How to pronounce Mandarin Chinese in under 15 minutes.

In late 2013 I set myself a challenge of getting conversational in Mandarin Chinese in one year. One of the biggest barriers to me reaching this goal was the pronunciation of the language, as it has many foreign sounds to a native English speaker.

Throughout my journey I came across a whole host of incredible resources, from the website Hacking Chinese to the Glossika approach, that really helped me to overcome this challenge. Over summer I sat down with my brother (who is now also learning Mandarin) to try to give him a bit of a crash course on what I had garnered from these resources. Please find a video of that lesson below with the associated document and links embedded below that. I hope that Mandarin learners of all stages find this a helpful article.

An additional tip that I didn’t mention in the video is the benefit of recording yourself and playing it back to check how you’re tracking with your pronunciation. I can’t recommend this approach highly enough. Good luck!

WHY CAN’T THEY REMEMBER THIS FROM LAST YEAR??? Help students remember key information: Spaced Repetition Software (SRS).

This post is one of a series detailing my current mathematics lesson rhythm and routine. This one outlines how I use spaced repetition software (SRS) at the start of my lessons to help students to remember key information. There is a video of me teaching with SRS at the bottom of this post. 

Thinking back to my own time at school, I distinctly remember one challenge in particular. I remember feeling that studying  mathematics in discrete topics (or units), made it really hard for me to remember the relevant concepts when it was time to revisit that branch of mathematics again, sometimes over a year later.

Through my post-schooling forays into language learning in particular, I have come across some research backing up those schoolboy intuitions.

What I was feeling was the effects of a cognitive phenomena called the ‘forgetting curve’ (Ebbinghaus, 1913). The forgetting curve (pictured below) is a graph that approximates the rate at which an individual will forget a given unit of information.

the forgetting curve

(image source:

In the late 1800s, a German chap by the name of Hermann Ebbinghaus constructed the first forgetting curve by trying to memorise nonsense syllables (such as “WID” and “ZOF”) and then testing himself at regular intervals, rating his level of accuracy, then plotting these points out on a graph.

Hermann Ebbinghaus

(Old mate Ebbinghaus:

As can be seen in the picture of the forgetting curve, if we want to remember something, we need to be reminded about it at regular intervals*. The good news is that the more times we’re reminded about it, the longer the interval until we need to be reminded about it again!

*(The necessity of reviewing a unit of information at regular intervals is obviously dependent on what the unit of info is, and how it relates to your prior knowledge/how emotionally charged that memory is. For example, It’s highly unlikely you’ll ever forget your first kiss! Ebbinghaus’ original forgetting curve is, however, a great approximation for units of info like; words in a foreign language, or even terms such as ‘perimeter’ or ‘circumference’.)

Such a curve has important implications for teaching and learning. If we want a student to remember the basics of trigonometry when we come around to the topic again a year later (e.g., basic terminology, sum of the angles in a triangle, etc), we had better ensure that several times between now (time of teaching) and next year, they get reminders at key intervals.

The basic idea underlying this reminding-at-intervals is the spacing of repetition. We all know that it isn’t a good idea to cram your study, but a recent meta-analysis of studies, Carpenter, Cepeda, Rohrer, Kang and Paschler (2012) brought together research on the actual effectiveness of spacing repetition. The following excerpt details the results from just one of the studies that they cited in their meta-analysis.

the benefit of spacing repetition

(Carpenter et al., 2012, p. 371)

This is all well and good as a concept, but how can we do it in practice? There are literally hundreds of new words and concepts that a student is expected to grasp in a year, is it realistic for a teacher to keep track of each of these terms and ideas, and remind students of all of them at periodic intervals?

I’m hoping that the answer is yes.

In 2014 I set myself the challenge to learn Mandarin Chinese in a year. As I delved deeper and deeper into effective learning methods,  I came across spaced repetition software (SRS). SRS is a program of digital flash cards (you can make them yourself, or download pre-made decks) that, based on self-ratings, uses an algorithm to calculate the optimum time to review each given unit of information. It is essentially plotting your forgetting curve and reminding you of that piece of information just before you forget!

This software has been notably used to great success by such polyglots as Scott Young (who learnt 4 languages to a very high standard in one year) and Benny Lewis (very famous polyglot). It definitely helped me, and with the help of the SRS program that I use, Anki, I was able to  reach my goal and achieve a conversational level of Mandarin within a year. These days I use it to remember a whole host of things; from people’s names, to new english words, to the countries of the world. I currently have a little over 3000 digital flash cards in my review ‘circulation’ and to keep on top of all this info it only takes between 10 to 15 minutes of my time per day. Here’s a snapshot of my study statistics from the last month.

Anki statistics

(my personal spaced repetition data from the past month)

I was really keen to bring this incredibly powerful tool into the classroom to try to help my students to overcome the memory challenges that I, myself, faced as a student. So I did!

Since I started teaching at the start of this year, I’ve been using an SRS program (Anki)  in all of my classes. We use it at the start of every lesson and I call students’ names with the use of coloured pop-sticks, a method that I’ve written about previously.

The result?

It’s hard to comment on the long term effects as it’s still early days, but student feedback has been good, for example: On the end of Term 1 feedback form that I handed out to students, many of them made comments such as the following:

But hey, I thought that the most helpful thing would be to give readers some eyes into my classroom to see exactly how it plays out. With my students’ permission, I’m sharing below a clip from my  VCAL (Victorian Certificate of Applied Learning) numeracy class. Just for a bit of context, VCAL is a program designed for students who are planning to explore post-secondary pathways into vocational training. I have students who want to be nurses, flight attendants, and many of them aspire to the a position in the military. What you see below is a classic beginning of lesson episode. One of the students (Sharnee) is in charge of the pop-sticks, pulling out student names, and the other students are sitting (with varying degrees of focus), considering what their answer would be, then answering if their name is called up. I’ve found that the students enjoy the routine and it adds a game show like feel to the start of the class. Hopefully this little clip gives you a bit of a glimpse into how Anki works, and how I feel it can help my students to overcome one of the challenges that I myself faced in school.


Carpenter, S. K., Cepeda, N. J., Rohrer, D., Kang, S. H. K., & Pashler, H. (2012). Using Spacing to Enhance Diverse Forms of Learning: Review of Recent Research and Implications for Instruction. Educational Psychology Review, 24(3), 369–378.

Ebbinghaus, H. (1913). Memory: A contribution to experimental psychology, (3).



A Problem Solving Spell!

I’m super excited about sharing this ‘Problem Solving Spell’. I modelled it on the problem solving template outlined in Charles & Lester (1984, p. 20), a pic of which I’ve also included at the bottom of this post.

Please feel free to use as you see fit, I’ve included the text below the pic incase you’d like to format in some other way.

Problem Solving Spell























A Problem Solving Spell
In a test or in a lesson
Come across a tricky question
No need to worry, fret, or doubt
This solving spell will help you out

Read the question carefully
Which words or phrases might be key?
Do you understand ok?
Now write it in another way

List what you already know
This gives us hints of where to go
Draw a pic, or act it out
Visualise what it’s about

List your info in a table
Spot a pattern, if you’re able
We now are only half way through
The many tricks that you can use

Struggling to make progress?
Working backwards could be best
Make the question simpler
Or solve a problem similar

But sometimes there will come a time
You’ve thought, and thunk, and tried and tried
Eventually say, ‘what the heck!’
And have a crack at guess and check!

You’ve found an answer, good for you!
And showed your working right way through
Before you’re feeling too spellbound
CHECK THE ANSWER that you’ve found!!!

Basis for the ‘spell’ (Charles & Lester,1984, p. 20)

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Charles, R. I., & Lester Jr, F. K. (1984). An evaluation of a process-oriented instructional program in mathematical problem solving in grades 5 and 7.Journal for Research in Mathematics Education, 15-34.

Extending linear arithmetic blocks (LAB) to a circle’s diameter:circumference relationship

In the quest to make a circle’s diameter:circumference ratio a little more tangible to my VCAL students I thought of a way to extend linear arithmetic blocks (LAB) to this new context.

Cut out 6 or 7 pieces of string/rope, each as long as your LAB ‘one’ length. Cut out two bits of rope of length equivalent 0.14 w.r.t your LAB resources.

Go outside with chalk. Use one of the one’s to draw a circle of diameter one as pictured below.

Make clear to students that the pieces of string are the same length as one.

Ask students: What’s the diameter of this circle?

Ask students: How many of these (holding up a string of unit one) do you think will fit around the outside of this circle? (You can tally answers if you like)

Get volunteer students to place the string neatly around the outside of the circle, as pictured below.Classify the answer as ‘3 and a bit’. Bring out your ‘bit’ (the length of 0.14). If you’ve done the circle neatly it should neatly fit!

Get some students to use LAB to measure the length of the ‘bit’. It’s equal to  0.14! (reinforce the language, it’s on tenth and four hundredths).Ask: So, when we have a circle of diameter 1, what’s the circumference?

Draw a circle of diameter 2, repeat the process!

Go back inside and draw the learning together on the board, give students 3 or so example questions to check their understanding.





Basic Auslan for Maths Teachers

Today whilst observing a fellow maths teacher at my school, I saw her use some Auslan (one form of sign language) with one of the deaf students. I thought, ‘Wow, I want to be able to do that’. So, at recess whilst in the staff room, I asked for a little impromptu lesson…

It’s not a pretty video, but I definitely think it was a worth while 4 minute time investment for me. Pardon the eating, and happy Auslan learning : )

‘The Points System’: One approach to differentiation

When I was in school I remember that I found nothing more boring than the instruction to ‘do questions number 1 to 5, parts a) to h)’. I would get my head around the concept by question b or c of each section, then have to spend what seemed like an eternity working through a whole bunch of exactly the same question with different numbers. With this knowledge of my own experience in mind, I’ve always known that I wanted to try to avoid this same boredom for my own students.

This approach to differentiation and boring repetition reduction was brought to my attention by one of my Masters of Teaching lecturers Nicky Dulfer, who said that one of her friends had implemented an ‘earn points’ system in their own mathematics class. I thought it sounded like a nice idea. Here’s how I approached it…

The slide I showed to students: 

For those unfamiliar with the proficiency strands of fluency, understanding, reasoning and problem solving (‘open-ended’ in this case), here’s an example of a few example Q’s for context (from the Pearson Mathematics 9 Textbook).


Did students like it?

This was implemented with a year 9 mathematics class.

Mid placement feedback: In response to the question ‘What should Ollie keep on doing?’ five students nominated the points system. In response to the question ‘What should Ollie stop doing or modify?’ no students nominated the point system. (Highest number of votes for any one category was 8, which was to suggest that I continue making videos of content).

End of placement feedback: In response to the question ‘What did Ollie do that most helped you learn?’, four  students nominated the points system. In response to the question ‘What are some things Ollie shouldn’t do in future, or things to modify’, one student said ‘Point system (15 in 30 minutes was too rushed and stressful)’. (Highest number of votes for any one category was 12, which was to suggest that micro-revisions (post on micro-revisions to come…) were what most helped students to learn).

So, on the whole, the points system was well received by students.

Did it help the students to learn?


Unfortunately I didn’t conduct this points system long enough to be able to tell if it increased student learning. But I can say that it appeared to increase engagement, and as ‘a major precursor to learning is engagement’ (Hattie, 2012, Chapter 8, Section 2, para. 1), it’s plausible that it increased learning.

I do however think that it’s fair to say that this task helped the higher achieving students to learn more. After they had gained their 15 points (some of them would finish this in under 10 minutes), students were able to move onto ‘challenge questions’, like the pythagoras challenge questions that I’ve written about previously. The traditional approach for these students was to get them to do a set of questions from each of the proficiency strands (fluency, understanding… etc), which would take up the whole lesson, and was pointless in many cases as these high achieving students could easily complete the task and weren’t being challenged at all.

The idea of students self-differentiating was also intended to help promote metacognition. Fostering metacognition is a key step to helping students to ‘become their own teachers, which is the core attribute of lifelong learning or self-regulation, and of the love of learning’ (Hattie, 2012, loc 168). But actually scaffolding this metacognition is something that I need to do better in this task and in the classroom more generally. I feel that it’s unreasonable to assume, as I implicitly did, that a year 9 student will be able to select a question at the appropriate level without any help.


I feel that this task was a step in the right direction and, coupled with the power of spacing repetition of content for students (Carpenter, Cepeda, Rohrer et al., 2012), has great potential to be expanded and improved upon in future. One immediate improvement to make would be to have ‘challenge questions’ (for students who work through the 15 points) of different levels of difficulty, rather than just the one ‘challenge question’ that wasn’t so easily accessible to some students.

Note: Sunshine College has taken a similar approach where students select for themselves a ‘just right’ task and form small groups to solve it. This is an approach that I’ll be exploring more in the near future. You can read a brief paper about it here.


Hattie, J. (2012). Visible learning for teachers. [Kindle version]. Retrieved from

Carpenter, S. K., Cepeda , N. J., Rohrer, D., Kang, S. H., & Pashler, H. (2012). Using Spacing to Enhance Diverse Forms of Learning: Review of Recent Research and Implications for Instruction. Education Psychology Review , (24), 369-378.

Teacher Blogger chat at MAV Conference 2015

At MAV Con the other day I sent out a tweet to catch up with other teacher bloggers:

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It was a small meeting (only 2 of us), but I was happy to have the opportunity to meet with fellow teacher blogger Michaela Epstein. Aside from a great chat that touched on our backgrounds, motivations for teaching, and even spaced repetition software,  Michaela and I turned to a few questions that I’d drafted up to get into the why, how, and what of our blogging approaches. Enjoy : )

Screen Shot 2015-12-08 at 8.26.43 amMichaela Epstein


    • twitter handle: @mic_epstein
    • blog address?: 
    • Where are you based (as much detail as you’d like to give)?: Melbourne

Juicy Q’s

  • Why do you blog?: Initially was to give non-teachers an insight into what actually happens in schools and give an understanding of the social side and social justice side of the school context. Since starting teaching it’s taken on a maths/social justice focus.
    • What part/s of your blog/blogging are going well?: Get good feedback from people who read it. A useful way to express some complex ideas that I think about then communicate that with others. Good way to start interesting conversations.
    • Which blogging/social media apps or programs do you find core to the way you do what you do in the blogosphere?: Twitter is being used more and more, easy, quick, can share stuff, low barriers to entry and great way to connect with others.
    • What is a challenge that you’re contending with at the moment w.r.t your blogging/use of social media?: Not doing it /not doing it regularly.
    • What’s your favourite Ed blog?:   it’s a U.S dude now in the UK (also social commentary on maths education). His blogs are usually just cartoons with annotations on those cartoons.
    • Why?: This website gets to the crux of the philosophical issues that we deal with as maths teachers.

Ollie Lovell


    • Twitter handle: @ollie_lovell
    • Blog address?:
    • Where are you based (as much detail as you’d like to give)?: Melbourne, gonna be doing research with a Northern Metropolitan Region school in 2016.

Juicy Q’s

    • Why do you blog?: To sort through my own ideas, share what I do in my classroom, and as a way to force me to reflect on books, conference, etc.
    • How would you describe the focus of your blog?: It’s really about my learning journey. I’ve taken the title so that I can be really flexible just to be me and explore and blog about what’s relevant for me. Main foci are wot-I-got from various conferences/books, what I’m trying out in my own class, and my learning journey more broadly
    • What part/s of your blog/blogging are going well?: I’ve enjoyed particularly sharing some of my classroom approaches recently.
    • Which blogging/social media apps or programs do you find core to the way you do what you do in the blogosphere?: The Google Docs Add-on Docs to WordPress. Allows me to write posts in google docs then export to WordPress. Saves a bunch of time in uploading photos and makes it easier to collaborate on posts.
    • What is a challenge that you’re contending with at the moment w.r.t your blogging/use of social media?:
      • Keeping up with twitter and sorting the wheat from the chaff!
      • Ordering/sorting the content on my website to make it easier for punters to use
    • What’s your favourite Ed blog?: Dan Meyer’s blog and the less well known BetterExplained.
      • Why?: Dan’s creativity and the way that he does things in his class blows my mind. Kalid’s work on BetterExplained has helped me to understand maths better.


MAV Conference 2015 Highlights

Selected notes and titbits from this year’s MAV conference  :)

Matt Skoss

Hungarian sorting dance

Can use this for decimal examples?

(assume this is a cube, phone stretched the pic…)

(Extension cube from above still to come…

Matt says to check out brilliant for heaps of awesome maths problems!!!

You can find Matt Skoss’ conference notes here.

Peter Sullivan and Caroline Brown: Turning engaging tasks into robust learning

Question: What’s bigger, 2/3 or 201/301?

A few that I was thinking about…, What’s bigger, 4/5 or 444/555? What’s bigger, ¾ or 306/408

Extension: is a/b always < (a+1)/(b+1)??? (always true, sometimes true, never true???)

Question: ‘I wasn’t paying attention in class but I heard the teacher say ‘a turning point is at (2, -3).’ What could the function be? (then, think of another one)

Enabling prompt: change the turning point to (0, -3)

Question:  I saw 10 legs under the farm gate. Draw which animals I might have seen there.

Another Q…

Peter’s Slideshow:Peter Sullivan-Turning engaging mathematics classroom experiences into robust learning

Caroline’s Slideshow: MAV secondary 2015 fractions-Caroline Brown

Yvonne, Jodie and Thao from Sunshine

The award winning Maths program at Sunshine.

The weekly lesson breakdown.

Keep the kids informed about their progress “You started 6 steps behind the other students in the state, and you’re catching up.”


Tasks look similar, but they are different

Students learn how to select task for themselves

In it for the long game. Supporting students to make the right choices for themselves!

Challenge with worded problems (Reciprocal Teaching)

Check out the amazing resources from Sunshine . See more on Sunshine’s numeracy program . They also recommended NAPLAN as a great place to source questions from.

The Steps of Reciprocal Teaching

  • Predict
    • Recognise key worlds and use them as keys to determine the area of maths that they’re looking at.
  • Clarify
    • Re-read the question. Get to a point where they’re comprehending the text. Identify vocab that they don’t know and extract the key info they think they’ll need to solve it.
  • Big Question (added on top of literacy approaches)
    • Recognise and articulate the main problems.
  • Solve
    • Solve and check your answer.
  • Reflection
    • Talk about how the problem was solved. What was there that you learned that you’ll be able to use in future
    • (This is the section that students often struggle with the most!)
      • ß High expectations are they key here!
      • Note: They used to ask students to write a reflection based on the learning intention but found that that was too difficult for students.
    • They’ve thought that they should encourage students to make a glossary!!!
  • ‘It’s a bit smoke and mirrors…
    • The effort goes in prior to the lesson to ensure that the questions are quality and pitched at the correct level.
    • Expecting students to do about 3 problems in a session BUT if it’s a very challenging question sometimes they’ll work on one problem for two lessons!!!
  • Cool tech. ‘Plickers’!!! (matt laminate them!!!)

(the Sunshine reciprocal teaching worded problem page looks like this…)

Sunshine’s Reciprocal Teaching Sheet (Also available on their website).

Yvonne’s tip. ‘A quick acid test to see how  good your teacher is to give them a set of questions and see if they ask for the solutions.

Scaffolding Numeracy in the Middle Years approach

They group the students. But it’s ok because there are 9 groups and it’s hard for students to work out which group they’re in.

Lots of teachers. Teachers have 2 groups each (each in a different zone). A teacher will take a lower zone group and a higher zone group. It’s all about the bigger classes, because that means there are more people in the groups and you’ve got the free teachers : )

Fluency (Speedy Maths)

Flash cards, time them, keep track of their times so they can track their improvement.

Students do graphs so they can see their own learning progress.

You can make multiplication sheets in excel with a random number generator!

Growth Mindset

No topic tests

Progress is valued above all else

Data Driven

On demand testing (4 tests per year, 2 number and 2 general)

Wendy Taylor and Sabine Partington’s session

Question from another punter: Take any ‘L’ shape and, without doing any calculations, determine a way to cut it exactly in half with one line (I don’t know the answer to this yet!)

Allan Thomson, Maths on OneNote

  • Students can have their own pages
  • com
  • Check out
    • Onenotecentral (on twitter)
    • OneNote Toolkit for Teachers

Some selected tweets extras

This blog post by Dr Nic on Engaging students in learning statistics using The Islands was brought to my attention by James Dann.

Regarding the tweet below: Sorry Sara McKee, spelt your name incorrectly!)

Keep an eye out for Sara’s upcoming paper:  ‘Using teacher capacity to measure improvement in key elements of teachers’ mathematical pedagogical content knowledge.’

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Lessons from Myanmar: Cartesian co-ordinates and Fruit Salad

On November the 8th, whilst millions of excited Burmese voters headed to the polls, I arrived bleary-eyed and hungry from an overnight bus ride in Myanmar’s second largest city, Mandalay.  Along with 9 other pre-service teachers and our two group leaders, I was about to start a two week teaching placement at the Phaung Daw Oo Monastic School.

This post is about what I learned from that two week placement. I’ve chosen to present it through the ‘case study’ of adapting a lesson on Cartesian co-ordinates from the Australian to the Burmese context. I feel that the process of adaptation provides a good framework for me to discuss and explore my two main learnings from the trip, one on the use of language in the classroom, and the other on modelling.

The genesis for this lesson was in August of 2014 when I was lucky enough to attend a Dan Meyer workshop at the Love Learning Conference in Sydney. Dan introduced attendees to a ‘fruitful’ approach to introducing Cartesian co-ordinates to students. Almost exactly a year after that first workshop, I used a very similar approach in the first lesson of my second placement with a class of year 9 students.

The following video shows how I did it in Aus[1].

Fruit Slideshow (in case you’d like to use all or part of it in your class)

Students appeared really engaged in this approach. They loved the debates about who was better at describing things, and about which fruit was tastier or ‘easier’ than the other. Upon leaving one student remarked, “That was a really good lesson, sir.”

When I arrived in Myanmar and my associate teacher, Thanta, told me that it would be good if I could do some lessons on Cartesian co-ordinates (she called them rectangular co-ordinates), this introduction seemed an obvious choice[2]. The task became, how to adapt it to the local context? There were three main challenges that I anticipated.

  1. Would students understand the concept of ‘rating scales’?
  2. Very limited English
  3. No electricity

Addressing challenge #1 – Rating scales:

This wasn’t too hard. It required me pacing the ‘Tasty’ spectrum (I altered it to go from -5 to 5 to make it clearer on the blackboard) and miming delicious at one end (rubbing stomach and making contented chewing sounds) vs. disgusting at the other (pretending to be sick). Then doing this a few more times. That was the easy part…

Addressing challenge #2 – Very limited English:

The first big lesson for me from this placement came through the challenge of surmounting the language barrier. To give you an idea of the level of English competency of my classes, if I asked ‘Please get your books out and write this down’, about half of the class would understand the instruction and begin, and the other half would copy the half that understood. This is where I was able to explore, in context, the concept of CLIL (Content and Language Integrated Learning). What CLIL means in a maths class is that the goal of every lesson isn’t just to teach maths concepts, but to simultaneously teach maths concepts as well as the language required to understand and talk about them.

Here’s what my lesson plan for the Myanmar fruit lesson looked like…

The green box down the bottom was the text I put on the board to help structure the lesson (note: It was way too ambitious, we only made it to ‘rectangular co-ordinate systems’).

Orange box up top represents the sentence that I wrote on the board to introduce the idea of a ‘scale’ to students.

You’ll note I changed the y-axis title from ‘easy’ to ‘easy to eat’ to reduce ambiguity.

More broadly, I adopted the Q:, A:,  format that permeates the lesson plan as a way to teach students that I wanted students to answer in full sentences (related to the CLIL approach). They were quite strong with their numbers, for example, if I asked ‘How tasty is a pineapple’ they would be quite confident saying ‘minus 5[3]’ but saying ‘On a tasty scale of -5 to 5, I think a pineapple is -5[4]’ was a serious challenge for all but a few of them. Through this challenge, and the placement more generally, I became aware of the importance of scaffolding the language needed to express the ideas. As can be seen, this whole lesson plan is structured around supporting the students to employ a few basic sentences, inclusive of key vocabulary, to communicate the mathematical ideas. For me this was a real revelation and an approach that I’ll definitely be taking into classes in future. In the past I’ve expected students to be able to replicate the language that I use, and to intuitively employ the relevant metalanguage. But this just isn’t realistic. Only by reflecting back on my Australia-based placements through this new CLIL lense have I been able to understand how much of a barrier language was for my students here, and how a language-conscious approach to teaching them would have helped so much more. Every question a student answers is an opportunity to encourage them to employ your discipline-specific metalanguage.

Addressing challenge #3 – No electricity (and foreign fruit):

Pictures help. Here’s how I tackled this one…

Photographer: Gabriella Sabatino

Photographer: Gabriella Sabatino

Photographer: Kira Clarke

Printed out tropical fruits, with the english names on them, and a bit of elephant snot (blu-tac) did the trick. If you look closely at the board you can see the sentences from the lesson plan’s green and red boxes there.

And just in case, here’s the PDF of the fruit in-case you ever find yourself teaching co-ordinate systems in a tropical area.

This brings me to my second big lesson from the placement, Modelling. The electronic approach that I used in the Aussie context was great for a few reasons. It was clear and easy for students to see, it was quick and enabled me to move through the lesson efficiently, and it was dynamic and enabled for quick transitions between tasks. But it had one major flaw. My axes just ‘appeared’ on the screen. This has ramifications related to board and book work more generally.

Traditionally my board work has been pretty atrocious. Focussing on the clarity of my digital presentations, I’d often free-drawn my axes and scribble working all over the board in random spots that I found free. In the words of one of our team leaders ‘Everything you do is modelling’. I hadn’t thought about this before and hadn’t noticed the intrinsic contradiction of my unstructured board work and my expectations for students to be neat with their book work. This also passes up opportunities to discuss some of the key elements of tasks like drawing axes: deciding how far apart to set your numbers and leaving space for axis and chart titles.

The thing that really drove this modelling lesson home for me was the language barrier. There was no way that I could rely on scribbling something up on the board and the verbally explaining to students the key points and the ‘don’t forgets’. That would just be met with blank faces (as it was in my first lesson…). Against the backdrop of this linguistic challenge, the importance of modelling was made undeniably obvious to me.

Summary of key lessons:

This post has really been a combination of two. One on what I have found to be an engaging approach to introducing Cartesian co-ordinates to students, and the other on two key lessons that I learned through the process of adapting this approach for a group of students in Myanmar.

The first key lesson was the importance of CLIL (Content and Language Integrated Learning). In the same way that this blog post has introduced the term CLIL to readers (I’m assuming it’s new for at least some readers) at the same time as introducing the concept itself, I will in future strive to better scaffold and explicitly teach the linguistic skills required by my students, in conjunction with the teaching of concepts.

Secondly, I’ve come to appreciate the value and importance of clear modelling in the classroom. This is important for all students, but especially for those who have English as an additional language or auditory processing challenges[5].

In a recent speech that I gave at the Australian College of Educators Media Awards, I spoke about how stepping into different realms can often bring the most important lessons and opportunities for innovation. For me, this Myanmar teaching placement brought this assertion home more profoundly than I could have expected. The chance to teach in such a different setting, and with such a supportive team[6], was the catalyst needed to bring me back to basics and strengthen some of the core foundations of my teaching praxis. I was able to consolidate many of the lessons learned in this first year of my Masters, and I look forward to continuing this fascinating journey through my teaching and research project next year.


For Dan’s very short mention of the fruit salad activity, check out this post (scroll down to ‘Anyway. Part 1’). His posts on personality co-ordinates and this one on co-ordinate battleships are also definitely worth a look!

A big thank you to fellow Maths teacher Dot Yung for her edits and suggestions during the writing of this blog post : ) 

[1] I recognise that using the binaries of ‘boys’ and ‘girls’ could be exclusionary to some more gender diverse students. In future I will choose non-gendered categories for such an exercise. Check out the work of the safe schools coalition for more on this.

[2] I only adapted the core ‘fruit salad’ element of the lesson and not the dot related introduction.

[3] I would usually teach students to say ‘negative five’ but being there for only 2 weeks and knowing they’d return to ‘minus 5’ after my departure I didn’t bother to insist on the change of terminology.

[4] Pineapples are DEFINITELY not -5 on a tasty scale of -5 to 5… Unless they’re not that ripe, in which case I find that they give me ulcers…

[5] If you’re keen to experiment with the importance of modelling in your own classroom, I came up with the idea of challenging teachers to teach a lesson in silence! Please let me know if you decide to take this challenge on!!

[6] Every class that I taught was observed by another teacher who gave me feedback and suggestions for improvement. This post has underplayed the importance of the ‘instructional rounds’ approach taken by the team, and the impact that that had on all of our teaching. The opportunity to have my own lesson critiqued as well as analyse other teachers’ lessons, and hear what was seen through other people’s eyes, was invaluable beyond my expectations. This instructional rounds approach is a process that I hope to learn more about and do more in future. As a starting point I plan to read the article: Ensuring Instruction Changes: Evidence Based Teaching–How Can Lesson Study Inform Coaching, Instructional Rounds and Learning Walks?


Footballers doing Ballet?: The Search for Sources of Innovation in Education

What follows is the speech I gave at the recent Australian College of Educators (ACE) national media awards. For the awards I was invited to present anessay that I recently submitted for ACE’s ‘Writing the Future’ competition, and for which I was awarded runner up. A big thanks to Seb Henry-Jones who provided the impetus for this essay format through introducing me to ‘Art Project 2023’, Thomas Firth for his incredibly helpful feedback on my first draft of the essay, and Bianca Li-Rosi for her final edits prior to this blog post. I hope you enjoy it : ) 


I’d like to begin by acknowledging the traditional owners of this land on which we stand, the Wurundjeri people of the Kulin Nation. I’d like to pay my respects to elders past and present as well as any First Nations’ peoples here today. More personally, I acknowledge that I have been, and continue to be, the beneficiary of various privileges in my life. These privileges have enabled me to gain a high quality education, and learn to read, write and communicate with sufficient proficiency to enter such competitions as the ACE Writing the Future Award. These privileges are built, in no small part, upon the land dispossession of the Australian Aboriginals. Land that was later farmed by my British ancestors, and mined for Tin by the Chinese side of my family. I think it is important to recognise this as the context in which I am, today, able to share with you the following essay.

The brief for this essay was very… brief. Australian Pre-service teachers were invited to submit a paper under 1000 words, including references, that engaged with this year’s ACE National Conference theme: “Educators on the edge: Big ideas for change and innovation”. After much umming, arring, and mulling ideas about, I sat down on the Sydney to Canberra train in early July and managed to distill the ideas that came to be the following essay. I’ll now read the essay in its original form and follow it with a few brief comments on how my thinking has evolved since that train ride five or so months ago.

Footballers doing Ballet?: The Search for Sources of Innovation in Education

Where do ideas come from? In his 2003 book, James Young wrote: ‘an idea is nothing more nor less than a new combination of old elements’ (Young, 2003, pg. 15). As we look to the future of education asking questions like such as ‘What could schools look like in the future?’ and ‘How could what it means to be a ‘student’ change throughout the 21st Century?’, it is my belief that the greatest sources of big ideas for change and innovation will come from honouring these words of James Young and looking outside what we have traditionally thought of as the discipline of education. It is by recognising the parallels that exist between educational contexts and other areas of endeavour that we can creatively combine ideas and solutions from further afield to help advance teaching and learning. This essay explores this assertion by considering two fields outside the traditional educational paradigm, public art and healthcare, to investigate how the roles and responsibilities of educational institutions and participants could change this century.

What could schools look like in the future, and what do museums have to do with it?

The internet-smartphone dyad has made the world’s masterpieces omnipresent to such an extent that museums are being forced to re-consider their historical monopoly on meaning-making in the public arena of art. If the public can see it on a screen in the comfort of their own home, is there even a need for museums anymore?

Does this query sound familiar to educators? In the same way that art is now accessible worldwide, so is the information necessary for individuals to learn the content taught in all schools.

A recent piece entitled ‘Art Project 2023’ goes some way to addressing this question for museums. It depicts a hypothetical future in which a Museum is transmogrified from a physical to a digital repository of art, facilitating a revolution in the museumgoers’ experience. Attendees move from being art spectators, to art users, and are enabled to browse collections from around the world and curate their own exhibitions in a supportive and interactive environment.

In Assessment and Teaching of 21st Century Skills, authors Patrick Griffin, Esther Care and Barry McGaw (2012) write of how, as we move from deficit to developmental approaches to teaching, ‘the teacher has to reorganise the classroom and manipulate the learning environment to meet the needs of individual students’ (Griffin et al. 2012, p.9). Parallels in challenges breed parallels in solutions. Art Project 2023’s imaginings could inspire future classrooms where students curate their own curriculum in flexible learning environments, more adaptable to teacher and learners’ changing needs. Just as museumgoers change from art spectators to users, so could the tools and techniques of museums map to teaching to help students take charge of learning.

How could what it means to be a ‘student’ change throughout the 21st Century? Let’s look at healthcare

Fitbits, Misfits and Jawbones. The emerging jargon of a new and flourishing sector of the healthcare industry: fitness tracking. But why is this industry rising so quickly? Because fitness trackers are helping to address the oft lacking prerequisite to exercise, motivation. By supporting individuals to set goals, and providing instant feedback and actionable metrics, these devices are gamifying fitness to the point that TV sofas worldwide are now experiencing welcome respite from seemingly perpetual occupation.

What these fitness-tracking devices are essentially doing is ‘making fitness visible’. They are helping exercisers to plan, monitor, and adjust their own fitness trajectories in a way that empowers them to take charge and stay motivated. The link to making learning visible is clear. As educators it should be our goal to make teaching and learning visible to our students ‘such that they learn to become their own teachers, which is the core attribute of lifelong learning or self-regulation, and of the love of learning’ (Hattie, 2012, loc 168).

What if we could take the motivational benefits of fitness trackers and apply them to learning? Rather than a Fitbit, what would a ‘Learnbit’ or a ‘Knowledgebit’ look like? Helping students to become evaluators of their own learning is obviously an area where educators are already focussing energy, but what could be gained by taking a more detailed look at the way the fitness-based metrics are made actionable to users? How are reminders sent? How are accomplished goals celebrated and rewarded? How are communities of exercisers (or learners) scaffolded to support each other to maintain motivation and focus? Drawing from this emerging healthcare sector could facilitate more creative ways of encouraging students to become their own teachers.

In opening

The goal of this piece is not to explicate how education should turn to museums or the commercial health industry for advice, but rather to provide examples of how casting our eyes further afield can clear the way for more and bolder ideas for innovation in education.

The questions we ask are the frames into which our answers fall (Seelig, 2013), and perhaps asking questions like ‘how do our best teachers teach?’ or ‘how do our highest achieving students learn?’ leaves latent innovation potential untapped.

If macho footballers are willing to do ballet in the search for greater footwork, balance, and agility (Cooke, 2008), what fields are we as teachers and educators willing to explore in the quest for innovation as we teach into the 21st century?


As I mentioned in my preamble I wrote this essay about five months ago and, as one would hope, I have read and encountered some ideas since then that I thought worth sharing as a follow up to the essay.

I felt quite validated recently when, during his Dean’s lecture, Anthony Bryk talked about asking the question ‘what might we learn from how others have improved?’ and more specifically said, ‘What can we learn from healthcare?’. But what most sparked my interest was Steve Dinham’s closing comment about the importance being judicious about which innovations, from which sectors, we choose to bring into the realm of education. He mentioned in passing his paper entitled “The Worst of Both Worlds: How the US and UK are Influencing Education in Australia” (Dinham, 2015). I was interested to read in Steve’s paper about how, to his mind, various so called ‘innovations’ in the commercial sector, such as vertical integration, deregulation, and reforms related to autonomy are having, in many cases, negative effects when applied to schools and the education sector more generally.

This is obviously an area where there is much debate and it’s an area that I look forward to continuing to explore more in the future. But I think that Norman McCulla really hit the nail on the head with respect to this, when he wrote, ‘schools and school systems are not businesses but delicate social ecosystems’ (McCulla, 2014).

As I said in my essay, ‘Parallels in challenges breed parallels in solutions’. As we do look to other fields for sources of innovation and inspiration, we musn’t lose sight of the context in which we as educators operate, and how serving our students and generating value from them, does and does not differ from the ways in which the commercial sector seeks to satisfy its customers and shareholders.

Thank you for the opportunity to share this with you today. It’s a real honour to be able to speak at an event held by the Australian College of Educators and I hope to have more opportunities to learn from this great organization and its members in future.


Cooke, M. (2008). American footballers do ballet!. [online] Available at: [Accessed 7 Jul. 2015].

Dinham, S. (2015). The Worst of Both Worlds: How the US and UK are Influencing Education in Australia , 23(49), 1–20.

Enxuto, J. & Love, E. (2014), Art Project 2023, [online] Available at: (Accessed 1 Jul. 2015]

Griffin, P. E., McGaw, B., & Care, E. (2012). Assessment and teaching of 21st century skills. [electronic resource]. Dordrecht ; New York : Springer, c2012.

Hattie, J. (2012). Visible learning for teachers. [Kindle version]. Retrieved from

McCulla, N. (2014). The Activist Teacher. Professional Educator, 13(3), 4–6.

Seelig, T. (2013). How Reframing A Problem Unlocks Innovation. [online] Available at: [Accessed 1 Jul. 2015].

Young, J. (2003). A technique for producing ideas (p. 15). New York: McGraw-Hill