The Art of Noticing

“All there is to thinking, he said, is seeing something noticeable which makes you see something you weren’t noticing which makes you see something that isn’t even visible.”
Norman Maclean, A River Runs Through It

‘Sometimes a teacher needs to hear what the student is NOT saying.’
Robert John Meehan

I spend a lot of my time as a mathematics teacher educator encouraging, enabling, and enacting the art of noticing with pre-service teachers.

Teaching is, at its heart, an act of noticing. Whether you are working with a preschool child learning to count, a primary student grappling with fractions, or a postgraduate student wrestling with learning how to teach, the process is remarkably similar. Effective teachers are constantly noticing, interpreting, and responding. We notice what students say, what they do, what they understand, what they misunderstand, and sometimes even what they choose not to say.

I first encountered the term professional teacher noticing at the 15th International Congress on Mathematical Education in Sydney in 2024. It was not the first time I had noticed things. I had been doing that all my life. What was new was discovering that this ongoing process of observing, interpreting, and responding had a name, a research base, and a structure.

Listening to researchers describe professional noticing felt a little like discovering that something I had always done instinctively had finally been given a label.

The more I reflected on the idea, however, the more I realised that my interest in noticing extended far beyond teaching.

One of my favourite tools for developing curiosity in students is the use of photographs, or as many mathematics educators describe it, putting your “Maths Eyes” on. It is something I have always done, often without even realising it.

What do you notice? What do you wonder? What do you know?

Here’s an example from a meal at Wakuda in Marina Bay Sands. I took a photograph of it, not because it was food—I rarely photograph my meals—but because of the arrangement. Four identical portions, carefully positioned and balanced in colour, shape, and space. Before I tasted anything, I found myself noticing the symmetry and pattern. Looking back, I realise I was doing exactly what I encourage my pre-service teachers to do: slow down, look carefully, pay attention, and appreciate what is there before rushing in, whether to eat or to judge its meaning.

Long before I became a teacher educator, I had been noticing patterns, relationships, contradictions, and stories in the world around me. I noticed them while travelling, while taking photographs, while sitting in airports, wandering through markets, watching sunsets, or simply observing the interactions between people.

Professional noticing may have given me a language for what I do as an educator, but it did not explain where that habit of mind came from.

Alongside the use of photographs to spark curiosity, two of the most powerful questions a mathematics teacher can ask are deceptively simple:

What do you notice?

Closely followed by:

What do you wonder?

I believe these are two of the most important questions any mathematics teacher can ask.

They invite students to stop. To slow down. To be curious.

Too often mathematics is perceived as a subject of answers. Find the answer. Find it quickly. Check if it is right. Move on to the next question. The emphasis can easily become speed and accuracy rather than thinking and understanding.

“What do you notice?” changes the conversation.

There is no answer to find. There is no race to be won. Students are simply invited to look carefully and share what they see. Some notice patterns. Some notice relationships. Some notice something unusual or unexpected. Others notice details that everybody else has overlooked.

Then comes the second question.

What do you wonder?

This is where the real magic begins.

Wondering gives students permission to be curious. It acknowledges that different people think differently and that curiosity can take us in many directions. One student might wonder how something works. Another might wonder why it happens. A third might wonder what would change if one element was different.

There is no single correct wonder.

There is simply the opportunity to explore.

As children, we are naturally curious. We ask questions constantly. We investigate, experiment, and imagine. Yet somewhere along the way, many of us learn that education is about getting the right answer rather than asking interesting questions. The curriculum becomes more crowded, the expectations become more structured, and curiosity can gradually be squeezed out.

For me, the power of “What do you notice?” and “What do you wonder?” is that they create space for curiosity to return. They remind students that learning begins not with answers, but with paying attention.

When we travel, whether it is to the next town, another state, or a country on the other side of the world, we have choices about how we move through the space. We can rush from attraction to attraction on what could be referred to as an “ABC Tour” – Another Bloody Cathedral. We tick the landmarks off the list, take the obligatory photographs, and move on to the next destination. Before long, everything begins to blur together and it becomes difficult to remember one place from another.

Or we can slow down.

We can sit for a while. We can watch. We can listen.

Noticing is not just a teaching skill. It is also a way of looking at the world.

We can ask the same questions that I ask my pre-service teachers:

What do you notice? What do you wonder? What do you think you know?

What do you notice? (It’s very symmetrical. It has a particular style to it. There’s grass growing on it. It could do with a good clean.)

What do you wonder? (Is it a Catholic Cathedral? Is it is a hot country? Is it really 4:45? Why is that woman standing there? Who took the photo?)

What is worth noticing here? What is happening beyond the obvious? What stories are being told? What values are being expressed? What relationships exist between people, places, and histories? What can this place teach us about itself if we are willing to linger long enough to pay attention?

Take, for example, these photographs of Adelaide Airport.

If I simply asked, What do you notice? most people would probably say the same things. The terminal appears almost empty. There are very few people visible. The shops seem deserted. There is little sign of movement or activity. For an airport, it feels strangely quiet.

Those observations are important because they are based on what we can actually see.

But then comes the second question.

What do you wonder?

Why is it so empty?

Was it taken early in the morning? Late at night? Was there a strike? Had flights been cancelled? Was Adelaide simply quieter than other cities?

At this point we begin moving beyond observation into interpretation.

Only when we know the context does the story become clearer.

These photographs were taken at the height of the COVID pandemic in 2021. Travel restrictions were in place. Borders were opening and closing. People were reluctant or unable to travel. What initially appeared unusual suddenly made perfect sense.

The photographs themselves had not changed.

What changed was our understanding.

Some of my most memorable travel experiences have not come from the famous landmarks. They have come from wandering through Little India in Singapore and noticing the contrast between traditional market stalls and modern high-rise apartments. They have come from standing in a monastery in the Philippines and wondering what a monumental act of faith says about the priorities and values of a community. They have come from exploring enclosed streets lined with colonial buildings and considering the stories of the people who once lived and worked there.

They have come from watching cargo ships waiting offshore and discovering the hidden city that supports the visible one. They have come from appreciating beauty, whether it is created from glass and steel or found in the natural world. They have come from spending a morning in a Balinese market learning how a meal is created rather than simply eating it.

The longer I travel, the more I realise that the most interesting stories are rarely the ones printed in the guidebook. They are the stories that reveal themselves when we stop long enough to notice.

That, perhaps, is one of the most important lessons that noticing can teach us. Observation comes before interpretation. Curiosity comes before certainty. Good noticing requires us to slow down long enough to look carefully, wonder thoughtfully, and resist the temptation to jump immediately to conclusions.

In teaching, travelling, and life more generally, context matters.

Before knowing comes noticing.

Before understanding comes wondering.

For years my friends have joked about my ABS photographs — Another Bloody Sunset. Wherever I travel, sooner or later there will be another sunset posted online. Yet I have never really photographed sunsets because they are beautiful, although many are. I photograph them because they remind me to stop.

Whether I am looking at a student’s mathematical thinking, a market in Singapore, a monastery in the Philippines, an empty airport during COVID, or the sun disappearing below the horizon, the process is the same. I pause. I look. I wonder.

The longer I teach, travel and learn, the more convinced I become that noticing is not simply a professional skill. It is a habit of mind. A way of engaging with the world. A willingness to linger long enough to see what others might miss.

And sometimes, if you are lucky, that lingering is rewarded with another bloody sunset.

Perhaps that is why, wherever I travel, I keep asking the same two questions: What do you notice? What do you wonder?

“What’s in a name? That which we call a rose / By any other name would smell as sweet.” -Shakespeare

Helen of Troy may have launched a thousand ships, but frankly, I’d have been far more interested in devising a mathematically elegant mechanism to sink them. Preferably one involving leverage, poor decision-making, and a failure to understand proportional reasoning.

The other day I met someone called Helena, and I was immediately envious. Not of her, exactly, but of her name. I have spent most of my life as simply Helen. Helena can become Lena, Nell, Nellie, or any number of variations. Helen is just Helen. Australians are famous for shortening names, adding an “o” or an “ie” to almost anything, but there is not much you can do with Helen. It has always seemed a rather final sort of name.

That encounter got me thinking about names and why they matter.

As you may notice from the title of this blog, I’ve played around with names for years: hel’n’commentary, hel’n’damnation, and 2hel’n’bac. Names matter to me. They always have.

And that, naturally enough, led me to Shakespeare and:

“What’s in a name? That which we call a rose by any other name would smell as sweet.”

Shakespeare asked, “What’s in a name?” and answered that a rose by any other name would smell as sweet. I’m not entirely convinced. Names carry history, personality, relationships, and expectations. They are often the first gift we receive and, in many ways, the last thing people remember about us.

Take Helen, for example.

The name is forever associated with Helen of Troy, the face that launched a thousand ships and sparked a war. A woman so beautiful that nations fought over her. Yet that image has never felt particularly relevant to me. I am far more interested in figuring out how to sink the ships than launch them.

In fact, every time I hear the story of Troy, I find myself wondering about entirely different things. Who was the idiot who let a giant wooden horse inside the city walls without checking what was in it? Come on, people, you’re at war. The enemy suddenly leaves you a massive wooden horse and sails away. Surely someone should have thought that through.

And then there is Helen herself. Did she actually want to be rescued? Did anybody ask her? The story assumes that because she belonged to Menelaus and Paris took her away, Menelaus had the right to reclaim her. But perhaps Helen was perfectly happy where she was. Perhaps there was a reason she left in the first place. History, mythology, and storytelling often tell us far more about what people expected women to do than what women themselves may have wanted.

Names come with stories attached to them, and sometimes those stories are difficult to wear.

Imagine being named Rainbow in the 1970s or 1980s and growing up to become a fifty-eight-year-old tax accountant or the CEO of a multinational corporation. Names carry images. They create assumptions. Some fit us comfortably; others feel like clothes we spend a lifetime trying to alter.

I can remember being absolutely furious as a teenager when my sister-in-law introduced me as “Bill’s sister, Helen.” I remember thinking, why am I being defined by the relationship first? Why couldn’t I simply be Helen, who also happened to be Bill’s sister? Ever since then, I have been very conscious of naming the person first, before the relationship. People are not extensions of other people. They are themselves.

Which is perhaps why I struggle so much with remembering students’ names.

Well, that’s not quite true. I know their names. I know their faces. The problem is attaching the names to the faces. Faces are easy. People take time.

A face tells you what someone looks like. A person reveals who they are: their humour, their interests, their strengths, their worries, the way they think, the stories they tell, and the way they interact with the world. It is only when I begin to know those things that a name settles properly into place.

I don’t really attach names to faces. I attach names to people.

This semester, with my fourth-year mathematics specialism pre-service teachers, I realised that after years of seeing them only once a week for a few hours each semester, I can finally remember most of their names. Not because I have suddenly become better at memorising faces, but because I now know who they are.

A face alone means very little to me. What matters is the person attached to it:

the student who suddenly understands proportional reasoning,
the one who lacks confidence but keeps trying,
the quiet one with the dry sense of humour,
the student who asks brilliant sideways questions,
the one who shakes your hand when they first meet you and immediately gives you a sense of who they are.

Once I understand something of the person, the name settles naturally into place. Before that, it is just a label attached to a moving blur that I see once a week for three hours over ten weeks, before they disappear again for six months.

It takes time to know people.

That is why names matter so much to me. A name is never just a label. It carries identity, personality, history, memory, and story. Once those things exist, the name becomes real.

And possibly that is also why, after four years with this group of future teachers, I can finally remember who everybody is.

After all these years of wearing the name, I have made peace with being Helen.

Not Helena. Not Lena. Not Nell.

Just Helen. Helen S Booth. The ‘S’ is important because there are many, many Helen Booths, but there is only one Helen Stewart Booth. There are Helen Booths, Helen Stewarts, but only one Helen Stewart Booth.

And perhaps that name has become interesting not because of what it means, but because of the life that has gradually grown around it.

I have been:

Hen,
Hell,
Lenny,
hel’n’commentary,
hel’n’damnation,
2hel’n’bac
teacher,
traveller,
researcher,
consultant,
widow,
storyteller.

Perhaps the name stayed the same, but I’ve accumulated a great many versions of myself around it.

Thinking about names and faces reminded me of an activity I use with pre-service teachers involving Cuisenaire rods and what we call a “Hundred Face” (Find a lesson plan from AMSI here)

For those unfamiliar with Cuisenaire rods, they are coloured mathematical rods with values ranging from 1 (a white cube) through to 10 (an orange stick equivalent in length to 10 white cubes). The challenge for the PSTs is to create a face using rods that add to a total value of 100.

Initially, we make fairly basic faces, but then I add a rider: they must include at least one rod of every colour. Suddenly the task becomes much more interesting. They now need to think much more carefully about combinations, values, structure, and checking totals. The faces become more complex, more creative, and far more individual.

What fascinates me is how quickly personality emerges from arrangements of simple mathematical objects. The rods themselves are just coloured wooden blocks, yet somehow students create faces with expressions, moods, and character. Some faces look cheerful, some mischievous, some startled, some thoughtful. It is amazing how quickly we begin to see identity in patterns and relationships.

Why do I use this activity with PSTs? Primarily because they are future primary teachers, and this is an activity that can easily be adapted for a Year 1 classroom as part of a unit on place value and numbers to 120.

At the beginning of the unit, students can create a Hundred Face as a form of pre-assessment. The way they construct the face tells you a great deal about their mathematical thinking. Some children use very simple constructions and rely heavily on smaller rods or repeated combinations. Others demonstrate more sophisticated understanding of grouping, equivalence, and efficient combinations.

Then, at the end of the unit, students complete the task again, this time with the additional condition that they must use at least one rod of every colour. Suddenly they are required to think much more deeply about how numbers can be composed and recomposed to make 100, while also needing to justify and check their thinking.

What I love most, though, is that the activity becomes about far more than simply reaching 100. Somewhere in the middle of mathematical thinking, coloured rods begin turning into personalities.

Perhaps that is not entirely unlike learning people’s names.

All in a day’s work

I am very lucky in that I love my work, even if it exhausts me. I get to work with both pre-service and in-service teachers to build their confidence and capacity as teachers of mathematics. Not only that, I get to travel around the state to work in their schools.

My beautiful, but scruffy, late husband in the backyard of the house on the Peninsula.

I have worked in this capacity with in-service teachers (teachers who have completed their degrees and are working in schools) for seven years. The first four years saw me on the road for nearly seven months a year, living away from home and in temporary accommodation. When I first took on the role, I was living by myself, with a cat and a dog, 100 minutes from the airport and struggled to manage the work and travel load. Fortunately, Josh, my nephew, agreed to house share and I moved to a rented property closer to the airport, so the cat and dog still had someone to look after them and I was only 30 minutes from the home when I got off the plane, instead of what could be a two and a half drive from Melbourne airport to home on the Mornington Pennisula if I hit rush hour. It was a difficult choice, moving out of my beautiful home into rented accommodation but I loved the work I was doing and I didn’t want to go back to where I was pre-2015. (I took that year off and did my Masters.) That choice started breaking the emotional thread that attached me to that particular house, which enabled me to sell it 2 years later and then nearly 3 years ago now, even move states.

After 4 amazing years with AMSI, I decided to start a new job, buy a new house and return to study, all in South Australia. And because I never do things by halves, I packed everything up, put it on a truck, and sent it to SA with Josh, (he flew,) while I drove across with the cat and dog on what turned out to be the hottest day of the year (only 46 C,) arriving late Friday. I then started my new job on Monday followed a week later with beginning my PhD. When undergrad classes began in March, I took up a bit of tutoring, just for the hell of it.

My new job enabled me to continue working with in-service teachers and instead of working in two states while living in a third, I got to travel all over South Australia. This happened throughout 2020, 2021 & 2022, even though there were a few last-minute cancellations with schools having COVID restrictions to enforce. However, unlike both Victoria and NSW, we didn’t have major lockdowns. In fact, besides the first rush to stop the spread in March/April 2020, SA only had two snap lockdowns; one in November 2020 and the other in July 2021. Both times, I was not in Adelaide – in November 2020 I was on Kangaroo Island, and in July 2021 I was in Cobber Pedy. The first time, no one had any idea about what was happening, whether flights would be grounded, if everyone had to go home or stay put. I couldn’t get off the island so I just stayed put as I couldn’t contact the airline I was flying with and my work colleague back in Adelaide couldn’t either. I guess they were completely overwhelmed with enquiries as everyone want to know what they could and couldn’t do. I phoned the police on KI to find out if they knew what the rules were and their response was, “We’re in the dark as much as you are.” So I went to the hotel/motel where I was staying and asked to be moved into a room with cooking facilities and a washing machine; I was only supposed to be on KI for 2 nights 3 days so I only had 2 changes of clothes. I moved to a great spot overlooking the ocean and spent 4 days watching the weather outside my room. (The initial lockdown was supposed to be 6 days, but it turned out someone lied about how they contracted COVID, so the travel restrictions were lifted after 3. I left on the first available flight because although the lockdown had ended, DfE schools weren’t allowed to let non-staff members on site.)

The second lockdown was in a slightly different environment; Coober Pedy. I had flown up on Monday for a week working in the school. Woke up Tuesday morning to find that the Road House was under ‘outdoor’ dining restrictions; by 4 pm, the entire state was in lockdown. Trying to leave Coober Pedy wasn’t an option; it only has 3 flights to Adelaide per week and anyone who could, booked on the Wednesday flight. As I was due to fly out on Friday, I just stayed out. Where I stay when in Coober Pedy (The Mud Hut Motel) is really comfortable, so it wasn’t a penance. Food was a bit of an issue as I usually eat out when up there rather than cook for myself, but I managed to find stuff at the minimart at the Road House. Flew back to Adelaide on Friday and drove home through very quiet streets.

Visiting Coober Pedy is always interesting as you are never sure what you’ll get. On one visit I took all my food with me because there had been massive floods in and around the place and the main highway, Stuart Highway, was cut in both directions. As a result trucks with supplies weren’t getting through and with tourists stuck in the town and dwindling fresh food, I thought I had better go prepared. The other problem was, with the road out the plane was loaded with extra freight, so they were bumping off the luggage of passengers that were over the limit. For me, the choice was either my work stuff or the food. Fortunately, at the last minute, someone offered to unload something that was actually supposed to be going to Port Lincoln; why the hell it was being sent to Coober Pedy, nearly 900km north of Port Lincoln in the first place is a bit of a mystery.

My latest visit was also a bit of a journey. The plane left an hour and a half late and took 30 minutes longer than usual, due to headwinds. Sunday, the day before, Coober Pedy, and a number of other small outback communities had been hit by wild weather, knocking out power supplies and causing a bit of flash flooding; 35mm fell in a couple of hours where the long-term average for the entire month of October is 14 mm with winds gusting to 102 km/h. If there had been trees, there would have been trees down but there are no big trees in Coober Pedy. It was nowhere near as windy on Monday but it was a pretty bumpy ride. Just as well I was weaned on single-engine aeroplane flights in the territory in the mid-eighties. It makes air turbulence in bigger planes a lot less scary. The wind was up in Coober Pedy all of Monday and Tuesday before dying down but fortunately, all the rain meant the dust was not.

The Break Aways, just outside Coober Pedy

These are just some of my adventures over the past 3 years, doing a job I love but the travelling does get a bit wearing at times.

If you think adventure is dangerous, try routine. It’s Lethal!
Paulo Coelho

What’s on your bucket list?

When it comes to my bucket list, the blame sits fairly and squarely with Netflix. When I first signed up for Netflix during my AMSI travel days, I came across a series titled “Chef’s Table.” The first series took you from Modena, Italy, to Järpen, Sweden, via New York, Buenos Aires, LA and Melbourne. The documentaries let you into the world of these amazingly innovative, passionate, but slightly crazy, obsessive chefs as they create food to tantalise the senses. I avidly watched each series as it became available and my bucket list began to form – to visit the top restaurants on every continent and saviour the sensory experience of great food, drink and atmosphere.

The only problem; well, possibly not the only problem. Things like global pandemics, wars, and in all truth, finding the time to do it also come into play. But the big one is lack of money, which is why I don’t have the time; I’m too busy earning money for the daily necessities that travelling to all those places, just to have a meal seems a bit ‘pie in the sky.’

When I started writing this postn it was coming into winter here in Adelaide, South Australia with long nights and short days. On a Friday, I started work before 8 and don’t finish until after 6, so I was up in the dark and home in the dark. It was also getting cold; not cold in comparison to other places in the world, but cold by our standards; Still not at the shortest day, and spring, a long way off. The quote below sums up my feelings about winter. Taking steps to survive the winter and find some joy is a necessity. Fortunately for me, I just needed to make it to July when I would have 12 days of warmth in The Philippines.

https://www.quotemaster.org/winter+depression#&gid=1&pid=5

So, how does this link to my bucket list, you ask in my delusional imagination? No, I was not suddenly jetting off to Copenhagen, Denmark, to dine at Noma, or Atxondo, Spain, to experience Asador Etxebarri’s delights, nor to the closer Odette in Singapore. (Mind you, having looked at the offerings in Singapore, I have booked a flight and a week in January.) I have been sampling the fare on offer here in Adelaide. Josh, my nephew, and I are trying out the top restaurants on a Monday evening when work, travel and other social happenings allow it. SO during those long cold weeks throughout May and June, we journeyed out.

https://glamadelaide.com.au/photos-your-actual-first-look-inside-shobosho-on-leigh-street/

Raw tuna, edamame, black rice with bonito cream and grilled nori

Firstly was Shobosho on Leigh Street in the CBD (https://shobosho.com.au/), which is listed across most, if not all, top restaurant www guides, and it did not disappoint. The raw tuna, edamame, black rice with bonito cream and grilled nori dish was delicious, as were the dumplings. My main was wood roast cumin Lamb Ribs with black vinegar and braised leeks. Definitely worth the trip out on a cold winter evening. The atmosphere and service were also good. The bustle and hum of the restaurant on a Monday in May attested to its popularity. I will, without a doubt, visit again and, this time, take photos of the food. I get preoccupied watching the working of the kitchen and the restaurant as a whole, I don’t remember to take a photo until halfway through the dish.

The following Monday we ventured out again, this time to Osteria Oggi on Pirie Street, also in the CBD. This restaurant also rates well in most guides, but we did not enjoy the experience as much as expected. Our first courses of Tripe (Josh) and Smoked Kingfish Crostini were yummy but the pasta dishes we had weren’t overly inspiring. I had Pappardelle with rabbit ragu, which while very tasty was overly salty. Josh had Squid Ink Fiori with prawns, pipis, and samphire, which looked impressive on the plate but not the palate.

The final restaurant visited was Fishbank on King William Street and, boy, was it a beauty. Everything from the interior, to the service, drinks and food was top-notch. In fact, it was so good, we went back again to try other dishes. Sited where Jamie Oliver had his Italian restaurant, Fishbank’s food is well-worth several visits. It’s delicious and beautifully presented. On one visit I had the steamed whole baby snapper, while on the other I tried a selection of their snacks and small plates. Fishbank also has an excellent selection of wines, spirits, cocktails and other beverages, SO if you are in Adelaide and you like fish, definitely put it on your bucket list.

Unfortunately, due to work and other things getting in the way of Monday nights, we haven’t venged out anywhere new recently, but that’s fine because when next winter arrives, and it is dark, cold and dreary, we can continue our exploration.

Revisiting “More heads are better than one.”

‘The most valuable resource that all educators have is each other. Without collaboration our growth is limited to our own perspectives.’
Robert John Meehan

I decided to revisit a post from another one of my sites which I have not added to for years. The focus was on a task from nrich.maths.org, one of the best sites around for inspiring mathematics activities, problems, investigations, articles and generally good stuff. I visit it, along with other sites, regularly to be inspired. I describe myself as a magpie when it comes to teaching mathematics. There are so many talented maths educators out there, sharing their ideas, that I am in awe. I will always try and acknowledge where I got information, lessons and activities from because I am a strong believer that credit should be given where it is due. I also believe in not reinventing the wheel. If someone has come up with a great way to teach a particular concept, why do I need to start from scratch?

That said, it is important that their ideas are suitable for your context. Teaching negative integers to a class of Year 6 students in Darwin probably needs to be addressed in a different context than teaching the same concepts to Year 6 students in Hobart. Finding great teaching ideas is relatively easy; making them relevant to your students is not. The best phrase I heard from a Deputy Principal about a set of ‘tools’ provided by the department was, “I tell my teachers to look at them and adopt, adapt, or be inspired.” I believe this is a great philosophy to embrace with all the resources available, particularly with the quantity accessible online.

There is, however, a problem; one that is at the root of all the political dialogue occurring at present around teaching, teachers and education in general. TIME. Teachers are expected to do so much outside of the actual job of teaching & learning, when do they have the time to adapt and inspire? So certain people with power and absolutely no idea about how to teach, suggest “let’s do all the planning for the teachers. That will give them the time they need to do their jobs properly.”

Anyone, with even the smallest idea of the art of teaching, can identify the problem with this. Teaching effectively is about knowing your students, recognising their individual points of need, identifying their ZPD, (for those not in the know that’s Zone of Proximal Development,) and developing instruction that addresses that ZPD while ensuring there is the right level of productive struggle so learning happens. Providing a set of lessons that are mandated for teachers to follow simply teaches to the middle; forget the struggling students and don’t bother extending the ones who have already mastered that concept. “But wait,” I hear you cry, “a good teacher can adapt the lesson to ensure that happens.” Yes, this is true, but isn’t that what good teachers do already? What is the purpose of mandating, and then expecting good teachers to adapt to suit their students? Are the mandated lessons to ensure not-so-good teachers are teaching something worthwhile, while good teachers are feeling undervalued, disempowered and frustrated, to the extent that they want to leave the profession? This is happening and will continue to happen if teachers are not given the time they need to do their job, which includes time to develop programs, units of work, and lessons that are suitable for all their students, not just some. And who knows their students best? The teachers who teach them, not some faceless person in an office somewhere.

This brings me back to where I started and the reposting of this entry, “More heads are better than one.” One of the best ways to ensure quality teaching is to give teachers time to work together in their schools to adopt, adapt or be inspired, using the resources available. By working together, sharing ideas, coaching one another, and supporting professional growth, all teachers will grow professionally, benefitting all the students in their care.

The fun for me in collaboration is, one, working with other people just makes you smarter; that’s proven.

Lin-Manuel Miranda

Fantastic example of collaboration and the amazing people I work with occurred today. The school year has started and after two days of presentations down on the Peninsula, I am back in the office today, preparing for a full week of school visits next week.

I’m really exciting about working with the teachers and year 9 students are Dromana College next week, over two afternoons. I want to really make an impression with the students, with a growth mindset presentation, followed by a couple of challenging and fun activities.

The presentation I plan on showing comes from the wonderful Jo Boaler’s website https://www.youcubed.org/. She is so inspiring and I talk about her work in all my schools. The presentation is about maths, believing in yourself, the importance of mistakes and the beauty of maths. Now I needed an activity to encourage and enable collaboration.

Going to nrich I found ‘9 colours’ which I believed looked thought-provoking, so I asked my colleagues if they were interested in solving it collaboratively to help determine how successful it could be. Being in a room full of mathematicians and maths teachers, they jumped at it and as a result I now have a real good lesson to present next week.
helnsyellin.wordpress.com/166

This is the task, but it is now so much more, relating it to the Australian Curriculum at 6 different year levels, extending it in many ways;

Draw it on isometric paper from different perspectives;

How many drawings do you need to show all faces?

Is there more than one way to place each small cube?

Is yours the same as another group?

If you gave another group a drawing can they reconstruct your design?

what is the minimum amount of drawing you need to give them?

Is there a pattern to the placement of your cubes?

Remove particular colour (3 blocks) – draw the design with missing blocks

What is the surface area and the volume?

How does the surface area and volume change when you remove one colour?

Can you predict the colour of the middle block (the one not visible)?

Is there symmetry in your design?

Can you determine the total number of combinations?

What can you determine about the number of faces of each colour you will see in the completed cube?

Can you explain this using numbers/algebra?

How many colours would you need for a 4 by 4 by 4 cube?

How many cubes in a 4 by 4 by 4 cubes?

Do the same rules and patterns exist in a 4 by 4 by 4 cube?

Is there a point at which the task is impossible? (5 x 5 x 5; 6 x 6 x 6; 7 x 7 x 7….)

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cube1-2 — Our cube; thanks Jac, Julia and Nadia.

As you navigate through the rest of your life, be open to collaboration. Other people and other people’s ideas are often better than your own. Find a group of people who challenge and inspire you, spend a lot of time with them, and it will change your life.” Amy Poehler

Define ‘holiday.’

So what constitutes a holiday?

from https://www.dictionary.com/browse/holiday

I didn’t know about number 6, but I have certainly created holidays when painting. Perhaps ‘vacation’ is a more appropriate word:

from https://www.dictionary.com/browse/vacation

I have had the first real vacation in years, 14 days ‘… of suspension of work, study or other activities,’ that require effort and energy. Sure, I’ve had ‘holidays’ over the past few years, but I realise I have always been busy doing, not actually resting. In the past 14 days, I have just done what needed to be done and little else. It has been great! I thought I’d be bored by now but, no, I’m not, although I did decide to start writing this blog again. Occasionally I experience pangs of guilt when I think about all the presentations I need to prepare for work, but when that happens, I actively seek out another K-drama on Netflix or Viki to watch. I have until Tuesday before I start my new part-time role, returning the following week to my present part-time job. I could talk about my two jobs, both of which I love, but I’m vacationing so I’m going to explain why my last holidays were not vacations.

September 2020 was my last holiday. It was my sixtieth birthday, and as ‘zero’ birthdays are supposed to have some significance, I was supposed to celebrate it with a house party and friends. Unfortunately, there were a couple of problems. One was that I moved States in January 2020 from Victoria to South Australia. As most of my friends live in Victoria, it would take some organising, but I was up for it. It turned out another unexpected problem was a more significant issue; COVID. Everyone was in lockdown and couldn’t come anyway. So I did what any self-respecting independent woman would do; I went and spent the week by myself. I know, but I thought I’d have a bit of me-time prior to a working week. We had visits scheduled at schools on Kangaroo Island, so I went down the week before to just relax. I chose a beautiful place, overlooking the ocean, in the middle of nowhere. The problem was, it was in the middle of nowhere, an hour to the nearest shop, on unlit and unsealed roads with no phone. It would have been great for a romantic weekend, but I got bored, resulting in me driving all over the island. Got some great photos and saw the devastation caused by the summer fires, but didn’t get much rest.

My previous holiday was even crazier. I went home to New Zealand and proceeded to do a ‘cousie’ road trip, i.e., I visited all my cousins and family in the South Island in 10 days. This involved literally travelling from one end to the other. I started in Christchurch with breakfast with Cousin Andrew, drove to Kaikoura and spent 2 nights with Cousin Susan and family. I then stopped in Blenheim to lunch with a friend before driving to Wakefield to stay with Bob and Esther (brother and sister-in-law). While in the area, I caught up with my eldest brother (Bill) and his family, as well as Cousins Peter and John. After a few days, I hit the road again, heading for Invercargill via the West Coast, traversing the Alps at the Haast Pass. I met my cousin Janine in Invercargill, and we headed to Riverton for 2 nights. Next, I drove up to Dunedin, where I had lunch with my niece Jane, before driving to Christchurch and finishing the day with dinner with my niece Claire. I then flew back to Melbourne to start work. If you are not tired from reading that, I’m exhausted just writing it. Got some great photos though!

I didn’t have a holiday between finishing my last job and beginning my present one; I decided to pack up and move States instead. That was fun, NOT! Organising, packing, selling, cleaning after 16 years living in Victoria was draining, to say the least. Then the drive to Adelaide turned out to be on a sweltering day in Victoria (44⁰ C), with Ella and Zerlina in the car. The heat was moving east as it had been 44⁰ C in Adelaide the day before, so after driving through to sweltering Victoria, we got hit with almighty thunder and lightning storms as we crossed the border into South Australia.

I guess what constitutes a holiday depends on what you want to get out of it, be it rest, experiences, family time, travel, relaxation or a combination of them all. Sometimes you have to travel distance to find it, while other times, it’s at home, in your own space. I’ll finish with a photo taken recently when I decided I just needed to sit by the sea, feel the seabreeze and watch a sunset. Wherever you are spending your holiday, I hope you get what you wanted from it, particularly during these more difficult times as we deal with a COVID normal world.

“Damn it! Someone will know what I had to say.”

I haven’t written anything for ages, mainly due to laziness, life, and why bother. I have been on holiday, i.e. not working, for a total of 14 days. This is totally unusual for me. Even when I am on ‘holiday,’ I am busy doing stuff. SO why start to write again? I have trouble sleeping; my brain is often way too active. My sleeping aid, rather than drugs, is listening to an audiobook. I always listen to the same one. I concentrate on the story if it is a different book, which keeps me awake. I listen to Andy Weir’s “The Martian,” read by RC Bray. I first listened to this story back when I was travelling through vast tracts of the Australian Outback, visiting places that at times could have been on Mars, except with air and plants. Sometimes the air was too hot to breathe, and the plants were scarce. There was something comforting about the style of writing and the narration that made the kilometres roll by without distracting from the road and the on-coming traffic. Now there is the same comfort in helping me drift off to sleep. As you may surmise, I don’t listen to “The Martian” while driving anymore.

Top of the Spencer Gulf, Port Augusta, South Australia

The road to Marble Bar, Western Australia

Red Dirt, near Port Hedland, Western Australia

Anyway, back to why I decided to start writing again. Last night, as I was waiting to drift off to sleep, Mark Watney was recording his thoughts on being the first to do lots of things he never planned on doing, lamenting on being the first person to be alone on an entire planet and how he wishes he could talk to someone.

Jesus Christ, I’d give anything for a five-minute conversation with anyone. Anyone, anywhere. About anything. I’m the first person to be alone on an entire planet. Okay, enough moping. I am having a conversation with someone: whoever reads this log. It’s a bit one-sided but it’ll have to do. I might die, but damn it, someone will know what I had to say.
Andy Weir -The Martian

I spent some time yesterday rereading my travel blog and the previous posts on this blog, and as I listened, drifting off to sleep, I thought about them and how much I enjoyed writing, sharing my photos of and thoughts on my experiences. As a result of my late night/early morning musings, I am writing this. Does it matter that I may be the only one who reads this? No. Does it matter if I write spasmodically? No. Does it matter if the topics are mixed and varied? No. In the words of Mark Watney, “… but damn it, someone will know what I had to say.”

“What dreadful hot weather we have! It keeps one in a continual state of inelegance.” Jane Austen

Sorry to be harping on about hot weather, but it is does sort of dominate your life at times. My favourite quote is:

“The heat index is somewhere between OMG and WTF.” (anon)

I’m just going to share some photos in this post that I’ve taken over the past couple of days.

The wind dropped out at Marble Bar on Friday and I got to fly my drone. A storm was coming in so there were clouds gathering.

This first one is down at the actual Marble Bar pool. The ‘marble’ is actual jasper but whatever it’s geological makeup, it’s a pretty place to visit even with heat and flies (DON’T GET ME STARTED ON THE FLIES!)

Afterwards, I drove to the flying fox lookout, which is up above the river. I got a couple of photos but, even though it was overcast, the air was still hot and the little fella heated up very quickly. The drone camera seems to have a more grey cast to the photos, making the dirt brown and the grass turfs grey green, which isn’t really their colour at all. The 2 photos below are a far better representation of the true colours.

The hills all round Marble Bar are rough red rock with spinifex grass. At the moment, all the spinifex is golden brown, so the contrast between the rust red rocks and the golden spinifex is eye-catching. The photo below was taken in February, after good rain, just to show the contrast in the spinifex.

The road to Marble Bar is an easy drive with a major upgrade finally finished. There are a number of smaller mines out that way, so the infrastructure needs to deal with heavy 60 metre quad road trains. While iron ore is the main mining focus in the Pilbara, there is an increasing number of operations looking for and extracting copper, rare earth metals, gold, and some minerals I have never heard of (molybdenum and tantalum for example,) from out of the way places. If you look at Google maps closely, you will find accommodation complexes, some very weird but definitely man-made markings, and man-made holes in the ground.

Driving back in to Port Hedland on Friday, there were occasional patches of showers and huge wind gusts, enough to make it hard driving. At one stage the visibility was pretty poor due to amount of dust being kicked up.

Unfortunately, there was no rain in Port Hedland, just increased humidity. Saturday morning after breakfast, I walked down to the edge of the harbour entrance channel; it was low tide. I had been meaning to do it for some time. The first photo below was taken Saturday while the bottom two show different weather conditions, taken at different times of the year. The leisure boat in the top photo is moving away from the jetty shown in the bottom two.

The most exciting thing was I saw a turtle while on the edge. It is turtle nesting time up here at the moment.

By the time I got back to the car, after only half an hour, I was feeling a little heat stressed, so I checked the temperature…it was already 41 degrees, so I went home and spent the rest of the day inside in air-conditioning. I could not find anything that kept me occupied for longer that 30 minutes, so boredom drove me to bed at 8 pm.

“I’m bored’ is a useless thing to say. I mean, you live in a great, big, vast world that you’ve seen none percent of. Even the inside of your own mind is endless; it goes on forever, inwardly, do you understand? The fact that you’re alive is amazing, so you don’t get to say ‘I’m bored.”
― Louis C.K.

On Sunday, I decided I couldn’t spend another day doing nothing, so after breakfast took after towards Broome. Earlier I decided to look up on trip advisor what there was to see/do between Port Hedland and Broome and the 6 answers included, besides Eighty-Mile Beach, ‘buy petrol,’ ‘One long road and whole lot of red dust,’ ‘I spy with my little eye, something beginning with “N”….Nothing,’ and ‘This topic has been closed to new posts due to inactivity.’ On the 600km drive between Port Hedland and Broome are two roadhouses, Pardoo and Sandfire, but off the Great Northern Highway are some semi-hidden gems.

Road to PH — Somewhere between Eighty-Mile Beach turn off and Pardoo.

Not far, by Pilbara standards, at only 250kms, is Eighty Mile Beach Caravan Park, which is a good entry place for Eighty Mile Beach. It is a thin strip of beach that actually runs for 220 km (140 miles) between the Great Sand Desert and the Indian Ocean, from Cape Keraudren at the Port Hedland end and Cape Missiessy at the other end. On the ocean side the sand is white, while on the land side of the dunes, the dirt is red. The contrast to something to see. These photos were taken with my drone.

Looking towards Cape Missiessy.

Looking towards Cape Keraudren.

To be perfectly honest, on a hot day, you’re not going to spend too much time out of the sand; it’s very inhospitable. During winter, when the weather is just right, it is a very different view on the weekend, with vehicles and people spread out for miles in both directions.

So after a very quick visit and the “walking on hot sand” dance, I jumped back in the car and headed for Cape Keraudren, which is a coastal reserve, and a bit of a surprise.(http://www.eastpilbara.wa.gov.au/Our-Region/East-Pilbara-tourism/Cape-Keraudren) It is stunningly beautiful with stark contrasts between white sand and red rocks. There are mangroves, tidal creeks, mudflats, rocky shires, incredibly white sand, salt pans and wild life. Apparently it is also the northern end of the Rabbit Proof fence. It’s a popular place for fishing and crabbing and just vegging out.

20191117_141557 — The very start of Eighty-Mile Beach, Cape Keraudren

20191117_142748 — Alone on the sand, Cape Keraudren

20191117_150202-001 — West side of Cape Keraudren.

20191117_144749-001 — East side of Cape Keraudren.

I saw Brolgas, an osprey, a kangaroo and dozens of little wading birds.

wildlife1 — Wading birds, Cape Keraudren

Osprey (sea eagle)

“Well, are we playing chicken or what?”

IMG_4844-001 — If it wasn’t for their red heads, brolgas would blend into their surroundings.

It was a great way to spend my Sunday. Some people might think spending it driving 550km isn’t that enjoyable, but, as I’ve said before, distance is relative.

I thought I’d finish with some Broome photos taken during one of my visits over the past four years, as I have talked about Broome, i.e there’s nothing between Port Hedland and Broome. Cable Beach is considered to be an amazing place to see the sunset, because there is nothing between you and the horizon. The moon rise at low tide, referred to as the Staircase to the Moon, at Town Beach, is also pretty spectacular. Enjoy.

IMG_3685-001 — Camel rides at sunset on Cable Beach, Broome.

staircase to the moon1 — Staircase to the moon, Town Beach, Broome

“You can shake the sand from your shoes, but it will never leave your soul.”

Arrived back in Port Hedland, stepped off the plane into the heat and humidity, and breathed in with pleasure. I always experience a feeling of coming home when I step off the plane even though I doubt I could seriously live here; not because of the weather but the lack of things to do. I’m not into camping or sports, there’s not a lot of restaurants, although there are a couple of really good ones. This time of the year, with the heat closing in, people tend to move inside because it’s too damn hot outside.

porthedlandtemp — Screen shot of the week.

The humidity can get as low as 5% as the heat burns it off, then, come evening, it bounces back up. It was at 48% when I got off the plane Monday night. Friday I’m heading out to Marble Bar with an expected max of 45. The thing you notice the most on these hot days is the air temperature, which is hot, even in the shade; you are completely surrounded by hot dry heat. As I walked from a classroom to the admin block, it was 41 and 8% humidity; I could feel the moisture being sucked out of my body. You have to hydrate not just your body but your skin as well. This is why people die when they go walking in the midday sun. Even if you take water with you, it’s probably not enough for your body’s needs. I have drunk about 1 and half litres of water today and I know it wasn’t enough because I am developing a headache, and I was sitting inside in air conditioning for 80% of the day and only went for a walk when it had cooled down to 35.

There’s something about the big sky country of the Australian Outback that is summed up in the quote, “You can shake the sand out of your shoes, but it will never leave your soul.” Mind you, sometimes you can’t get the dirt off your shoes; I have several pairs of shoes that are stained red from the Pilbara dirt. It’s probably why I buy pinkish shoes; it doesn’t show as much. It may be hostile but it is so beautiful. There is nothing soft and gentle about it, even on the east coast; there is a sense of raw energy.

It is really interesting to look at the early oil on canvas landscapes of the Australian bush. These early artists were trained in England and they represented the country with a softer light and the wrong colours. The prominent colour in so much of Australia is red, follow by a silvery green of the gums, yet they used brown and deep green. It took time and a change in style (Australian Impressionism) for the real Australian colours to be present. If you wander through one of the main art galleries, after awhile you begin to notice the difference in those that accepted the hash, bright light and those that continued to dream of Australia as England down under. Have a look at the following website for a more informed view: www.montmarte.net/creativeconnection/articles/show/a-short-history-of-early-landscape-art-in-australia.

The contrasts that exist in the Pilbara are amazing and I’ll show you a few in the next post, but at the moment, at this time of the year, it is simply hot. It’s a bit like the build up in the Top End which at this time of the year, it gets more and more humid until it just has to rain and everything cools down and then it starts all over again. Here, it’s not the humidity that’s the killer; it’s the heat. It builds and builds, then a ‘cool’ change comes through and it drops to …. 38.

This photo is of the sandwich container (minus sandwich) which I left in the car all day. And by the by, the rental vehicle I got this trip has leather seats; sounds grand doesn’t it, but you should try sitting on one, in a dress, after the car has been sitting in the sun all day. I need to put a towel over the seat before I receive 3rd degree burns!

I wasn’t going to talk about maths in this post but I watched a great lesson Wednesday and I want to share. Year 7 class, introduction to algebraic equations. The teacher brought a balance scale into the classroom and used it to demonstrate balancing equations. He initially set it up with 3 pen lids on one side and 15 1 cm³ blocks on the other, asking the question, what was 1 pen lid equal to? The students pretty quickly suggested 5 1 cm³ blocks were the same as one pen lid, so they tested it and, sure enough, that was right. Next the teacher added 2 1 cm³ blocks to each side asking is it still balanced and why. He then physically set up another problem, with 2 pen lids and 3 1 cm³ blocks on one side and 13 1 cm³ blocks on the other. He then walked the students through the CRA process. CRA stands for concrete, representational, abstract. What it looked like is below:

They then repeated with yellow weights that looked like a sombrero, which they labelled as ‘s.’ The students were totally engaged, which for this group was pretty impressive, and they were solving algebraic equations without realising it. When the teacher informed them the end of the lesson, they were all pretty impressed with themselves.

I’m hoping to fly my drone sometime this week but it’s really windy. I’m off to Marble Bar tomorrow, so I think I’ll take it with me and see if I can get some shots. I’ll also be taking a lot of water, just to be on the safe side. You don’t want to break down in 45 degree heat and be short of water.

Signing off with a sunset taken at the salt ponds here in Port Hedland.

“Now this is not the end.”

Now this is not the end. It is not even the beginning of the end. But it is, perhaps, the end of the beginning. Winston Churchill

First last days started this week; it’s sad, that after 4 years of visiting these school, their staff and students, there will be no, “I’ll see you next term,” as I walk out the door. Having said that, I am excited about the future so really, like Churchill’s sentiment, it is the end of the beginning. I have spent the last 4 years learning so I can confidently move to the next stage. I guess leaving the people I have met in Port Augusta isn’t too upsetting as I will be coming back in some role or another, and I will still be in contact and see many of them in and around Adelaide.

This week, I have had a number of discussion around planning for next year and what should be taught first. I have a number of views in this and most of them are not, as far as I’m aware, research based, but the result of years of teaching, talking with other teachers and the round-about of education. If you disagree, sorry and if you have research to demonstrate what I think is wrong, please point me in that direction.

I talk to teachers at all year levels about the importance of putting maths in context and my personal belief that starting with fractions, time, money and/or measurement, depending on the year level, are as good a place to begin the teaching and learning year as any.

Telling time using an analogue clock is a dying skill as most people, these days, use digital time. If you want students to learn to tell the time using an analogue clock then you have to give it a purpose. So teach it at the beginning of the year then, as the teacher, make the commitment to refer the students to the clock constantly. When they ask, “Can I go to the toilet/get a drink? What times lunch/recess/home time/PE? How much longer until…?” respond, according to level, “At quarter past/half past/quarter to/ 5 past/ 20 past etc., in 10 minutes, in five minutes….” Always look at the clock and refer the students to it, expect them to use the clock to tell the time and not view it as a room decoration. Time then becomes part of everyday life and not a 2 week unit. Once upon a time, (okay, when I was young, which was some time ago,) getting a wristwatch was considered a milestone, and it was an analogue watch, not digital. Most wristwatches are now digital; Fitbits or something similar.

Set up a classroom economy at the beginning of the year and have the students managing it by the beginning of term 2. Again this builds in money as an ongoing teaching and learning strategy rather than a ‘two week’ unit and it becomes part of everyday schoolroom life. There are lots of websites on the classroom economy as it can be adapted to work for all age levels. I have seen it working very well in a year 1/2 class, as well as in year 6 level. The sophistication of the economy is dependent on the year level, but, again, you as the teacher, must commit to it.

strip_fractions2 — “Why my half bigger than your?” Reinforcing the concept that the size of the half is dependent on the size of the whole or collection.

$strip_fractions3$

Why fractions early on? In the national curriculum in Australia, half past and half are taught in Year 1; half, quarters and eighths of objects (whole) and collections and quarter to and quarter past are taught in Year 2; the concept of unit fractions and their multiples in year 3 along with telling time to the nearest minute, which, personal, I think is a huge jump so would focus on five minute intervals. Beyond Year 3, the curriculum begins to contain an increasing amount of content, with a lot of which is fractions, decimals and percentages focused. By the time students are in Year 6, more than 50% of the achievement standard has this focus, yet, in all honesty, these extremely important concepts are addressed as a separate unit of work maybe in term 3 for a few weeks and less than 25% of the teaching and learning time is spent on it.

Lastly, measurement. If you unpack the using units of measurement component of the Measurement and Geometry strand, the following action verbs reoccur; compare, order, measure, convert, all of which use number. Even in years 1 & 2 where uniform informal units are used there are opportunities to link measurements and number particularly with the extended subtraction concepts of missing addend and comparison.

My foot is 12 unifix long but I only have 8. How many more unifix do I need? or My height is 16 paddle pop sticks, Jane’s height is 10 paddle pop sticks. What’s the difference in paddle pop sticks?

Often strands are taught separately with students not seeing the connections between them, while teachers struggle with the ‘crowded curriculum.’ In Year 6 a content descriptor in the Measurement strand clearly states ‘connect decimal representations to the metric system’ while in the Number strand ‘multiple and divide decimals by powers of 10’ directly supports ‘convert between common metric units…’

Off back to Melbourne for 2 nights then back on the plane for my final trip to Port Hedland. Safe travels everyone.