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

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.
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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

“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.

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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.

PA_SpencerGulf_Stillness1 — The stillness that settles at times over the Spencer Gulf, SA

Same view at low tide and when it’s blowing a gale and dust is whipped up

SO it begins….

I am going to try and do a post a week for the next 8 weeks as the count down to the end of the year and the completion of my role as an AMSI ORO (Outreach Officer) begins. Today, Sunday, I am up early and at the airport to catch a flight to Adelaide, South Australia. From there I pick up a car and drive 310 km to Port Augusta. I quite enjoy the drive as, while it can be very busy, it is a good road. The wonderful people at the Majestic Oasis Apartments look out for me and if I’m later than expected they check to make sure I’m okay. As a single traveler, frequently on the road, I greatly appreciate this as it’s nice to know someone is watching your back. I always get one of two rooms from where I have taken many photos of the Spencer Gulf.

Port_Augusta6 — View from the balcony, calm Spencer Gulf.

As I said I quite enjoy the drive. Sometimes on the way back to Adelaide, if the road is really busy, full of grey nomads and road trains, I will turn off and head for Wilmington and take the route through the Clare Valley, which takes longer but is quieter and prettier. If I have time I love wandering through the back roads of the Yorke Peninsula. The settler history of South Australia is fascinating and scattered all over the Flinders Ranges and the Yorke Peninsula. As I am moving to Adelaide in the new year, I will have the opportunity to capture digitally as many of these old places as I can. Maybe I’ll have an exhibition sometime.

I have got used to driving long distances over the past 4 years. I remember my first long drives in the Territory were a lot more difficult and Tim did most of the driving. The trick is to have a good book to listen to…Yay for audio books on mobile; no changing discs. Music tends to allow the brain to wander, which isn’t great when you are driving or it puts me to sleep (also not good.) A number of my colleagues recommend podcasts particularly true crimes but not really my cup of tea.

I have been very fortunate to have had the role of ORO for 4 years. I have learnt so much about the teaching and learning (T’n’L) of maths which has made me even more passionate about the importance of increasing engagement in maths and developing teacher confidence and capacity. Some of the most interesting aspect of T’n’L that I have learnt over the past 4 years have been not the actual content or pedagogy but the neuroscience, the mindset and the psychology of learning. I have thoroughly enjoyed developing my own depth of understanding around the T’n’L of fractions, decimals, ratios, rates and proportional reasoning. I always knew these were important components of mathematics but the research that demonstrates the direct links between competence in fractions and division in years 5 and 6 and general mathematical understanding and success at years 10 and 11 was a revelation.

playdoh7 — I’ll share this activity in a later post.

It was, however, the understanding of how the brain learns, the importance of mindset and adolescents’ beliefs when it comes to learning maths that have really challenged my way of thinking about T’n’L of mathematics. Students ‘switch on and switch off’ maths and often it takes only one teacher to do either. Maths is the poor cousin to English. As maths teachers, when asked what you do, are generally greeted with comments such as “I hate maths,” “I’m hopeless at maths,” “I had the worst maths teachers, that why I can’t do maths,” “I’m not a maths person,” or something of similar ilk. Maybe occasionally you might get a story about a great maths teacher and how they really help build confidence and self-perception of the speaker as a maths learner. If you announce that you’re an English teacher, you seldom get, “I had English” or “I’m hopeless at English.” We have to address the negativity around maths that exists in the wider community. And while parents’ perceptions and beliefs play a big role, we, as educators, must strive to make maths most relevant, useful and interesting in schools. And NO I am not talking about making it FUN. Professor Di Siemon, a well respected Australian mathematics educator, talks about success breeding engagement, not the other way around.

Bells and whistles will not guarantee success. Which is a problem when an excited teacher talks about how fantastic a lesson was, and a colleague asks for the lesson so they can ‘do it’ too. The first teacher may have delivered that lesson as the 3rd, 4th even 5th lesson in a sequence with the students experiencing success along the way, building their confidence and capacity. A one-off lesson, removed from its basis, is not going to have the same impact. David Ingham, a former mentor of mine, called these the Kaos Torturer’s theory of teaching. Max is strapped to the torture table while the Kaos torturer consults the Koas Book of Torture. He finally finds something and says, “That’s a goodie.” It is obvious he’s already tried something else which hasn’t worked even though it should but Max seems immuned. Too many lessons are presented as ‘goodies’ rather than considering what is really needed.

I am going leave it there for today as I have now arrived in Port Augusta. I want to talk more about Di Siemon’s work in the Big Ideas in Number, the work of Dr David A Sousa’s on how the brain learns and Professor Jo Boaler’s work on Mathematical Mindsets. Along with research into adolescents’ engagement and disengagement in maths and maths anxiety, these 3 have had a big impact on how I think about the T’n’L of mathematics in both primary and secondary schools.

I’m finishing with a sunset, taken in Port Augusta, but not today. I am planning to try out my drone tonight which I have recently bought. Hopefully some interesting photos to come.

MERGA in Perth

So where am I this week? Perth, Western Australia. Why? For the MERGA (Mathematics Education Research Group of Australasia) Conference. This is my first MERGA conference and already I have a few new ideas and/or elaborations for lessons.

Yesterday (Saturday) was teacher day so the workshops were very hands-on and focused on research that has very practical applications to the classroom. The keynote was delivered by Professor Doug Clarke, a name any maths teacher in Australia worth their salt, should know. He shared research on many things but perhaps the thing that hit home to me was about time, in particular wait-time after asking a question. Research from 35 years ago suggested that 1 second was the average time given to students to supply and answer before the teacher reframed, reasked or redirected the question. Waiting just 2 more seconds before doing so makes a huge difference. Interestingly, someone queried the validity of still refer to this research, because: ‘The teachers in that survey (35 years ago) were from a COMPLETELY different generation. I’m leery of basing change recommendations based on it.’ I visit classrooms on a regular basis and observe teachers teach, and my response is it is a valid now as then. Teachers often feel awkward in the silence and rush to fill it, even more so at secondary level than primary. And the problem at secondary level, the students quickly learn that if no-one responds the teacher will move on or supply the answer so very little thinking needs to be done.

I went to listen to Paul Swan first up. Paul is a well known WA Mathematics educator who always has good, practical ideas (https://drpaulswan.com.au/ ) In a Paul Swan session you know you will be playing with stuff as well as learning something. The workshop was titled “Problem Solving and Reasoning in The Early Years,” so we started with some subitising with dominoes. This quickly moved on into problem solving and using language to explain your thinking. Using dominoes, making a train (each domino is a carriage) that contains 10 dots. You have to abide by the rules of dominoes i.e. like to like. Now make the longest train with 10 dots. At a much higher level than Foundation (First year of school in Australia) use 5 dominoes to make a train with 20 dots. Lots of opportunities for older student to really think about addition of multiple single digit numbers. Then we moved onto attribute blocks as basic sorting equipment but again he extended in many ways including using all blocks to complete a circle where each subsequent block had two attributes different.

The second workshop I went to was with Jana Visnovska (The University of Queensland) and Pamela Vale (South Africa) called “On supporting students’ mathematical conversations:The case of fractions as measures. I found this session very interesting as teaching fractions is of particular interest to me. They talked about introducing fractions through measurement without direct reference to fractions. When we first start to teach measurement we use informal measures to encourage students to discover the need for formalised units of measure. They have written a wonderful picture book called “Mama Khanyi and the Pots” to introduce informal uniform measures and ‘smalls.’ The stick is the measure, but there are the 2 small, which fits along the stick exactly 2 times, the 3 small, which fits along the stick exactly 3 times etc.. What is being created is essentially a linear fraction wall, but you only have one 2 small, one 3 small, one 4 small etc., rather than 2 one half, 3 one thirds, 4 one quarters etc.. you do not refer to these in their fraction form but as smalls. I am going to explore this concept further as I think it has merit and may get students thinking.

$fraction wall 1$

Area Fraction Wall

Stick with a 3 small (exactly 3 fit the stick)

The last workshop was with Doug Clarke (keynote speaker) and Anne Roche (both from ACU). The research into teaching fractions, decimals and percentages these two, along with other colleagues, have done over the years is at the heart of the professional learning my colleagues and I deliver to teachers as part of our role as Schools Outreach Officers. It was a pleasant to sit and listen to them and an reaffirmation of the work we are doing in the area of fractions, decimals and percentages, a topic as I have mentioned already, I am passionate about. It was even better having the opportunity to share how I’d had extended a couple of aspects; e.g. The use of the part of a whole shape to scaffold parts of a collection and the importance of rewording the question if it is presented solely in abstract form.

$fractions2_1$

An interesting day over all.

Sums, sets and sunsets

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Mathematics has beauty and romance. It’s not a boring place to be, the mathematical world. It’s an extraordinary place; it’s worth spending time there.

Marcus du Sautoy

Professor du Sautory words ring so true to me and is something I live and breathe every working day. It, however, is at times a struggle to persuade others that it is true. I have an incredible job; along with 7 colleagues, we travel the width and breadth of this amazingly beautiful and diverse country, Australia, working with teachers, school leadership, students, parents and the general community, trying to encourage and enable people to spend time in the wonderful world of mathematics. At the same time, we get to experience some stunning, and not so stunning, parts of the country. While we outreach officers are out on the road, there is also a talented team that manages marketing, media, research, careers awareness and mentoring around the country, as we all work towards raising the profile of mathematics across every aspect of the community.

I have had this job for 3 years now and, with 2019 the last year of the project, I decided to blog my way through the next 12 months, sharing stories, thoughts, discoveries, hopes, mathematics and sunsets.

The idea for this blog came from Chris, my brother-in-law, when he suggested I write a book called, ‘Sums, Sets and Sunsets,’ about my job and travel. Why sunsets? Well, it has become a standard practice among the team to share what we refer to as ABS (Another Bloody Sunset or Sunrise) and I frequently share my ABSs on my FB page so friends and family can see the beauty that this country can throw up.

I also thought it would be a great opportunity to share the amazing journey I have been on, both professionally and personally as, while I have 35 years plus experience as a teacher, the last 20 as a numeracy specialist, the last 10 as a teaching and learning coach, I have learnt so much over the past 3 years, I seriously wish I had another 35 – if only I knew then what I know now and what I will no doubt learn in the coming year.

I decided to go with a blog because there may be others out there in this wonderful global world that are interested in what I do, I think, I hope and I see. If there are, I hope you will join me on the journey.