It’s where the community is active, which motivates the poster. In the right space, at the right time, it will gain a responsive audience and that response is a very powerful motivator.
    (b). It’s where people visit, every day and for no particular reason, which is how the viewer sees it in the first place. People come to dedicated sites like MathsLinks when they (i) are after something, (ii) have the presence of mind to look for what someone else has made/found first, and (iii) have the time to commit to browsing for a little while. That happens far less often than people pulling up their social media feed of choice (which seems to happen reflexively once people get to a bus stop or train station these days).
  2. Precisely because it does not aim to preserve, only the trendy and really engaging things bubble up to the top (either through Facebook’s black magic sorting algorithm or Twitter’s more organic system of retweets).
  3. I alluded to this above, but MathsLinks (and other similar repositories like TES Australia and Scootle) has become its own worst enemy by being so good. There are hundreds of objects there – which is awesome, but also means that a new user doesn’t even know what’s there or where to begin. There’s awesome stuff there but (coming back to the time issue that has already been identified) someone needs to commit to searching thoughtfully through it to find what will be useful to them in the present moment. This is an issue with faculty resource files just like it is for MathsLinks.

So what can be done to improve the situation? I have a handful of thoughts, corresponding to the points above.

  1. Clearly, MathsLinks is awesome as it is. We just need to connect it with the community more effectively. I feel like this is a market problem – it’s a great product, in a quiet spot. Stick it in the middle of George Street and it’ll go nuts because people will be exposed to it more frequently and the conversation about how good it actually is will spread from there. How practically to do that in our context is another question entirely, though.
  2. Maybe there needs to be a dedicated team (and by team, I mean more than just Simon) of people dedicated to capturing those cool posts when they come up on social media and then preserving them. We don’t want to discourage the spontaneous sharing and ensuing discussion; we want to leverage it and keep it somewhere that it can be found for future reference.
  3. Perhaps we need to do something like a “weekly featured resource”? I have considered doing something like that in my department with “my best lesson this week” as a regular feature of faculty meetings. It would just help people become aware of the riches that are hidden away there, rather than letting them gather digital dust in the cellar of the internet.

Just some food for thought.

Practical tips for maths teachers: the growth mindset (TER Podcast follow-up #2)

Last time I wrote some thoughts I had after completing my interview for the TER Podcast about maths education. You can go back and read that if you’re interested in thinking through some of the big-picture issues surrounding the problematic state of maths education in Australia. Following on from that post, I want to share some more practical pointers that I’ve observed to be helpful in a variety of different classes and contexts. Each one is its own idea, so I’m going to devote a few posts to unpacking them in a bit of detail.

What are some of the effective approaches you’ve seen people use? Answer number one: adopting a growth mindset.

First things first. It’s vital that teachers regard their students with a real growth mindset. This is a phrase familiar to anyone who has read the work of psychology professor Carol Dweck, who gives the best summary of what the idea is about:

In a fixed mindset students believe their basic abilities, their intelligence, their talents, are just fixed traits. They have a certain amount and that’s that, and then their goal becomes to look smart all the time and never look dumb. In a growth mindset students understand that their talents and abilities can be developed through effort, good teaching and persistence. They don’t necessarily think everyone’s the same or anyone can be Einstein, but they believe everyone can get smarter if they work at it.

You can see why this is such a big deal to maths education. Maths, perhaps more than any other subject in school, is dominated by a fixed mindset. There are people who are good at maths and then there are the rest of us. In fact, the phrase, “I’m no good at maths” has entered into our cultural vernacular and sadly become an acceptable response to anything encountered in everyday life that involves numbers or numerical thought.

The problem here is that this kind of thinking becomes a sort of self-fulfilling prophecy. When we think of ourselves as unable to do mathematics, we don’t bother trying – and hence deprive ourselves of the very experience that will allow us to develop mathematical skill (namely, struggling to grasp numerical concepts and master the tools necessary to solve problems that require their application).

It doesn’t take too much imagination to realise that our self-concept when it comes to our mathematical ability isn’t just self-generated. It is formed, in large part, by those we trust to nurture and develop us as mathematicians – our maths teachers. What kind of an effect do we as maths teachers expect to have if we consistently communicate that “This is too hard for you, and you will never be able to succeed at it no matter how hard you try”?

And sadly, whether it’s through the bevy of tests that end in failure, or the advice to children to take the mathematics course that will maximise their ATAR rather than challenge and enrich them, or even just the little interactions with students every lesson that erode their self-confidence – this is the message that students often pick up from us, their maths teachers. Some students survive this process, but many don’t. They aren’t just disempowered – they’re paralysed. No wonder “maths anxiety” is a thing (who ever heard of any other subject that has its own psychological malady associated with it?). What a tragedy.

It’s obvious that people can take the growth mindset too far. One of the most enduring characteristics of truth in all spheres is that it will always be abused by someone with the wrong idea about how it should be interpreted, and this is no exception. If you’re curious about this and want to know how to avoid that particular trap, you can watch a vlog I recorded about it a few months ago.

But that isn’t most of us. For most of us, the growth mindset is a breath of fresh air. Yes, anyone can master maths! Sure, it takes some more time than others – but who is surprised by that given that every human being is unique and brings a new perspective and set of skills to the table? Rather than view those differences as a cage locking us into a certain level of achievement, let’s embrace them and see how they can be brought to bear on the pursuit of mathematical understanding that we should all be a part of.

TER Podcast follow-up: the big issues

2014 has been a year full of firsts for me. First year teaching in a comprehensive school (student teacher placements notwithstanding). First year as a head teacher (which has produced a whole lot of firsts of its own). First time recognised in public because of the videos I make. And as I type this, I’m at my first MANSW Annual Conference (arguably the biggest gathering of maths teachers in the state all year), my head spinning from considering new ideas and meeting new people (or in some cases, seeing people face-to-face who I’ve been interacting with online for a long time now).

Another first happened last month, when I participated in a phone interview with Corinne Campbell (@corisel) for the TER Podcast. The topic was Is Maths Education Broken?, and I was there to provide a sort of foil to an interview that Corinne had with the luminary Conrad Wolfram (of Wolfram Alpha fame). You can listen to the entire episode (and if you’re in education and haven’t subscribed to the podcast, you really ought to). It was an interesting experience, not least because it was so unusual to actually interact with a voice that I was so used to just listening to passively through a podcast.

I’m the kind of person who thinks of the perfect witty comeback or joke ten minutes after the conversation is over. So even though I had prepared my own thoughts and notes before the interview and tried my best to cover everything that would be important, I found myself in the shower that evening thinking, “Oh, _this_ would have been the perfect answer to that question!” and “How on earth did I forget to say _that_?” So here are a few of the things that I should have said, but forgot to. In this post I’m going to talk about the large-scale issues that are related to the “STEM crisis” Australia is experiencing, and in a follow-up post I’ll talk about some of the smaller practical strategies that can be employed in the classroom to help our students from day to day.

How do we improve STEM skills in Australian schools?
There’s no simple solution to this one – so you can know with a fair degree of certainty that if someone tells you they have a straightforward way to fix this problem, they’re probably just oversimplifying the situation. The so-called STEM crisis is a perfect storm of different factors and so there won’t be a single actionable item to fix things.

But there are definitely many identifiable aspects of the challenge. For instance, the syllabus is by-and-large divorced from real mathematical practice (both in everyday life and in vocational contexts). Here’s a great little quote from Optimising the Future with Mathematics (via The Conversation):

Current mathematics education, in schools and universities, is satisfied with programming students to carry out certain mathematical processes, and assessment rewards students who can calculate everything even if they understand nothing.

So what can we work on at the ground level? Firstly, it’s vital to recognise the enormous continuity of learning in maths. All key learning areas exhibit a degree of intra-dependence within their skills and knowledge, but it seems to be especially noticeable in maths where a single “weak link” in the chain can be disastrous! Once student confidence is lost, it is hard (not impossible, but significantly challenging) to rebuild it.

Secondly, top-down (syllabus level) change is required, but we can’t wait for that to happen. Policy is always hard and slow to change (it must be in a democratic and bureaucratic environment), but we can push the envelope of our daily practices right now and see what works. We can undertake action research projects into what is effective and helpful. Another insightful quote:

We need mathematics “to be taught more like it is done” by those engaged in it, in both the innovations economy and research. This is a cultural change that involves the discipline itself, one that must be mainstreamed into school and university systems.

These cultural changes almost never come as mandates from above – they are typically born out of grassroots movements from below that are then recognised and ratified by authorities.

Beauty & Mathematics continued (25 July 2014)

Hello class! Apologies that I can’t be there with you today – but you have some very interesting material to cover today nonetheless.

VIDEO 1: Donald Duck in Mathmagic Land

This video is quite long (about 27 minutes) and covers a wide range of topics. As you watch it, take notes on the following:

  • What mathematical ideas are presented?
  • Select two that interest you in particular and research them further. How do they relate to the mathematics you already know? Where else in the world do these concepts reappear?

You may take notes on your laptop, but you will definitely need to have a pen and paper available anyway as most of the concepts addressed in the video are visual and you will need to illustrate them in some way. Now that you know what you’re looking for, here’s the video:

After the video is finished, take 15 minutes to look over the notes you have taken and reflect on them as usual. (You should use the questions I wrote about in this post to guide your thoughts.)

VIDEO 2: TedXEast – Matthew Cross

The next video you watch is a TED talk. Again, take some brief notes (but be aware that the presenter goes through the material very quickly). Similar to before, select the two most surprising examples that he talks about and briefly describe why you think these are so unusual. Here’s the video:

VIDEO 3: How to measure beauty

Here’s the last video you’ll be watching. As you watch it, you simply need to answer this question: “Is human beauty just about numbers? Why or why not?” Answer in some detail and try to justify your response with evidence and examples.

As usual, please compose your thoughts in a post and email it to me. Some of you have kept on top of each lesson’s assigned tasks, but others of you are slipping behind – use this opportunity to catch up! (And don’t forget to carefully follow the instructions I gave you in the very first lesson.)

See you again next week!

What is “Exploring Mathematics”?

Exploring Mathematics is an elective semester course offered to Stage 5 (Year 9-10) students at Cherrybrook Technology High School.

To understand what this course is, you must first understand what it is not:

  • This course is not about acceleration (learning content from years 11-12 in advance so that you will be more familiar with it when you encounter it in the future). In fact, topics in the Stage 6 mathematics subjects have been intentionally avoided so that they can be given their proper introduction in the Preliminary and HSC courses.
  • This course is not like your regular mathematics class in its classroom activities or its assessments. In fact, there is a very conscious emphasis on branches of mathematics that are not understood through repetitive exercises, nor assessed in traditional examination formats.

By contrast, the goals of this course are:

Continue reading “What is “Exploring Mathematics”?”

Extra teaching thought: will the real basic transformation please stand up?

I’m a pretty slow thinker. In an argument, I’m that guy who comes up with the perfectly witty comeback… about two hours after the conversation is over. This doesn’t just happen to me in social settings – it also happens to me in the classroom! Often I’ll teach through a skill or concept only to realise, after the lesson is over, that there was something else I should have said, or some other analogy that would have been immensely helpful, which would have added valuable insight or made things clearer.

Something like that happened when I taught this lesson on congruence transformations:

In geometry, a congruence transformation is – roughly speaking – a way that we can change (“transform”) a figure in such a way that it is still the same shape and size (“congruent”). There are three main kinds of transformation that we cover in year 7: translation (sliding the shape to a different position), reflection (flipping a shape over) and rotation (spinning the shape around).

After introducing the idea of transformations and how they work, we start to think about “composite transformations” – what happens when you combine more than one transformation and consider the total effect from original to final image. An interesting fact emerges: that not all transformations are created equal. In fact, one of the transformations is more simple and basic than the others. One transformation can be used to create each of the other two. Which do you think it is?

It turns out that the most basic transformation is reflection. You can make translation and rotation out of a series of reflections, but not the other way around; though it’s counter-intuitive, reflection is the most basic kind of geometric transformation. Perhaps that’s why reflectional symmetry is so deeply ingrained into our natural sense of beauty.