Reflection is a key to learning (by @misterwootube)

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When trying to learn something new, it’s really important to think about what you’re thinking. The fancy name for this is metacognition. The way to do it is to ask yourself questions like:

What new concepts/skills did I learn?

How does this relate to things I already know?What old ideas have been challenged?

Was anything surprising?

Was anything particularly difficult to understand?

This is just a starting point. I’m really looking forward to reading and engaging with your thoughts!

#exploremaths

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”?”

Semester 2 returns with a bang!

After a pretty intense Term 2, I’ve hit the ground running in Term 3. Highlights include: preparing a new Year 8 program aligned to the NSW Syllabus for the Australian Curriculum; motivating my year 12s to make the most of their final term in school with a stirring story from the 2000 Sydney Olympics; and having a cracker of an introductory lesson to the Stage 5 elective maths course that I’ve started teaching this semester!

A brief note about that last point: the elective course (open to year 9-10 students) is called Exploring Mathematics, and it’s an incredibly exciting opportunity for me. It provides the chance to dig into all kinds of maths that have to be passed over in the BOS mathematics courses (due to lack of time, difficulty of assessment, and a variety of other factors). I intend for it to feature fairly prominently on this site; Í’ll write more details about this in the future as everything is still is in a state of flux for now.

What’s on the cards for your Term 3?

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.

 

I survived a semester!

As I accurately predicted, I’ve had less time to write than I wanted to. That doesn’t say very much, though – ever since I was about 16, I don’t think I’ve ever had enough time to do all the things I was interested in doing. That says more about how many things I’m interested in doing than it does about how much time I “have” (the latter of which is the same as everyone else in the universe not travelling at relativistic speeds – namely 24 hours each day). But that’s okay – I’ve still gained a lot from having this blog and I anticipate to continue to do so.

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The point of me writing this is not to lament my inability to post more frequently, but simply to stop in on the last day of Term 2 and say: I’m still alive after my first six months as a head teacher! I know that probably doesn’t sound like much to many of you reading this (“What, it isn’t even a whole year yet and he’s already celebrating?”), but I honestly feel like I’ve climbed a mountain since the year began. I am tired but still love what I’m doing, and I count that to be a small victory worth smiling about.

I feel this is an appropriate time to stop and say thanks to many of the people who’ve encouraged me in the last few weeks and months. I’ve been through my fair share of moments filled with self-doubt, and many kind people have done the equivalent of patting me on the back and saying, “Keep going, mate – you’re doing alright.” This is particularly meaningful from those of you who have already taken the executive/leadership step up that I have just made – either in recent times or a long while ago – and therefore have a deep and personal understanding of the specific struggles and tensions that I’m now encountering for the first time.

There are too many people to name individually, but I’m thinking of people like @corisel, @dickfaber, @glenn_langford, @sailpip, @jennyluca and many others, whose positive words to me carry a tremendous amount of weight because I know they come from years of hard-earned experience. To everyone who’s nudged me along, thank you! (As a side note to this side note, this reminds me of how we should all recognise that even our small words here and there can have a surprisingly disproportionate effect on those around us!)

Happy holidays, everyone!

Inaugural Alumni Conference

I have fond memories of university. It was a time of growth and change, where I face immense personal and intellectual challenges that have proved to be definitive in my life. If people who know me well were asked to describe me in objective terms, I am confident that the major aspects of my character and personality (both positive and negative) can be traced back to things that happened to me during my time at uni.

It was such a formative stage for me, which is why when I received the invite from Judy Anderson (@JudyAnderson6) to attend and participate in the inaugural Alumni Conference for graduates of the Secondary Maths education degree at Sydney University, I was genuinely delighted by the prospect of returning to my alma mater and reliving some old times.

SUSMAC2014B

It was during the school holidays, which made me pause before I decided to commit to attending, but eventually I decided it would be a worthwhile thing to go to – and I don’t regret it. I haven’t felt so energised and excited by a gathering of people in quite a long time, and it would have been hard for anyone to walk away from the door with a renewed passion for mathematics education.

I wish I had time to write a bit more about my experiences on the day – perhaps once the school term settles down, I might (though it very likely will not) – but for now I just want to say that I was able to video every presentation during the day and I’ve made them all available on a single easy-to-browse page: SUSMAC 2014. Enjoy and share with any maths teachers you know!

168 hours & 857 tweets later…

What a week! It was a fantastic privilege to host EduTweetOz last week – I gained so much (in terms of conversations and connections), and can only hope that others got to benefit by coming along for the ride. Many thanks to the admins of the account – Corinne, Michelle, Donelle and Liz – for initiating such a fantastic community-building project and working tirelessly behind the scenes to make sure it’s valuable for everyone involved.

One of the things I loved most about my experience is that it confirmed something for me that I was hoping to be true but that I wasn’t sure of yet: namely, that there is a wonderful world of educators out there who I can connect touch with and form a mutually symbiotic relationship. There are many kinds of ecological relationships between species in the animal kingdom, the most common being predator/prey, competition and parasite/host. In each of these one group’s gain necessarily means the other’s loss. But in a mutually symbiotic relationship, everyone wins.

That’s what I was hoping to tap into when I first joined Twitter. My first tweet proves it. But it took me many months before I got in touch with anyone who could actually show me that this could become a reality. And seeing others get involved with Edutweetoz showed me it was possible – and outlined a path that I myself wanted to take and contribute to as well.

In the lead-up to my 7 days in the chair, I provided answers to some interview questions that each of the hosts gets given – and thought it would be nice if those were recorded here for posterity!

The content below was originally posted on the EduTweetOz blog.

Please tell us a little about your background in education. Why did you decide to become involved in education? What are some of the roles you’ve had and what does your current role involve?

During high school, I found that I loved to explain things to my friends – I got a real kick out of seeing the light bulbs come on inside someone’s mind, so the idea of being a teacher and doing that all day every day seemed attractive to me. In addition, I was deeply drawn to the profession due to the massive personal impact that teachers can have on students.

I trained to teach mathematics and computing studies. Immediately out of university I got a position at Fort Street High School teaching Software Design & Development (among other ICT courses), till I landed a job at James Ruse Agricultural High School where I was given the opportunity to use both of my teaching methods. One of my highlights at James Ruse was overseeing many of the school’s technological resources and migrating the entire staff to an information ecosystem built off of Google Apps for Education (GAFE). My work in that area contributed to paving the way for the DEC to adopt GAFE as one of their officially endorsed software tools, with the goal of moving toward a state-wide implementation. That’s an exciting project that’s still very much in motion.

This year I just took up the role of Head Teacher Mathematics at Cherrybrook Technology High School.

Who or what keeps you inspired and motivated in your work?

There are a whole host of things that inspire me every day – from the elegant simplicity and profound insights of the subject matter I teach, to the piercing insight and unwavering dedication of my fellow teachers – but I think the main thing that keeps me motivated is the thing that got me into the profession in the first place. I constantly encounter powerful reminders of the enormous positive influence that teachers can have on students – it’s an unmatched opportunity, and it’s endlessly novel for me to see it happen in diverse ways for each unique student.

What do you see as some of the biggest rewards and challenges for people working in education today?

Having just become an executive member of staff, I’ve been exposed afresh to the reality of just how much people working in education are expected to devote their time to things that are quite peripheral to actual teaching and learning. To be sure, the vast majority of administrative tasks and extra responsibilities do make their own valuable contribution to the school environment and hence to the educational experience as a whole, but I still feel myself and the staff I lead being tugged away from focusing on that most wonderful privilege: engaging students in the classroom. I think that regaining and maintaining that focus is one of the primary challenges for teachers today.

As for rewards, sorry to keep banging on the same drum, but I feel that the most precious reward is seeing students succeed in life. For some students, it means a university scholarship. For others, it means getting their ROSA and starting that apprenticeship they’ve been eyeing for ages. For some, it means finally understanding the connection between the volume of a sphere and the process of integration. For others still, it means being able to sit with a group of peers at lunchtime and being able to have a conversation that isn’t awkward. Whatever it might be, seeing students overcome their fears or self-doubt and achieving something they had never dreamed of reaching – being able to participate in that moment is priceless.

If you had the ability to make changes to the education system in Australia, what would you do?

I don’t know how I would practically achieve this – if I did, I would already be doing it – but I somehow would want to work toward an education system that placed value on things even when they cannot be directly assessed or quantified. For instance, I’m convinced that whole generations have a bad attitude toward mathematics because the mathematics taught in schools is heavily skewed toward mastering a set of processes that can be applied to a relatively repetitive set of problems to produce desired answers. The reality, though, is that actual mathematics involves play, abstraction, imagination, exploration and the formation of unanswered questions – but none of these are easy to assess, so they fall by the wayside in the syllabus documents.

I’m sure mathematics isn’t the only KLA that suffers from this problem. I wish I could change this situation but I don’t know how yet!

What role do you see EduTweetOz playing on the education scene in Australia and what are your hopes for the account this week?

EduTweetOz, like the internet in general, is a disruptive technology. It takes something that ordinarily takes place in the “real world” (namely, professional relationships and dialogue) and disrupts the ordinary supply chain by providing a way to get it without any of the extraneous elements (e.g. a physical location, food, pre-existing networks of relationships). It lets people dive in and connect with people they might never cross paths with otherwise, and provides them with avenues for learning that they might never have encountered even if they availed themselves of all the real world opportunities that were available to them (that’s certainly been my experience!).

So I view EduTweetOz as accelerating the formation of those kinds of wonderful symbiotic professional relationships that you might only make one or two of during a conference for your professional association of choice – without all the stress and fuss of actually physically attending such a conference!

My hopes are pretty simple: (1) that together we’ll raise some interesting and valuable conversation, (2) that we’ll all be exposed to people and ideas in the educational world that we wouldn’t normally see, and (3) that I won’t drown in tweets!! (I can see the headline now: “Sydney teacher dies in horrific self-inflicted Twitter accident.”)

Why A Head Teacher? The Forgettable Generation

This is the third post in a series; if you haven’t yet, read the earlier posts:

Something that everyone must struggle with to varying degrees is working out how much of their identity and character is inherited from the surrounding culture. The reason it’s so important to struggle with this is because I’m convinced that every culture gets things wrong, but when you are in the middle of the culture they don’t look wrong – so you can be unknowingly carried along with what everyone else is doing, even when it’s a really bad thing to do. Of course, it doesn’t usually feel like you are being carried along – it usually feels like you are following the desires that you yourself want as an individual – but that’s because your culture is at least partly responsible for planting many of those desires in you, so of course they feel like they are yours.

This is evident to anyone who looks at history (or even other cultures in the world today) and wonders how people in other cultures can be so stupid. I mean, take the slave trade. (Forget for a moment that slavery is still a modern problem, it just gets given a different name – “human trafficking” – and it isn’t officially endorsed by governments. It’s still just as real. I’m referring right now to the institutionalised relocation of people with particular racial identities, selling them to others for financial gain and then forcing them into labour and inhumane living conditions.) We look back on the slave trade and wonder, “How could people ever think it would be morally justifiable to own another human being and deprive them of their basic human rights?”

But to say this is to ignore the pervasive influence of culture. The culture (for instance, in the United States) of the time accepted this as a given, and it was unusual to think otherwise. When this assumption was challenged, it was met with (literally) violent opposition. As you can see, our cultural context has a far greater influence upon us than Western post-Enlightenment individualism would have us believe (which is ironic, since Western post-Enlightenment individualism has itself had a massive cultural impact on the society that we live in).

So what does this have to do with becoming a head teacher? Well, my cultural identity is bound up in my “generation” (Gen Y, for anyone who’s keeping score at home). Gen Y is renowned for refusing to grow up and take responsibility. My generation is famously filled with man-sized boys who prefer to live at home into their 30s playing video games while their mothers do their laundry and cook meals for them – rather than moving out, getting a job and starting a family.

It took me a long while to realise this, but I began to see that part of the reason why I had resisted becoming a head teacher for so long is because I was doing the Gen Y thing: saying to myself, “That job is for someone else – just leave me alone and let me keep doing the thing I’m enjoying.” To be sure, there were other reasons why I didn’t want to become a head teacher, but at least some of it was this selfish thing that my generation is so good at: refusing to do the hard thing and take responsibility for something beyond my own personal comfort.

One of the funny things that all of us do in one way or another is look down on others for doing exactly what we are doing, so long as it is different enough to us so that we can distance ourselves from it. So we might mock those who earn twice as much money as we do and live in obscenely extravagant and wasteful ways, but the people who earn half as much as we do would say we do exactly the same things but on a smaller scale. I was looking at others who weren’t growing up and taking responsibility (especially with regard to family life, an area where I am relatively advanced for my age) and scoffing at them – not recognising that I was doing exact the same thing, only in the professional sphere.

Why A Head Teacher? The Architect’s Influence

This is the second post in a series; if you haven’t yet, read the first post:

Head teachers may spend less face-to-face time with students than regular teachers, but they actually have a much broader effect because they make decisions that don’t just affect their class; they make decisions that affect all teachers in their faculty, and hence all classes for that subject. In some ways, classroom teachers are like builders but head teachers can be like architects: the latter design things according to their convictions about what works best in their context and the former are responsible for implementing these designs in concrete ways. (The analogy isn’t perfect – the line is not nearly as clear cut as that, but you still get the idea.) I can illustrate this idea anecdotally.

I knew a head teacher who was the first to enforce an exam-setting system from year 7 to year 12 that involved all assessments being set by teachers who did not teach the course (i.e. the year 7 exam must be set by someone who does not teach year 7 that year). Obviously, this is not the only way to do it; the opposite approach is far more popular (where the year 7 exam is set by one or several of the year 7 teachers). I won’t go into length on the pros or cons of each, but I will say that this specific head teacher firmly believed that exams should not be set by those who taught that year (or that course). His decision had a massive impact on the faculty and on students as a result; it led to higher standards for classroom teachers (they had to be very diligent in teaching every single aspect of the course, because they had no idea what might be assessed in the exam) and became a crucial part of students’ preparation for the HSC.

Let me tell another story. In my recent years of teaching, I’ve noticed a few alarming trends. One was increased stress levels (particularly in the senior years); another was a higher prevalence of distractedness (which manifested in many students’ inability to focus on a single task and do it well, both in academic and extra-curricular contexts). But the thing that irritated me most was the increasing frequency of this kind of conversation:

Me: So that’s why this kind of question is so interesting and challenging.
Class: Do we need to include that line to get full marks in an exam?
M: Ummm, well, it would probably be a good idea – but more importantly, do you understand this concept and see how it makes sense of so many other things you have learned about over the past few years?
C: Yeah, but we want to know how to do the correct setting out. Will we lose half a mark if we forget to mention the plus minus?
M: I’m not sure, maybe, but the point is that the plus minus actually tells you something significant about the kind of equation you are solving…
C: But can you find out whether we’ll lose marks or not?
M: Fine, I’ll go and ask…

I despise having this kind of discussion. It embodies everything that I think is wrong with maths education in school (particularly high school): all the emphasis is on getting the right answer and being able to perform well on an exam, rather than on actually understanding an idea and seeing how that reveals interesting and sometimes surprising patterns and relationships.

The thing is, I know it’s not the students’ fault. They aren’t asking me these questions because they have thought about the philosophy of maths education and come to the conclusion that it is all about exam performance. They are just responding naturally to a simple reward/punishment stimulus: working that doesn’t have every single required element gets marks deducted, which leads to a lower overall mark, which leads to a lower ranking, which leads to being put into a lower class, which leads to the parents being disappointed and being really strict. (I’m exaggerating a little… but not that much.) So they learn very quickly: learn what hoops the maths teachers want us to jump through (whether it’s writing “or” instead of a comma, or including restrictions, or drawing things to scale, or add in some seemingly arbitrary lines of additional working), and then jump through them regardless of whether you understand the concept or not. It’s the hoops that matter.

How did things get this way? The short answer is: one head teacher’s incredible attention to detail and unrelenting desire to maintain high standards of mathematical working and setting out. In the staffroom, the head teacher makes the final decision on what receives marks and what does not, and he was a firm believer in the “half mark”! Since he held that kind of belief about how maths should be taught and assessed, it trickled down to all the staff and then through to every student until it led to those kinds of conversations that I described earlier.

So, what’s my point? In both cases (and I could name dozens of others), a head teacher’s conviction led to certain decisions that had an enormous impact on the learning environment of the day-to-day classroom. This is part of the head teacher’s role as an “architect”: to lead the faculty and hence direct student learning – and that’s a level where I want to have a positive impact, not just in my own classroom.

Why A Head Teacher? The Leadership Vacuum

Some teachers set their eyes on “career climbing” from a very early stage, but I wasn’t one of them. It took me a long time to warm to the idea of even wanting to become a head teacher, let alone trying to become one. In the process, I reflected a lot about what matters to me as a person and as a teacher, which I’ve found to be a difficult but very worthwhile process. I’ve discussed some of these thoughts with various individuals recently, and hope that sharing them here will be beneficial to others and open up further dialogue. So this is the first of three posts where I try to articulate why I became a head teacher. Today’s reason sounds negative, but it’s a necessary starting point: it’s the leadership vacuum in mathematics education.

It’s generally recognised that there is a shortage of qualified maths teachers out there at the moment (mainly because people who are good at maths tend to gravitate toward professions that use those skills but earn more money and have better social status, such as engineers and actuaries). At the same time, maths teachers are among the least likely to want to enter leadership and management roles because – to put it bluntly – mathematicians can be pretty weak in the people skills department! This means that there seem to be relatively few people who have genuine interest in becoming mathematics head teachers.

This is a problematic situation in and of itself. But it becomes drastically worse when you realise that, up there with English and science, maths is one of the biggest subjects in our schools (and therefore needs many teachers and HTs). Not only is it a big subject in terms of sheer enrolment of students, it’s a big subject in importance: any time any country does a large-scale review of its education system and school curricula, maths figures prominently in what needs to be emphasised (and the reason political chaos in connection to Christopher Pyne and his proposed review of the Australian Curriculum is no exception).

Now, that whole discussion may seem high and lofty compared to one teacher’s decision with regard to his career – so what’s the point? The point is that if competent maths teachers don’t step up and become maths head teachers, it’s not that there is no head teacher. This is a required role. There must be a head teacher. So if competent maths teachers don’t step up, the bar gets lowered and we get bad educational leaders in head teacher positions.

So, I decided to step up to the plate because students and schools deserve good leaders, and there aren’t enough of them around. I think I have a skill set that can be genuinely useful in serving in an executive capacity, so – hopefully – I will be doing more good than harm by taking on this role!