Five reads for September

For teachers in Australia, the long Term Three is drawing rapidly to a close. Indeed as I write this just ten days remain before a two-week break. This is the perfect time to consider a holiday reading list. Just enough time to raid the school library or place an order with your favourite book store. Here is what’s currently occupying space on my nightstand.

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1. Limitless Mind: Learn, lead and live without barriers by Jo Boaler

Boaler’s new book is high on my reading list. Having gained so much from previous books including “Mathematical Mindset”, “The Elephant in the Classroom” and the hugely practical “Mindset Mathematics” series, this book is highly anticipated. The question to be answered is does this book build a compelling case that anyone can learn anything. Do our beliefs about intelligence and ability hinder our capacity to learn and might we be limiting the learning our children are capable of?

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2. Transformational Professional Learning: Making a difference in schools by Deborah Netolicky

We have all sat through professional learning that leaves us wishing we could wind back time and retrieve the hours we just lost. Why does so much professional learning fail to transform our practice? Why is it that within a profession that is all about teaching and learning, we get it so wrong when it comes to professional learning. As a practising academic who comfortably straddles the boundary between the practical world of the classroom and the informative space of academia, Deborah is well placed to offer insights with impact.

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3. In Search of Deeper Learning: The quest to remake the American High School by Jal Mehta and Sarah Fine

Join with the authors on this tour of American High Schools as they unpack why some schools are delivering pockets of deep learning, but few if any, have found a model that truly works. This is not the usual banner-waving with stories of transformative practice. This book is deep dive into the pedagogy and curriculum of schools which claim to be delivering deep learning and look at the truth behind the claims. If education is going to transform itself, we need to be able to honestly assess what is working and what is not. Bold claims about school transformation are easily made; this book uncovers a more complex reality.

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4. Nuance: Why some leaders succeed and others fail by Michael Fullan

“The more complex the problem, the more that people with the problem must be part and parcel of the solution.” Schools are particularly complex places; an observation that would not surprise anyone who has spent much time in one. Large organisations which exist to serve a diverse population in varying stages of development and with hugely differing needs and wants is bound to result in near chaos levels of complexity. Leadership in schools, therefore, needs to be adept at managing this complexity. In “Nuance”, Michael Fullan unpacks the leadership style that schools and education require. This is a book that every teacher should read. Don’t leave it on the shelf for the Principal to read. Every teacher has a part to play in school leadership, and an understanding of nuanced leadership will enhance the impact we can all have.

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5. The Power of Making Thinking Visible: Using routines to engage and empower learners by Ron Ritchhart and Mark Church

If you are making use of visible thinking routines, if you have read “Making Thinking Visible” or “Creating Cultures of Thinking”, you will be waiting for this new release by Project Zero’s Ron Ritchhart and Mark Church. The big enticement is the promise of 21 new thinking routines which will bring new ways of making thinking routine in our classrooms. Beyond this, the book promises to explore the ongoing research behind why visible thinking is a powerful tool for learning. “Exclusive to this book will be a careful examination of what it means to engage and empower students as learners working with big ideas, reaching into the world to take action, and collaborating with others.”

By Nigel Coutts

Do We Truly Understand Place Value?

Number Talks are a wonderful way to see where our students are with their mathematical thinking. As a part of a daily routine a Number Talk promotes number sense and mathematical reasoning. In this post I take a closer look at what a Number Talk can reveal about our students’ understanding of mathematics and how they might be used to promote a fresh perspective.

James Tanton shattered my understanding of the vertical algorithm. More than that, he helped me to see how poorly I understood place value and that many of my students function with the same misunderstanding. What made the experience more humbling was that it took him less than two minutes to do this. Imagine a simple addition scenario involving two three digit numbers, something like 236 + 543 = How do you solve this? The mathematically inclined will know that there are many ways to achieve an answer. Undoubtedly the mathematics teachers reading this will be well armed with strategies involving rounding, or partitioning that make the addition more manageable. Most people with years of experience in the traditional mathematics classroom deploy the vertical algorithm. It probably looks something like this:

The vertical algorithm worked left to right.

The vertical algorithm worked left to right.

The average person knows that to solve the equation you work right to left. If you ask a student to verbalise the process you hear something like, “first you add the 6 and the 3 to get 9, then you add the 3 and the 4 to get 7 and the 2 and the 5 to get 7, the answer is seven hundred and seventy three”. The fun begins when you demonstrate how to solve this but reverse the order. Instead of working right to left, work left to right, just like you do when you are reading. “First you add the 2 and the 5 to get 7, then you add the 3 and the 4 to get 7 and then you finish by adding the 6 and the 3 to get 9, the answer is seven hundred and seventy nine”.

Do this with a class of students and by this point they will be howling. “You did it wrong!”, “That’s not how you do it” or my favourite “You have to start with the 6”. Claiming that the answer you got is the same as the answer they got doesn’t help. Some will point out that it only works because you picked small numbers. Some throw words at you like “trading”. Many will resort to the highest form of classroom reasoning and argue “But that’s not how you do it”.

Another example of the vertical algorithm worked left to right. The answer might leave some unhappy.

Another example of the vertical algorithm worked left to right. The answer might leave some unhappy.

So you offer to change the numbers. Make them larger, be sure that when the digits in each place value are added they surpass the magic number of ten. Try something like this:

Again explain to the students how you solve this beginning with the seven in the top left corner. If you want to really mess with their heads, start with the four but be prepared for claims that you always have to start with the top row. “First you add 7 and 4 to get 11. Then you add 6 and 9 to get 15. Then you add 8 and 5 to get 13. The answer is 11 hundreds and 15 tens and 13 ones or what might be playfully expressed as eleven hundred, fifteenty and thirteen”. In the interests of conventional counting it can and should be seen that we can unpack this number into a simpler form. Our fifteen ones allow us to add one to our collection of tens. We now have 16 of those and we can easily move ten of these into our collection of hundreds. We end up with 12 in our hundreds column, 6 in our tens column and 3 in our ones column and can call our answer one thousand, two hundred and sixty three.

What does this reveal? Our students have learned to follow the vertical algorithm but they may not truly understand how or why it works. The fact that we can work it backwards, or middle out, or upside down should not come as a surprise. We should see that in our numbers we have collections of ones, and tens and hundreds etc. and that we can combine these and have totals of any value. I proved this thinking to a student by offering them $10 notes. They didn’t mind the idea of having eleven such notes, or twelve or more, even though the idea of putting 15 in the tens column just minutes earlier seemed like the work of the devil.

What does this have to do with Number Talks? I have taught many classes who can perform page after page of vertical algorithms without error. There are any number of text books which provide just this sort of practice. I can dress up the question by wrapping it in a seemingly real world problem, something like “John has 768 watermelons, he buys 495 watermelons at the market. How many watermelons does John have?” (The only sensible answer here is too many) Regardless of whether the students get the answers right or wrong, a page full of vertical algorithms tells me very little about their understanding of the fundamental aspects of place value that it exploits. But, a short number talk will.

In a number talk I am inviting and requiring students to explain their thinking. Mathematical reasoning becomes more important than correct answers. Ask students to solve an addition like 68 + 95 in a number talk and you will know which students understand place value. While participating in the Number Talk students share numerous approaches to each question. They share and hear a range of strategies. Provide students with a whiteboard so they might make their thinking visible and you open new possibilities. Include the option of an extended Number Talk using concrete materials and you allow for diverse representations of mathematical thinking. In each instance the students are revealing how they understand number and each response offers new insights to the teacher for future learning. Number Talks by design close the gap between student performance and teacher action to address and remediate misunderstandings.

The particular misunderstandings revealed in our reversal of the vertical algorithm are beautifully addressed by Tanton’s use of “Exploding Dots”. The basic premise is simple. You can add dots into a place value box until it reaches a set value. In Base Ten that value is 10. Once you have more than ten dots in a box they explode and one dot appears, as if by magic, in the box one place to the left. If you model the above addition problem with dots the process becomes very visual and it is much easier to understand why you can start with any column. The process is not done justice when explained in words, it is one of those things you have to try for yourself. The website Exploding Dots is a great place to start. The diagrams show the three stages in the process.

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Above the question 768 + 495 is modelled in dots. There are orange dots to represent seven hundred and sixty eight and green dots to represent four hundred and ninety five. Clearly some of our boxes have more than ten dots, so we get some explosions as below.

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Finally we get to an arrangement that is mathematically stable and we can easily read off an answer that everyone is likely to be happy with.

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Modelling the addition question we posed above with dots might not be the norm. It might take longer and require more space, but it does ensure that students understand what is going on. Exploding Dots can be used for so much more than addition. As an introduction to place value, perhaps beginning with binary counting, Exploding Dots provides a strong foundation from which mathematical understanding can be built. If you are keen to correct some misunderstandings amidst your students, definitely explore the world of exploding dots. It can be a great addition to you Number Talk routine.

By Nigel Coutts

Seven Language Moves for Learning

Language unsurprisingly is a powerful force in education. As Ron Ritchhart notes in ‘Creating Cultures of Thinking’, language “is at once ubiquitous, surrounding us constantly, yet we hardly take notice of its subtleties and power.” If we wish to maximise the impact we have, if we hope to achieve particular goals, and if we wish to shape the culture of our classrooms, we must consider the role that language plays. 

Our language choices communicate both intended and unintended messages. In the choices we make, in the subtlety of these choices, lies a truth more powerful than that conveyed by a literal reading of our words. When we look closely and critically at our use of language, we begin to see particular patterns which reveal much about what we genuinely value and expect from our learners. 

There are words which we use with high frequency. Work is one such word. We remind our classes to get back to work, to start their work, to work carefully, to finish all their work. We should not then be surprised that students imagine their role in the classroom is to do the work. This might not be the message we had hoped to convey about learning. Once you notice the number of times that you use the word work, you become open to the idea of using alternatives. In recognising the overuse of this word, we see the possibility that a more deliberate approach to our language choices might have. 

If we are going to leverage language to achieve our goals, we need to become aware of its subtle power. Ron Ritchhart identifies seven language moves that teachers make. Awareness of these seven moves can be the first step towards more facilitative language choices. 

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The first is a language of thinking. The teacher who is aware of this language move will utilise questions which engage their students in thinking. Often the most powerful change we can make to our teaching is the addition of one simple question: What makes you say that? By asking this question, I invite my students to move beyond providing what they imagine to be an accurate answer. By asking ‘What makes you say that?’ I require that my students offer a reasoned logic for the responses they provide. By asking this question often, I send the message that I value their thinking. When I then notice and name the thinking moves made by my students, I reinforce this message. If I praise a student for their critical thinking, for their efforts to make connections or to reason with evidence, I send clear signals that learning requires thinking. 

My language choices can build community. Noticing that we are a class of learners and that we have exciting learning to engage with today reflects a subtle choice of language. I might have stated this differently. You are learners, and you have much learning to do is much less inclusive than the first telling of the same set of facts. Use of the words we, and us and our indicate community in ways that you, I and my or mine do not. When the teacher talks about the learning that we are doing the message is clear that the community of learners includes the teacher as a member and that we are all learning together. 

Do we do mathematics or are we mathematicians? Do we study writing, or are we authors? Do we learn about places and spaces or do we think like geographers. By utilising a language of identity, we bring a new mindset to our classrooms. We empower our students to step into the shoes of the expert. When we use a language of identity, we invite our learners to become active participants in a discipline rather than temporary visitors, just passing through. 

When I outline the steps to be taken in a project or activity, I remove opportunities for students to demonstrate initiative. When I ask them to describe their plan, I allow them to take initiative. When a student comes to me because they don’t know what to do, I have a choice to make in how I respond. If I rescue them and show them how to proceed, I promote dependence. If I ask them to describe the steps they have already taken and then prompt them to think of what else they might try, I allow them to retain ownership of the process. Powerful questions such as ‘How might you see this differently?’, ‘What do you think is going on here?’ and ‘What parts of this do you understand?’ are supportive of student initiative. 

In some instances, the power of language is so subtle that it comes down to the choice of one word. If I ask the question “What can we do about this?” my language choice has unconsciously restricted the responses I will receive to those that are imagined to be possible. I have limited the scope of options I will receive back simply because I selected the word ‘can’ instead of more open and inviting ‘might’. When I ask ‘What might we do about this?’ I indicate that I am open to any and all suggestions. The responses offered to questions using a mindful ‘might’ are shown to be more diverse and more creative than those elicited by the use of ‘can’ or ‘could’ or ‘should.’

We might like to be told that we have done a good job. It might be nice to be told we are intelligent and talented. The trouble is that as feedback, this sort of praise is practically useless. More useful is feedback that provides me with specific and actionable detail of what I have done well and what I might want to do less of in the future. In place of praising a student for a great piece of writing, we can notice their choice of discipline-specific vocabulary, their effective paragraph structure and their clear opening sentence which made their argument apparent and understandable. 

The final language move requires us to become skilled listeners. Sometimes this means saying nothing. If we are talking all the time, what space do we leave for other voices to be heard? When we are listening, we make choices about how we respond that indicate how we value the role of listening. Reflective questions which show we desire to clarify our understanding of what the speaker has shared suggest that we appreciate what they have to say. Questions which encourage the speaker to reflect on their understanding or that invite an alternate perspective, allow us to become a valued participant in the speakers thinking.

Becoming aware of the seven language moves might serve to enhance the impact that our language choices have. As with each of the eight cultural forces, language is an inescapable part of our classroom culture. We can leave it to chance and hope for the best or we can practice noticing the choices we make and become more deliberate with the language moves we make.


By Nigel Coutts

A new literacy for understanding and communicating knowledge in the post-truth era.

These are undoubtedly interesting times, post-normal times. This is an era where our norms are reinvented, and our everyday assumptions challenged. This is a time for questions and reflection combined with a great search for understanding.

In this time, our notions of truth and the epistemological foundations of our knowledge are in flux. A battle rages between powerful factions which compete to shape our notions of truth, falsehood and belief. Politicians, corporations, media conglomerates, social networks and special interest groups each bring to the table their version of the truth. Competing constructs for how the world and its events are best understood abound, and evidence in support of any version of the truth is scant and muddied.

Once philosophers and scientists sought to uncover the truth. It was imagined that this one version of the truth existed in the reality of our world waiting to be found. Science was the great tool with which we would make sense of our worlds. As we explored further into the mysteries of the world, we believed that we were building enormous reserves of knowledge. These banks of knowledge, once analysed by those with wit and wisdom, would explain away the mysteries of our age and unlock a new age of enlightenment.

Today, information has become ubiquitous. Each day we generate more and more information, and most of it is never seen. While once those with access to knowledge were made powerful, today recourse to facts and information seems to hinder the power of the stories we tell. Reputation, emotion, status, and likes on social media seem to carry more weight when debating the truth than does scientific research. A compelling fiction wrapped in an appealing narrative appears to carry the day. Facts are most likely to spoil the party and ruin the fun.

As we rush towards 2020, more than ever, it seems our future depends upon our capacity to see true truths. And yet everywhere we look, we find ourselves confronted by multiple re-tellings of a truth. Each truth story has its foundation in some version of reality. Each story is told in compelling rhetoric. Each teller assumes a mantle of confidence in the story that they have to share. Each assumes that all other versions are manifestly false and that this falsehood is tangible to the wise. Each storyteller has their followers who ardently retell the story and add their weight to its validity. Truth becomes not that which is true, but that which is sold to the largest band of the most vociferous followers.

Today’s students enter this world, trusting in their educators to provide them with the skills they require to uncover the truth. It is likely that during their time at school, they will be taught numerous strategies to evaluate claims. They will learn to think like scientists. They will become literary critics. They will interpret historical events and engage in debate over significant ethical and political dilemmas. They will become skilled in the knowledge arts.

But will this be enough? In the post-truth era, does the capacity to utilise knowledge prepare one adequately to do battle against falsehood? When those selling untruths know the falsehood of their stories, does the bright light of truth shine through? Perhaps not.

The young truth-seeker requires a new literacy. The capacity to read each truth story, to understand its origins, its motivations, its place in the world and the purposes it serves. The defence of truth requires a close reading of each truth story rather than a search for the one true version of it. The literate defender of truth must seek to fully understand the beliefs which compel each story’s believers. Armed with this knowledge and their capacity to evaluate one set of claims against another, they can begin to weave a more compelling and truer truth. They will rely on powerful tools and evaluate multiple sources of knowledge as truth-seekers have always done.

What changes is how they share their insights with the world. A full-frontal assault will be avoided. Instead, they will deploy subtlety and nuance. Each audience will receive an alternate telling of a truth story woven from threads of true and tested knowledge. Each story will be personalised to best exploit its audiences weaknesses, appeal to their beliefs and gently guide the listener towards a fresh understanding. This is the deliberate politicisation of the process of spreading truth, wisdom and knowledge. This is empowering those who believe that knowledge founded in reason and logic should be our guide.

“If you know the enemy and know yourself, you need not fear the result of a hundred battles. If you know yourself but not the enemy, for every victory gained you will also suffer a defeat. If you know neither the enemy nor yourself, you will succumb in every battle.”

In The Art of War, Sun Tzu points the way forward. Our students must be taught to know not only truth from falsehood. They must also possess an understanding of the origins of the untruths they seek to extinguish.

By Nigel Coutts

Powerful Provocations for Learning: Sparking curiosity and increasing engagement

Powerful learning begins with the perfect provocation. Creating, refining and skilfully presenting the perfect provocation is an essential capability for teachers hoping to engage their class in rich dialogue. Claims that the percentage of students engaged by their learning declines from 75 percent in fifth grade to 32 percent by eleventh grade suggests a need for a more provocative environment.

A well-crafted provocation should encourage curiosity. Perhaps it has a certain degree of ambiguity such that it demands clarification. Maybe it challenges existing knowledge or beliefs in a way that guides the learner towards a fresh perspective. When we unlock the curiosity of our learners in these ways and provide them with opportunities to engage in inquiry to satisfy their curiosity, we increase learner agency. Matthias Gruber describes the effect that curiosity has on learning; “Curiosity may put the brain in a state that allows it to learn and retain any kind of information, like a vortex that sucks in what you are motivated to learn, and also everything around it,”. A powerful provocation is the seed for such a vortex.

The right provocation sparks questions and invites exploration. Entering a new city for the first time, the traveller experiences varying degrees of cognitive disconnect. There are some vistas which make sense and others which do not fit with any previous experience. There are new sights, and smells and sounds and while at first, the sensation may be overwhelming, the minds innate desire to explore soon takes over. We wander through the city, awash with questions and wonderings. What is around that corner? What are these people doing and why? What is that sound I hear in the distance? We may not be able to take our class to a new city each day, but we can create experiences which provoke a similar reaction. We can seek to provoke a sense of wonder and a desire to explore.

A powerful provocation should challenge our paradigms. We become readily set in our beliefs. We have knowledge that we believe to be true that goes unquestioned until a provocation is encountered that causes us to doubt what we were once certain of. Great art seems to achieve this goal almost effortlessly. Think of the painter who challenges us with a piece that forces us to review our reality from a new perspective. Or the poet, whose subtle choice of phrasing opens our mind to a new interpretation of stories that we once found truth in.

Julie is an exceptional teacher who routinely provokes her students to think, wonder, question and explore. Her class has started reading “Young Dark Emu”, a powerfully provocative book by Bruce Pascoe. By choosing to read this with her class of fifth graders, Julie has set up the possibility for an engaging lesson, but choosing the right book is only the start of the process. Looking for a powerful way to start the learning journey with her class, Julie sought to find the right provocation. Her Year Five teaching team utilises a ‘teaching for understanding’ approach to planning. An important part of this process is the establishment of a Generative Topic that serves to guide the teams teaching towards learning that matters. A generative topic as the name implies should generate opportunities for rich, broad learning around significant topics. This term, Julie’s team is exploring “Perspective” as their generative topic. The hope is that reading “Young Dark Emu” will invite a different way of seeing. Julie describes how she used the book to achieve this goal.

I was introducing the book Young Dark Emu by Bruce Pascoe and we were looking at the first paragraph where he explains that in European astronomy, they look at the constellations to tell the stories, whereas the Aboriginal people look at the darkness between the stars to tell the stories. The outline of the dark emu in the night sky was on the opposite page. The paragraph ended with the sentence – “It’s a different way of seeing”.

Source - Young Dark Emu

Source - Young Dark Emu

This was what Julie needed to spark the curiosity of her class, a powerful provocation to see things differently. An invitation to engage with a reading of the book as a doorway to a new perspective. A chance to see history through a new lens and to challenge preconceived ideas of how the world is to be interpreted.

‘Throughout history, humans have looked to the night sky to explain their existence, but the conclusions peoples draw from the same sky can be remarkably different. European astronomy uses constellations of stars to tell a story, but sometimes Aboriginal Australia uses the darkness between the stars. Dark Emu is a shape in the dark areas between the stars of the Milky Way. It’s a different way of seeing’. Young Dark Emu by Bruce Pascoe

The power of that one sentence sparked so much discussion about perspectives. Students made so many connections with the author’s message and the analogy given made this very clear to them. They spoke about why that paragraph is at the front of the book when considering their predictions of the content. This really highlighted to me the power of a good question or statement in provoking so much rich discussion.

Stellina teaches Kindergarten. She understands that the stimulus materials she chooses and the environment of her classroom acts as the third teacher. With this in mind, Stellina crafts collections of materials which invite her students to explore, wonder, engage and question. Stellina utilises her creativity and understanding of the curriculum to arrange collections that are likely to lead her learners towards the understanding she knows they need. The image below and the accompanying provocations were designed to engage young learners in a mathematical inquiry linked to the concept of number. Enticingly presented, the collection invites the learner to come and explore, to play and make connections. Having unlocked her learners’ curiosity, Stellina now artfully observes how they interact with the collection and decides when and how to interact with them so as to nudge them in the desired direction.

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Both of these examples demonstrate the potential of a powerful provocation. They also reveal the added value that a great teacher brings to a provocative stimulus. Julie knew how to manage the conversation. She understood the potential in the text and utilised it as a catalyst for conversation. The culture of her classroom supports debate and her students feel safe contributing ideas. Julie knows when to be the quiet one in the classroom, and when to gently guide the conversation towards an alternate perspective. Stellina creates opportunities for her students to explore and in doing so, makes space for her to become an observer of her students in the act of learning. When she does inject herself into the learning, her actions are well-timed and strategic. Quality learning requires the right provocation and a teacher who can maximise its potential.

How will you provoke your learners? What provocation will you deploy, and how will you maximise its possibility?

By Nigel Coutts

Bringing Mathematical Reasoning into our Classrooms

Reasoning is at the heart of mathematical thinking. It is what mathematicians do. 

The importance of reasoning is acknowledged in most if not all mathematical curriculums. In New South Wales it is a part of working mathematically which is described as the thinking and doing of mathematics. Mathematical reasoning is defined by the writers of the Australian Curriculum as follows:

Students develop an increasingly sophisticated capacity for logical thought and actions, such as analysing, proving, evaluating, explaining, inferring, justifying and generalising. They are reasoning mathematically when they explain their thinking, deduce and justify strategies used and conclusions reached, adapt the known to the unknown, transfer learning from one context to another, prove that something is true or false, and compare and contrast related ideas and explain their choices. - ACARA

With this in mind and a desire to build the capacity of our students to reason, we do well to ask how this might be achieved. How do we teach our students to bring such high order cognitive dispositions to their mathematics?

We begin with creating opportunities which allow for and which require mathematical reasoning. This is likely to involve a shift in our approach. 

If I begin by teaching my students a procedure and do so by guiding them step by step through the required process, they are unlikely to be called upon to reason. For the students, the reason for step two of the method is that it comes after step one, and the reason that they are doing any of it is that they were told to. If I then proceed to give my students a page of similar questions which closely resemble the ones used in the guided component of the lesson they will continue to apply the learned method, but will never be required to reason.

Perhaps we begin with something different. Maybe we alter the plan, or maybe we work towards a more significant question. 

Let us begin with something different. Let us begin with a prompt that forces us immediately towards reasoning. On the website “Which One Doesn’t Belong” you will find a series of prompts like the one below. The premise is simple; look at the prompt and decide which one doesn’t belong. So far, you have not had to do much reasoning. The next step is the key. Having shared the prompt with a class of students and having received a range of response back from the students, the teacher plays their trump card and asks one of the students to explain and justify their choice. There is no right answer and no wrong answer. What matters is that the student must offer a justification for their response. Repeatedly the teacher calls on a student, asks “Which one doesn’t belong?” and then follows that up with “What makes you say that?”. 

Image Source - Which One Doesn’t Belong -  https://wodb.ca/shapes.html

Image Source - Which One Doesn’t Belong - https://wodb.ca/shapes.html

The suggestion is not that we spend our days asking our students to make choices from four possibilities. Nor is that we abandon opportunities to teach our students a mathematical method. What is suggested is that the simple pattern demonstrated by the use of “Which One Doesn’t Belong” style prompts is utilised across the mathematical curriculum. When I choose to demonstrate a mathematical procedure, I include time to ask the students to reflect on what we are doing. Slowing the pace and asking students to explain why the process works, begins to engage them in mathematical reasoning even within a direct instruction model. 

And we should be clear, problem-solving and inquiry-based mathematics is not guaranteed to result in mathematical reasoning. I must also require my students to justify their thinking, explain the choices that they made, prove their working by an alternate method or through a different medium. Unless I do these things, they may get the right answer but could be relying on memory alone. 

And we learn what mathematics is when we are young. If the early years of mathematical life are filled with hours of tasks which only require a good memory, what concept will I have of the discipline? I am likely to pursue a pattern of study where thinking is barely required and creativity is absent? How will I cope when I must transition from learning to memorise methods to reasoning mathematically if I have never been compelled to do this before?

When we are young is also the perfect time to engage with mathematical reasoning. Curiosity is a natural disposition. We learn our way out of it. The young learner wants to know why. It is their favourite question. The clever early years’ teacher will construct environments and learning opportunities which encourage mathematical reasoning. In her book, aptly titled “In the Moment”, Jen Munson describes how this is done. Having placed the child in a situation permissive of mathematical reasoning, the teacher attends to what their learners are doing. They carefully interpret the actions and then decide how they will inject themselves into the moment. Through this process of observing and analysing what is seen, the teacher devises a plan and then provides just the right nudge to allow the child’s thinking to evolve. In classrooms where this pattern is the norm, mathematical reasoning is abundant, and students acquire the foundation they require for a passionate pursuit of the discipline. 

While the prospect of teaching mathematical reasoning may seem daunting, it does not need to be. Careful questioning within a classroom culture where thinking is the norm combined with an expectation that methods will be debated and that answers alone are insufficient provides the right environment for reasoning to thrive.

By Nigel Coutts

Supporting Mathematical Thinking through the Eight Cultural Forces

At the heart of mathematics are a set of connected thinking dispositions. The mathematician uses these dispositions as the cognitive tools of their trade. While the traditional imagining of mathematics might be all about the accurate application of well-rehearsed algorithms and processes, in the real world of mathematics, it is all about the thinking. As we consider what our students need from their mathematical education, we should not overlook the importance of these dispositions.

The five components of Working Mathematically describe how content is explored or developed − that is, the thinking and doing of mathematics. (NESA, Mathematics K-10 Syllabus)

In Mathematics, the key ideas are the proficiency strands of understanding, fluency, problem-solving and reasoning. The proficiency strands describe the actions in which students can engage when learning and using the content. (ACARA, Australian Mathematics Curriculum)

The references above capture the importance of these thinking dispositions within the Australian and New South Wales Curriculum. In New South Wales students are expected to engage with mathematical content and concepts through reasoning, communicating and problem-solving. In doing this, they develop fluency as they choose procedures and think flexibly, accurately and efficiently with the content they learn. The result of this is an understanding of the content that allows them to apply what they know to unique situations and to make connections between concepts. Peter Sullivan, the curriculum writer for ACARA, describes understanding, fluency, problem-solving and reasoning as the verbs of mathematics. “This approach has been adopted to ensure students’ proficiency in mathematical skills develops throughout the curriculum and becomes increasingly sophisticated over the years of schooling”.

For teachers, the challenge is how do we ensure that our students develop these dispositions. The research of Ron Ritchhart from Project Zero and the author of Creating Cultures of Thinking is a useful starting point. Ron shares that “We can’t teach dispositions, we must enculturate them”. To support this process, he identifies eight cultural forces which shape our classrooms and that we may manipulate to create an environment that serves our purposes. Being aware of the shape of the cultural forces requires close attention to the nature of our learning environments. Armed with an understanding of the forces which are shaping the culture of our classrooms allows us to notice how they are currently enacted. From that point, we begin to make adjustments to achieve the desired effect. In this sense, the cultural forces can be both a lens with which to see and lever with which to shift our practice. For more on understanding the Cultural Forces as a Lens & a Lever - Read this. And then read Creating a Culture of Thinking for the full picture.

Image courtesy Ron Ritchhart

Image courtesy Ron Ritchhart

The following questions are offered as a starting point for the teacher of mathematics looking to audit how the cultural forces are impacting learning in their classroom. Good questions should allow you to see things from a new perspective. Great questions should lead you to more questions. Hopefully, this list does both.

Opportunities

  • What opportunities are you currently creating for problem-solving?

  • When are students required to explain their reasoning? How might you add other opportunities for this?

  • What opportunities do students have to communicate their thinking? To whom and how?

  • What opportunities are there for students to select strategies? Are they required to evaluate and justify their choice?

  • How many ways are there to solve the problems students engage with? Can you alter the problem to make it open-ended?

  • Do the problems your students solve have one answer or many?

Time

  • What time is currently allocated for problem-solving, reasoning, communicating?

  • When is time allocated for problem-solving, reasoning, communicating? Do students begin their learning journey with a problem, or is his the bonus question at the end?

  • What changes if you alter the order of a unit? How might things change if you begin with a problem?

Modelling

  • What modelling of mathematical thinking do students benefit from? Do students see you having to think? Do they see what mathematicians do when they are stuck?

  • How might modelling of mathematical thinking be increased?

  • How might we use modelling of mathematical thinking to enhance learning?

Language

  • What language do you currently use when teaching mathematical thinking?

  • Are answers right or wrong? What might change if answers were interesting, surprising, challenging, beautiful?

  • Do we praise answers or the struggle of the progress? Does our language choice suggest that struggle is a bad thing? How might we change that?

  • How might language be used to scaffold, name and notice mathematical thinking?

  • Are our students labelled as mathematicians? How might this change their mindset?

Environment

  • How does the environment of our classroom promote mathematical thinking?

  • Do we show works in progress or solutions? Do we celebrate answers more than questions?

  • Do our displays emphasise rote memorisation of facts or encourage flexible thinking?

  • How might the environment of our classroom promote mathematical thinking?

Expectations & Interactions

  • What expectations do we have for mathematical thinking in our classrooms?

  • How are these expectations communicated and lived?

  • What do our interactions with students communicate about our expectations? How might we change that?

  • What expectations for mathematical thinking might we wish for?

  • Do we believe all students can be mathematicians? How do we communicate this belief?

  • What would change if all of our students believed they could be mathematicians?

  • Do our interactions encourage persistence or do we rescue our students?

Routines

  • What routines are currently used to support mathematical thinking?

  • What routines might we use to support mathematical thinking?

  • How might we make mathematical thinking routine?

  • What does our student’s mathematical thinking look like?

  • How might we use visible thinking routines to make their thinking visible? What will we do with the information we gain from this?

  • Might our students select and use visible thinking routines to enhance their mathematical thinking?


By Nigel Coutts

The Conditions Required for 'Learner Flow'

How do we design learning experiences that our students will want to participate in? How do we maximise engagement and participation in the courses we design?

A presentation on attendance rates for university students sparked these questions. It shared the results of an ongoing research project that is seeking to understand factors influencing attendance rates. One particular finding stood out. During one of the two semesters each year, attendance rates were seen to decline earlier in one semester than the other. This was attributed to the timing of examinations and the reality that students would miss lectures and tutorials to do independent exam prep. It revealed that the clear intent for the students was to achieve high examination marks rather than engage fully with the learning opportunities that the course offered. The students were there to achieve marks rather than learning. Further was the realisation that success in the examination was achieved best by means other than attending the course, but perhaps that raises questions about the nature of the assessment.

What might it take to change this scenario? What might it take to ensure students choose to be in our courses because the value of the learning achieved through mindful attendance is such that they would not want to be anywhere else?

Making the learning fun was offered as one solution. We have probably found ourselves in a class or professional development programme where the presenter has made an effort to make the learning fun. In the moment, sometimes reluctantly, sometimes against our natures, we are swept up in the momentum of the singing, the dancing, the humour. The presenter may be highly engaging and does a great job of lifting the energy levels in the room. As the course continues, participation in the activities increases and the learning concludes with a rousing round of applause before everyone spills out of the room buzzing with excitement.

It is not until the next day or week that you begin to question the outcomes achieved. Despite all of the fun, it seems there wasn’t a great deal of learning. You are left wondering what was the purpose of it all, what was the core message, what were you supposed to do with it all? Was it that you missed something? Did others leave with great ideas that they are now putting into practice or did the fun hide a lack of substance?

Making the learning fun seems to miss the point. If we want genuinely engaging learning, we need to take a closer look at why we might want to engage in learning in the first place.

Mihaly Csikszentmihalyi describes the peak experience of engagement in a project as ‘flow’. Might we begin with this idea and consider what it would require to design learning experiences which create the necessary conditions for our learners to enter a state of flow. Such thinking should uncover the conditions required for truly engaging experiences, which by design result in learning.

“Flow is being completely involved in an activity for its own sake. The ego falls away. Time flies. Every action, movement, and thought follows inevitably from the previous one, like playing jazz.” (Csikszentmihalyi. 1997)

I propose that we aim for something a little more specific to our goal as educators than is achieved by a direct reading of Csikszentmihalyi’s description of flow. I suggest we seek to understand ‘learner flow’, the state where learning achieves a level of meaning, purpose and relevance that the learner becomes completely immersed in the experience. As educators, we want to ensure that the result of all this engagement and thinking is learning. We want to be focused on creating an environment in which the participant’s actions, thoughts and movements lead them towards a meaningful learning goal. This requires becoming comfortable with the discomfort experienced when we step beyond the limits of our existing capabilities, it demands an openness to exploring new ideas from fresh perspectives, and it results in us achieving new capacities.

There are conditions which overlap between those broadly required for flow and those that might be referenced in ‘learner flow’ while some are unique. The following are my initial and early thoughts on this.

Agency is perhaps most important. Learning is best achieved when it is driven by the learner. When the learner owns the process and when their success in the learning endeavour results from the strategic actions that they take ‘learner flow’ becomes possible. When the key decisions are made for the learner, when the learning requires that they merely follow directions, when learning happens to you rather than because of you, engagement declines. The worse scenario is where the learning environment merely requires the learner’s attendance. In this instance, learning is assumed to occur because you were present for the allocated number of hours even if during this time, your mind was elsewhere.

Purpose and relevance seem to come next. The learner must be aware of why the learning matters to them either because of the direct benefits that result from the learning or because of the significant place of the learning in a more extensive learning arc. In response to calls for learning with relevance and purpose, it is frequently argued that there are some things which we just have to learn. The implication is that these things are requisites for later learning that is full of relevance and purpose. When you speak to advocates of this ‘foundational model’ it becomes clear that they are able to see and understand the relevance or purpose of what they are describing. Our role as educators is to reveal this to our learners. When we are clear on why the learning matters, we are more likely to present this content in ways that make this clear. Creating experiences for our learners that require their use of these foundational skills is one way to enhance the visibility of its relevance and purpose. Spending large blocks of time drilling students on foundational knowledge in isolation from experiences which reveal its purpose has the opposite effect. A simple analogy helps us to understand such an approach. In sport, it is our desire to play the game well that encourages us to engage in training drills. Flip this pattern and introduce a potential player only to drills they are unlikely to ever discover a passion for the game.

Extrinsic motivators serve to limit the possibility of learner flow. When grades or certificates motivate us, we will do what is required to achieve a satisfactory grade, and nothing more. Learner flow requires that the learning opportunity engages the learner. Feedback must be delivered in ways that reveal to the learner where they are with their learning and how they might proceed. When positive feedback becomes the goal, learning is limited. If the goal is a high mark the likelihood of the learner choosing to engage with learning that is challenging is bound to decline; why risk a poor score when you can choose an easier path and be assured of success.

An achievable level of challenge is a must. If the learning is easily achieved, we will master it quickly and move on; learner flow is never achieved as it is not required. If the challenge is far beyond our capability, we are just as likely to give up or find alternate strategies to protect our ego. When there is sufficient challenge, when we are challenged in ways that encourage us to try and persist and when we can see ourselves succeeding, we are much more likely to achieve a state of learner flow. In this process, the teacher, mentor or coach has a vital role to play and how we approach this will shift the learner either towards flow or away from it. When we see our learners struggling with learning, our first response can be to rescue them. Rescuing blocks flow and removes learner agency. Sometimes doing nothing is a better response. The skilled teacher or mentor will know when their learner needs a great listener who provides them with time and space to reflect on where they are, why they are stuck and what they might do to resolve the issue. Asking the right question, providing the required nudge, suggesting an alternate perspective on the problem are all ways that the learner can be supported without having to surrender agency. Knowing when to offer advice, guidance or scaffolding is an art.

Each element described above seems to play an equally important role in establishing the conditions for learner flow. Each can and should become a part of our learning environment and considering these as we design learning experiences should support our goal of increasing learner flow.

By Nigel Coutts

AAMT Why Maths? - Inspiration beyond the classroom

This week I spent three days in Brisbane attending the Australian Association of Mathematics Teachers’ national conference. The theme of the conference was “Why Maths?” and along with 500 other mathematicians, we looked to find inspiring answers to this provocative question beyond the classroom. Here are my key takeaways from this event.

“How to think brilliantly and creatively in maths” was the title of the opening keynote from James Tanton. James is a research mathematician deeply interested in bridging the gap between the mathematics experienced by school students and the creative mathematics practised and explored by mathematicians. Having been a college professor for a decade, James realised that high school mathematics was where he could have the most significant impact. Today he is the Mathematician in Residence at the Mathematical Association of America in Washington D.C. James offered the following strategies for being brilliant at mathematics.

  1. Do Something - replace the fear of not knowing how to start by taking some action, evaluate the results and adjust your strategy accordingly.

  2. Use Visualisations - rather than relegating visualisations to our early years of mathematical learning, we should embrace the approach as a life-long path to brilliantly thinking. Visualisations not only help us to solve problems, they also help us to build deep-understandings and see patterns and connections which otherwise may remain invisible

  3. Work Hard to avoid working hard - one of the best ways to be truly brilliant at mathematics is to look for an easier way to solve a problem. Simple, elegant and beautiful solutions should be our goal. If our thinking relies upon complex methods, maybe we don’t truly understand what we are doing.

  4. Seek the story behind the topic at hand - Thinking in stories is a powerful strategy to understand what is truly going on. When we start to tell the story behind the mathematics, instead of merely looking at the numbers and symbols, we allow ourselves to build a more complete understanding

  5. Got haze - Walk into hazy thinking - There will be times when a confusing haze confronts even the brilliant mathematical thinker. The path forward is unclear, and you will need to confront the unknown. Brilliant mathematicians are comfortable with admitting what they don’t know, but they don’t retreat. Instead they extend their thinking into the haze by building on what they do know.

James is the mathematician behind Exploding Dots, a strategy for visualising and understanding many mathematical concepts, especially in the area of number. Where other methods for explaining place value, the four operations and algebra obfuscate the essential concepts at play, the Exploding Dots method makes this transparent and allows students to develop a true understanding of the mathematics. In a fast-paced fifty minute workshop, James explained the fundamentals of Exploding Dots. For those wanting to explore the possibilities of using Exploding Dots with your class, these websites are the best place to start. G’Day Maths - Exploding Dots

In the image below, we see how Exploding Dots are used to visualise counting with Base 2. The aim is to demonstrate how as the number of dots increase, we show the larger quantity by using the next spot in our place value table. James refers to this as a two into one machine as it takes two dots in any square, explodes them and replaces them with a square in the next one to the left. This sequence shows a single dot in the one column. Then two dots in the one column which in the next image explode and are replaced by a single dot in the twos column. The final image shows what happens when we add a fourth dot. The two dots in the ones column explode, and one dot is added to the twos column. As there are now two dots in the twos column they explode and one dot appears in the fours column. This principle can be extended to any base value and can be used to demonstrate the four operations and algebra.

ExplodingDots_Binary_1to4.png

The value of mathematical reasoning quickly emerged as a common theme for the conference. By asking students to explain their thinking, validate their solutions, test their proofs, solve problems in multiple ways and reframe questions, teachers are including opportunities for students to develop mathematical reasoning. By valuing mathematical reasoning, teachers require their students to think like mathematicians.

Tingalpa State School is supporting mathematical reasoning in many ways. They have created a culture that is tolerant of mistakes and understand that much can be learned by reflecting on the mistakes we make. Their students engage in mathematical reflections through the use of Maths Journals supported by a metalanguage for mathematical understandings. Teachers and students utilise a common set of prompts for mathematical reasoning such as “Convince me...?”, “What stays the same and what changes?” and “Is it just sometimes true, or always true?”. The use of these prompts ensures that the students are thinking throughout their maths lessons and that passive absorption of mathematical methods is banished. These prompts are used alongside visible thinking routines within classrooms which value thinking. This use of a common language for learning, coupled with routines for thinking maximises learning opportunities over time as students engage with new concepts and strategies in a familiar learning environment.

Dr Toh Tin Lam of Singapore’s National Institute of Education shared strategies for developing mathematical investigations. The emphasis once again was on the use of strategies which would require thinking and in particular mathematical reasoning. A mathematical investigation is described by Dr Lam as a task that is open-ended and where the goals are ill-defined. A problem-solving task, by contrast, most likely has a solution and while there may be multiple ways to solve it, the set of possible strategies one might deploy and the mathematical concepts involved are likely to be limited.

One particularly useful strategy for designing a mathematical investigation described by Dr Lam is to explore the common mistakes made by students. He used the example of a common mistake seen when students are investigating fractions. A student may think that the strategy used to simplify the fraction as shown in the example below is valid, particularly as in this example, it results in a correct answer. When students are invited to investigate this further and to test this solution in multiple instances, they begin to understand where they went wrong. Encouraging students to investigate their errors and find an explanation for where their thinking goes wrong seems like a much more effective strategy than returning work full of red crosses and hoping the students correct their strategy before the next assessment.

FractionSimplificationError.png

Libby Foley shared her experience of working in remote regions of Far North Queensland. She reminded us of the importance of building positive, supportive relationships with our students and especially those of Aboriginal or Torres Strait Islander descent. The strong message here is that our pedagogy must always be aligned with the context in which it is practised. Foley’s deep respect for the culture of her students and the community in which her teaching is situated is impressive. There is a range that our faith in Western epistemology as the one path to truth and understand can blind us to the cultural bias of such a view. The wisdom and knowledge of our Indigenous Australians, founded on over 65,000 years of living in harmony with the land cannot be ignored and should not be diminished by cultural elitism.

Cathy Foley, the Chief Scientist for Commonwealth Scientific and Industrial Research Organisation (CSIRO), offered a strong case for rethinking the capacities we focus on in education. The CSIRO has an impressive record in science, and its contribution to our collective understanding should not be overlooked. Foley outlined the work of the CSIRO in response to Australia’s greatest challenges, which could also serve as a starting point for exciting investigations in schools:

  • Resilient and Valuable Environments: Enhancing the resilience, sustainable use and value of our environments, including by mitigating and adapting the impacts of climate and global change.

  • Food security and quality: Achieve sustainable regional food security and grow Australia’s share of premium AgriFood markets.

  • Health and Wellbeing: Help enhance health for all through preventative, personalised, biomedical and digital health services.

  • Future Industries: Help create Australia’s future industries and jobs by collaborating to boost innovation performance and STEM skills.

  • Sustainable Energy and Resources: Build regional energy and resource security and our competitiveness while lowering emissions.

  • A secure Australia and region: Help safeguard Australia from risks (war, terrorism, regional instability, pandemics, biosecurity, disasters and cyber attacks).

In response to these the CSIRO is evolving eight future science platforms each as exciting as the next and all demanding mathematics:

  1. Active Integrated Matter - Creating Industry 5.0

  2. Deep Earth Imaging - Unlocking our resource potential

  3. Digiscape - Digital solutions for the land

  4. Environomics - Environmental genomics to care for biodiversity

  5. Hydrogen Energy Systems - Next generation energy industry

  6. Precision Health - Integrated and tailored health solutions

  7. Probing Biosystems - Innovative medical devices and diagnostic technologies

  8. Synthetic Biology - Artificial engineering of biological systems

This is but a small taste of al the ideas shared over the three days. As is so often the case much of the best learning came from conversations with other educators along the way. What was clear is that mathematics education in Australia is in good hands. We are fortunate to have many teachers with a genuine passion for mathematics who believe that all learners can be successful in their learning. It is also clear that mathematics has a vital role to play in our collective futures. And, Why Maths?, there were many answers shared but perhaps Dr Cathy Foley offered the definitive answer, because it will help us solve the challenges of today and the future.

By Nigel Coutts

How might we prepare our students for an unknown future?

How might we prepare our students for an unknown future?

If we accept that we are living in times of rapid change and that the world our children will inhabit is likely to be very different from the world of today, or perhaps more importantly, different from the work our current education system was designed to serve, what should we do to ensure our children are able to thrive?

One approach to this conundrum is to contemplate what that world of the future might be like. We can expect that technology will continue to accelerate and that it is likely to expand its sphere of influence. The first industrial revolution resulted in the replacement of human labour by machines, the next is expected to remove humans from much of the cognitive labour we currently perform. Artificial intelligence is set to expand and while we can guess at some of the ways this might impact our lives, the full impact is yet to be imagined. We might readily imagine a world where the transport industry is revolutionised by driverless vehicles and can perhaps fathom many routine information processing tasks being taken over by computers, but what happens when AI allows computers to move into domains that we believed required a human touch. Will we accept that the telephone counsellor who listens tirelessly to our woes and offers sage advice might be a robot?

When we look back to 2007 we begin to see somewhat of the challenge that we confront when we try to predict the future and make plans based upon today's circumstances. 2007 was a busy year. Apple introduced the iPhone and with it the notion of a device that fits in your pocket, performs many of the tasks which previously required a computer and thanks to an always-on internet connection gave you access to all of the world's information, anywhere you are. The iPhone was just the shiny tip of the iceberg for 2007. Big data became a big thing thanks to a still little known company called Hadoop. GitHub became the go to repository for computer code and by making it easy to share code accelerated the pace of software development. Twitter expanded, Google bought YouTube and we all became video stars. The Kindle eBook reader launched. Airbnb launched us into a new world of sharing and with it a new economic model was born. 3G communication meant that mobile data was beamed into our devices at a pace that made it practical.

Thinking about the consequences of the technologies launched in 2007 is made more interesting when you consider that most children currently in Primary School were not alive then. They have grown up in a world where all of this technology was neither new nor shiny, but normal. Trying to predict what the world will be like in 2030, when our current Kindergarten students leave high schools seems like pure folly and yet the challenge confronting school systems is to prepare our students for this world.

What thinking might guide us? Is there a way we can approach this question that does not rely on potentially flawed predictions of what the future might be like? Can we prepare our young people in ways that will allow them to rise to whatever challenge the future brings?

Such thinking leads us to identifying a set of dispositions and capabilities which are flexible, adaptable and when sought in combination perhaps most importantly uniquely human. A machine may possess some of these capabilities but it is at least for now inconceivable that a machine would possess them all.

At the heart of this is a perceived demand for graduates capable of creative and critical thinking, collaboration, problem finding/solving, self-organisation, empathy, innovation and agency. Students who have this skill set should be able to quickly develop the technical expertise required of specific tasks and it is this skill set that prepares students for the unknown. As writer and futurist Alvin Toffler (1970) puts it ‘the illiterate of the twenty first century will not be those who cannot read and write, but those who cannot learn, unlearn, and relearn.’

My belief is that our focus should be on developing our students' ability to think and to do so in ways that allow them to confront unfamiliar situations with confidence backed by relevant educational experiences. David Perkins says we have impoverished models for thinking. This results from excessive emphasis in schools on the transmission of knowledge. 'Education is a process of self transformation that enables a person to negotiate changes that are as-yet indeterminate, as well as the changes that must surely come.’ (Kalantzis & Cope 2012 p92) For this to become the reality our students experience we need to empower them to become the driving force behind their learning now and beyond school. Thus the output of our education systems shifts from being educated people to being people well prepared for a life of education; true life-long learners.

Beyond accepting that education shall be a life-long endeavour, our children will need to embrace their agentic potential and understand that they have the capacity to shape their world. By combining a sense of Agency with empathy we prepare our young people to make sense of the challenges faced by themselves and others and to then take action which makes a difference. This combination of empathy and empowered agency if anything is the distinction between the human and machine world that matters most. It is said that a machine charged with making paper clips will do so until all matter is transformed into a paperclip. A human will understand that there are richer goals to be achieved and change course.

The challenge of the future is real but now is not the time for despair. Education surely has a central role to play and learning and the dispositions of the learner have greater value now than perhaps ever before. Now is the time for new Renaissance for education not as preparation for an unknown future but as the one constant which flows through our lives and allows us to flourish amidst unceasing change.

By Nigel Coutts

Kalantzis, M. & Cope, B. (2012). New learning: a charter for change in education. Critical Studies in Education, 53, 1, 83-94.

Toffler, A. (1970). Future shock. New York: Random House.

Becoming a reflective practitioner

There are particular behaviours and a mindset that accompanies effective reflective practice. Understanding and applying these allows us to become reflective practitioners. The process for most people will begin with a recognition that reflective practice has value and a part to play in our professional learning. It is also true that it can be easier to act our way into a new mindset than it might be to change our beliefs. To that end, by adopting the behaviours of reflective practice, we may find ourselves valuing the change, and that might result in a new mindset. 

Reflective practice takes time and making time for deliberate reflection is an excellent place to start. Setting aside time for thoughtful reflection may not be easy and requires a degree of planning for most people. Some are fortunate or are perhaps forced to spend time alone with their thoughts. Maybe this results from a long commute or time spent waiting for children to finish sports training or the like. For those who do not have time for reflection built into their day by default it is worth scheduling time for it in the same way that you might schedule a meeting; set up a recurring event with yourself as the sole attendee. 

Now that you have time for your reflective practice consider the environment in which this will occur. If you are hoping to turn your mind inwards, it is essential to be in a place that is free of distractions. A quiet mountain top might be the gold standard but is perhaps not accessible on a daily basis. What works for the individual will vary, but you should avoid places or proximity to devices which will draw your attention away from your reflective mind. Research shows that a phone, even when set to silent, is likely to be a distraction as you wonder if a notification has arrived. 

To be effective, our reflective practice should be grounded in our close noticing of the events of the day. This requires us to be attentive in the moment. If we are not looking closely at the impact we are having, at the reactions our actions cause, at the ripples which are formed by our presence or the results of our effort, we are likely to fall into ponderous navel-gazing. Our reflection on our practice as a teacher begins by making space in our teaching to step back and observe our learners. Our goal should be to notice them in the act of learning. We can do this through our strategic use of routines which allow us to become an observer of their learning. 

Now is also the ideal time to consider how we may document or capture our students thinking. One of the strengths of employing a selection of Visible Thinking Routines is that they include opportunities to capture the thinking which our teaching is facilitating. By deploying strategies which make our students’ thinking visible, we gain access to insights which can inform how we subsequently guide or nudge our students in the desired direction. When we include this documentation as evidence within our reflective practice, we enhance the impact that both the capturing of the thinking and the reflection upon our teaching can have. 

This leads us to the question of what we might consider to be evidence of learning. The evidence gathered from our considered use of thinking routines, student responses to rich tasks and our observations of students engaged in the act of learning provides us with invaluable information. Tasks which offer us numerical data alone provide a different perspective. When we look at a data set, it should lead us towards questions and wonderings. If a data set makes us wonder why a student achieved a particular result and what this might reveal about their learning, then it has a valuable role to play. If shifting the data becomes more important than the learners, which it purports to measure, we may have forgotten our purpose. 

Having observed our learners practising their craft, we can begin to consider what other information we might include in our reflections. What questions will we ask that might reveal the thinking that our learners are engaging with? Carefully designed questions, framed through language that encourages our students to describe where they are with their thinking, and where they are going are most effective. Questions which test knowledge or lead the learner to believe their task is to guess what the teacher is thinking, should be avoided. A question which uncovers the thought processes of our students is one where the answer is only revealed by the student’s response. If the answer to the question can be found in a text or online, then it is not probing our student’s thinking. 

Our observations and our questioning reveal a picture of learning in our classroom. We should be able to discern what our students are understanding from our instruction and also what is causing confusion. We will also create the conditions necessary for us to notice and name what we value from and for our students. An honest observation of our practice in the classroom should reveal who does most of the talking, which students are engaged and which could have spent the lesson elsewhere. There will be learner behaviours which are puzzling ad these can be the most interesting fodder for our reflections. The student who seems to struggle to verbalise a particular letter sound might lead us to a deeper understanding of the decoding skills being deployed. A group of learners with a shared misconception of a mathematical concept may reveal an opportunity for us to represent the idea in a new way. It is only through the close-noticing of what is occurring and the practice of reflection that we are likely to capitalise on these moments.

Finally, reflective practice is made more effective when it is shared. By sharing our reflections with others, we engage in a mix of practices which support a deeper understanding. As discussed previously, explaining our thinking to others allows us to better understand our own thinking. Engaging in co-construction of reflections opens our mind to fresh perspectives as our collaborators notice things we may not or offer a perspective which challenges our stance. And, the process of engaging with others as a participant in their reflective practice allows us to achieve new insights into our thinking. Further, we may wish to open our reflections to ongoing scrutiny by ourselves and possibly others by capturing it in some way. By recording our reflections, we build an archive which we can review and which can itself prompt further reflection when we take the time to look back. 

By Nigel Coutts




Realising the benefits of reflective practice

It is generally accepted that learning is enhanced by the inclusion of deliberate, reflective practice. Indeed the act of reflecting on the impact that our actions have towards the achievement of any goal (learning oriented or other) is shown to have a positive impact. Reflective practice is defined as the praxis (interdependent and integrated theory, practice, research, thought and action) of individuals or groups to move from ‘better thinking to better action' as a result of reflection for, in and on learning (Harvey et al. 2010 p140). With this in mind, it is worth considering what reflective practice might look like and to consider it in a range of contemporary contexts.

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Design thinking is a highly iterative process in which a problem is attacked through a cyclical process. A typical design thinking cycle includes:

  • developing an understanding of the context of the problem with empathy for the user being a common element

  • a deliberate process of ideation to allow many ideas to emerge

  • a convergent thinking process where ideas are evaluated and set aside

  • a prototyping phase where ideas are brought to life and tested

  • an ongoing process of refinement and consolidation

As Looijenga et al. identify ‘Iteration during the design process is an essential element’ (Looijenga et al. 2015 p1), and this process is facilitated in part by reflection. 'Reflection, critical thinking and developing metacognitive skills concern: Planning, evaluating, and justifying inquiries, designs, explorations, investigations, actions, performances, etc.’ (Looijenga et al. 2015 p20). Further, a key to successful design iteration identified by Looijenga et al. (2015) is a process of collaboration. In design thinking, the iterative process is driven by ongoing reflective practice inside a collaborative environment. Ideas are proposed and shared within the design team and with stakeholders outside of the team. The process moves forward because of the collective embrace of a reflective process.

It should not be assumed that this collective embrace of the reflective process will occur. A team is unlikely to benefit from a design thinking process if its members are unwilling to have their ideas criticised, modified, blended with others and potentially rejected or set aside. If the team does not value a gradual move from divergent thinking where many ideas are shared towards convergent thinking where one or two ideas emerge as dominant, the process is unlikely to be flawed. A team culture that values correct answers, where there is a fear of being wrong, where questions are not valued is unlikely to promote divergent thinking. Divergent thinking requires a culture where risk-taking and open sharing of ideas is the norm. Individuals must know that they are respected for what they offer the group even when their ideas do not survive to the end of the project. Building such a culture requires deliberate attention to the establishment of norms which support the free flow of ideas into and out of the design thinking process.

While we often think of reflective practice as something that is done by the individual for their benefit, the potential of reflecting on the thinking and learning of others offers many advantages. Peer assessment is shown to encourage deeper thinking and reflection (Cheng & Warren, 1999) and encourages individuals to think deeply about what they have observed (Stefani 1994). Li, Liu and Steckelberg (2010) showed in their study that the quality of feedback provided by individuals in the role of assessor improved the quality of work they subsequently produced and the authors recommend that efforts to enhance the quality of feedback should be pursued. However, Li, Liu & Steckleberg (2010) found in their research that the quality of feedback provided did not have the same impact for those it was provided to and cite research suggesting feedback could be more constructive and detailed. The implication here is somewhat contrary to the perceived wisdom of who is best served by the provision of feedback. This research reveals that the person providing the feedback has the most to gain and that the act of reflecting carefully on the thinking and learning of others enhances our learning more than it improves the learning of those we have observed. The implication here is that if we wish to gain the most from reflective practice, we should include opportunities to reflect upon the work of our peers.

Sandi et al. (2011) found that metacognitive skills can be developed through collaboration and that skills developed in this way are transferable to the individual solution of a problem. Sandi et al. provided students with a problem and allowed time for reflection and collaboration enabled by prompts enacting meaningful social interaction, which they found enhanced metacognition. Hausmann et al. (2004) have gathered evidence that supports three mechanisms to describe why collaboration is effective in enhancing understanding and task performance:

  • Other-directed explaining where the individual takes the stance of a teacher or instructor.

  • Co-construction of reflections with elaboration or critical evaluation of a peer’s contributions to the reflective practice

  • Participation in self-directed explaining by listening to others’ self-explaining.

The implication is that reflective practices which occur in isolation are less effective than collaborative reflection. Collaborative reflection allows us to benefit from explaining our thinking to others and in doing so to clarify our thinking as we seek to be understood. In explaining ourselves to others, the social cues inherent in conversation with an active listening partner provide us with instant feedback on the clarity of our self-explaining, and we are able to modify our reflections in response to this. The collaborative, reflective dialogue allows opportunities for us to also modify our reflection as we co-construct meaning with our collaborators. When we share our reflection and expose our thinking to questioning and alternate perspectives we create space in which fresh ideas might emerge; a process enhanced when we recruit collaborators with diverse perspectives who might offer alternative interpretations. Lastly, by listening to the reflective practices of others, we allow new ideas to enter into our stream of consciousness and in doing so, generate a fresh perspective on our reflections.

Becoming a reflective practitioner has much to offer. Reflective practices are an essential element of learning, and it might be argued that true learning cannot occur without reflection on learning. The quality of our reflective practice is worth considering, and we can enhance our process by adopting an open mindset and through engaging in collaborative reflection. Amidst the business of our daily lives, it can be easy to fall into patterns where our thinking shifts rapidly from one task to the next without time to pause and reflect on what we have been doing or thinking. If we understand the value that quality reflective practices play in our learning, problem-solving, creativity, social interaction and personal growth, we are more likely to make time for it.

By Nigel Coutts


Cheng, W. & Warren, M. (1999) Peer and teacher assessment of the oral and written tasks of a group project, Assessment and Evaluation in Higher Education, 24(3), pp. 301–314.

Harvey, M; Coulson, D; Mackaway, J. & Winchester-Seeto, T. (2010). Aligning reflection in the cooperative education curriculum. Australia Pacific Journal of Co-operative education, 11 (3), 137-152.

Hausmann, R. G. M., Chi, M. T. H., & Roy, M. (2004, August). Learning from collaborative problem solving: An analysis of three hypothesized mechanism. Paper presented at the proceedings of the 26th annual conference of the Cognitive Science Society, Chicago, IL, pp. 547–552.

Li, L., Liu, X., & Steckelberg, A. (2010). Assessor or assessee: How student learning improves by giving and receiving peer feedback. British Journal Of Educational Technology, 41(3), 525-536.

Looijenga, A., Klapwijk, R., & de Vries, M. (2014). The effect of iteration on the design performance of primary school children. International Journal of Technology & Design Education, 25(1), 1-23. doi:10.1007/s10798-014-9271-2

Sandi‐Urena, S., Cooper, M., & Stevens, R. (2011). Enhancement of metacognition use and awareness by means of a collaborative intervention. International Journal Of Science Education, 33(3), 323-340.

Stefani, L. (1994). Peer, self and tutor assessment: Relative reliabilities. Studies In Higher Education, 19(1), 69-75.

Four perspectives on truth, normality and education in times of rapid change

We are living in interesting, frightening and rapidly changing times. Where rapid changes and transformations through technology, politics, globalisation and the climate, conspire against normality. These times demand a fresh approach to education, one that provides learners with the thinking dispositions they need to turn challenges into opportunities.  "All that was 'normal' has now evaporated; we have entered postnormal times, the in-between period where old orthodoxies are dying, new ones have not yet emerged, and nothing really makes sense.” But what thinking might guide us through this time of volatility, uncertainty, complexity and ambiguity?

The four reads shared below are a good starting point. Each presents a particular perspective on the modern era and suggests a way forward. Each has its own bias and particular flaws. The purpose of this list is not to point the reader towards a solution but to start a conversation.

21 Lessons for the 21st Century by Yuval Noah Harari

In this essay, the author takes us on a journey through our history to argue that the situation in which we find ourselves today is perhaps not as unique as we might imagine. The author shows how a superficial reading of our history and the stories we deploy as we make sense of the world blocks us from achieving a more nuanced understanding of how we arrived where we are. It invites the reader to engage in a close inspection of our histories and an even closer investigation of our stories. Yuval is blunt in his attacks on social conventions and clear in his belief that humanity has more in common than we might imagine. His detailed description of the challenges one might face in organising an event like the Olympic games in 1016 compared to today clarifies this point well. For educators, there are many points worth noting but the standout is perhaps, "In such a world, the last thing a teacher needs to give her pupils is more information. They already have far too much of it. Instead, people need the ability to make sense of information, to tell the difference between what is important and what is unimportant, and above all to combine many bits of information into a broad picture of the world.”

Post-Truth: The New War on Truth and How to Fight Back by Matthew d’Ancona

"The notion of science as a conspiracy rather than a world-changing field of inquiry used to be confined to cranks. No longer. It seems to me intolerable that this should be so.”

In 2016 the Oxford dictionary declared Post-truth the word of the year indicating the move of the phrase into mainstream use. If as is often stated, we are living in the post-truth era, what are the implications for education? If knowledge, wisdom and expertise are no longer trusted and easily dismissed, how do we armour the intellect of our learners against such rebuttals? How do we produce young people who will seek the truth and question those who spread falsehood? These are the questions that d’Ancona tackles in “The New War on Truth”. Who and what lies behind this war on truth, what part do individuals play, and how might we tip the balance back towards a society that seeks truth and values wisdom over emotion and base reputation?

“Welcome to PostNormal Times” by Ziauddin Sardar

In this article, Sardar proposes that we have moved into post-normal times, where all that we once relied upon has dissolved, and we are left with no sense of normal. Change is rapid and unpredictable. The structures and stories which helped us to navigate our world and predict the near future have fallen and we are yet to replace them. In this in-between time, we struggle to make meaning, find certainty and know who or what we may trust. "We will have to imagine ourselves out of postnormal times and into a new age of normalcy—with an ethical compass and a broad spectrum of imaginations from the rich diversity of human cultures.” So how might educators prepare learners for post-normality, and how will we ensure that they leave our schools with the ethical compassion they require? What is the ideal preparation for thriving amidst complexity, chaos, contradictions and uncertainty?

In Search of Deeper Learning: The Quest to Remake the American High School by Jal Mehta & Sarah Fine

Having dived deep into the “why” of a rethink of what and how we teach, this book describes the authors' search for the antidote in the schools of America. What started as a research project to examine the practices of America’s more innovative schools quickly transformed into an analysis of what was missing and a search for answers. Even in schools with a reputation for being cutting edge, the authors found large numbers of students best described as disengaged from the learning process. From this starting point, the authors embark on a search for examples of teaching practice that support ‘deep-learning’. For anyone interested in developing an insight into what school might be like as we approach the challenges of this post-normal, post-truth era, this book at least asks the right questions.


By Nigel Coutts

Learning about change from a home cooked meal.

Last week I decided that a good home cooked meal was in order. Lacking inspiration I turned to a recipe book I had been gifted the previous Christmas and found what appeared to be a tasty and nutritious option. I read on with enthusiasm and was soon imagining myself dining on this wholesome meal. If the end result looked half as good as the glossy picture that accompanied the recipe, I would be in luck.

I began the process of preparing this culinary delight by reviewing the list of ingredients. Keeping in mind that the recipe had been prepared by an expert chef with years of experience, I had no qualms at all planning a few adjustments to this list based on my personal taste and what I knew I already had in the cupboard. Other items would need to be sourced from the supermarket and despite many claims that they are the fresh food people, some of the ingredients had to be sourced from the tinned foods aisle while others came snap frozen. At least one of the ingredients came in a box, and even though the recipe made no mention of a ‘light batter’ I felt confident that this substitution would work well.

Returning home, I placed the ingredients out on the bench and began the meticulous process of preparing my meal. Once again, some adjustments needed to be made. Some of the equipment that the recipe called for were lacking from my kitchen, others were in the wash, some just seemed unnecessary. Sadly the quality wine which the recipe suggested was consumed in advance and so that didn’t make it into the pot (which should have been a small cast-iron pan). After an initial process of sautéing a selection of mostly fresh vegetables in a light fish sauce (which had become Soy Sauce, because I don’t like fish sauce), I realised that in my rush I had left some of the vegetables in the fridge. Not to worry, there seemed like there was enough greenery going into the meal.

Twenty-five minutes later, I removed the battered ocean trout from the oven. This was not a highlight of the process as the recipe had strongly suggested that the trout spends not more than fifteen minutes in the oven. My thinking was that the barramundi I had substituted for the trout would need longer, but it turned out (as revealed from the plumes of smoke emanating from the oven) that twelve minutes might have been ideal.

I was nearing completion of this task with just the sauce to complete. I had forgotten to pick up a lime while at the supermarket, but I did have a bottle of what was described as freshly squeezed lemon juice in the fridge, something I think might have come with the refrigerator, I can’t recall ever having purchased it. The sauce came together quite quickly, mostly because I had managed to find a sachet of what sounded like a very similar finishing sauce and which required just ten minutes in the microwave (actually two minutes but who cooks with their glasses on).

The meal was ready. I plated it up with care, added a splash of lemon juice to the sauce, partly for flair but mostly to reconstitute it after its extended stay in the microwave and sat myself down for what was bound be a splendid meal.

A few emails later I tucked in, and it was . . .

Well to be very honest it was terrible. Not only was it cold, (perhaps it was more than a few emails) but it also lacked any real flavour. The fish was like leather. The sauce tasted like lemon room deodoriser. The sautéed vegetables were both soggy, crunchy, burned and in parts still frozen, how any of that is possible I have no idea. The whole sorry affair was a complete letdown. It held absolutely no resemblance to the picture in the book. Clearly, I had been cheated.

The recipe book is now in the recycling bin where it belongs and good riddance to bad ideas.

So what does this have to do with education? Well often, when we are implementing a new idea, we do precisely what I did with my glorious home-cooked meal. We fail to implement our great idea in full. We substitute in ideas which are incompatible with our stated objective. We leave out some of the key components of the plan, either deliberately or accidentally. We let some parts of the plan sit and stew unattended for far too long. Other parts are rushed and never given the degree of thought they deserve. We seek out advice from experts or look to comprehensive research papers to guide our thinking but then promptly ignore the advice and implement something entirely different.

We do all of these things and then genuinely stand back and wonder why the plan failed. Clearly, the whole idea was flawed and indeed when we are asked why we have abandoned it, we will explain at length how we knew all along it wasn’t going to work.

Perhaps there is something wrong with our approach to change.

By Nigel Coutts

Learning And Teaching for Understanding - A day of learning with PZ Sydney Network

Today I had the pleasure of joining over three-hundred educators for a day of learning and sharing. That this was a Sunday and that the event was organised as a free event for educators by educators speaks volumes of the quality and care that educators bring to their role.

This event was organised by Project Zero Sydney Network, which is a collective of educators who share an interest in the ideas which emanate from Harvard’s Project Zero. The networks aim is to share professional learning opportunities with educators at no cost and in doing so, facilitate the expansion of pedagogical philosophies that are supportive of deep-understanding, critical thinking and lifeworthy learning. Drawing on Project Zero pedagogy and practice, PZ Sydney Network believes that:

  • learning is a consequence of thinking

  • understanding is not only something you have, but something you do

  • intelligence is not one thing, but many, and is something that can be learned

  • thinking skills alone are not sufficient; we must also have the disposition to use them

  • thinking and learning are processes that are deepened when we make them visible

  • collaboration is the stuff of learning.

Today’s event is the third annual conference offered by the network and interest continues to grow. Its founding members are committed to learning, and there is extensive experience within their midst. What unites them is their desire to collaborate with others and to facilitate learning through dialogue and facilitative coaching rather than banner waving or dictatorial instruction. Attending a PZ Sydney event is more like participating in a conversation with a trusted friend than listening to a lecture. There is a clear understanding that learning is best when it is mutual and that questions drive learning in new directions while answers suggest an ending.

On this particular Sunday, we were joined by the inspiring Tina Blythe. Tina has been a researcher at Project Zero for nearly 30 years. She is part of Project Zero’s online learning leadership team and is the education chair of the Project Zero Classroom summer institute. She is also a Lecturer on Education at the Harvard Graduate School of Education. Central to her research and teaching are how to create and sustain learning environments that support understanding. Collaborative inquiry and the collaborative assessment of student and teacher work are key focuses of her work

Among many gems, Tina shared a story of her personal learning. It was a story I have shared through this blog previously and involves Tina’s reflections on a professional learning event which did not live up to expectation. Tina utilised the metaphor of searching for driftwood on a beach to describe the process of connecting learning opportunities with our particular needs. The beach wanderer passes by many items which do not meet their needs. Only a few of the pieces of detritus will fit the wanderer's needs, maybe fitting into a particular project or perhaps offering enough possibility to be collected for one yet to be imagined. For the professional learner, the journey is the same. They engage with many ideas, strategies and solutions, but only a few are implemented or saved for future use.

“Sometimes, I go to the beach and I know exactly what I’m looking for: sea glass of a certain color, shells of a particular shape or size. Sometimes, I see something that catches my eye, and I’ll pick it up and bring it home, even though I’m not sure at that moment what I’m going to do with it. - you never bring home the whole beach.”

I found a few pieces of driftwood today that I will keep and make use of, but perhaps my favourite was one of those delightful wonderings that force you to reconsider what we might be best focusing on with our teaching. “What questions will our students inherit?” We know that the students we teach today will become adults in a world shaped mostly by the questions or challenges that we create for them today. The questions of climate change, displaced communities, a global population on the move in a world dominated by globalisation and rapidly evolving technologies are unlikely to be adequately answered in the short term and so will be passed on to the children of today. With this in mind, how will we educate our children so that they may find answers to the questions we have created?

Checkout #pzsyd on Twitter to see what others found.

By Nigel Coutts

Focusing on What Matters - From Identifying to Enacting our Big Rocks

There is a delightful story frequently told of a philosophy professor who shares a valuable life message with students through the story of the “Big Rocks”. There are many versions of the story, and the protagonist varies from philosopher to business guru to teacher, it goes something like this.

The professor places a large glass jar on the bench at the front of the hall. It is empty, and this fact is verified when the glass is turned upside down. From a small bag, the professor places one rock after the other into the jar until it can take no more. He holds the jar aloft and asks the students who are wondering what the point of this demonstration might be, “Is the jar full?”. In unison, the class responds “yes”. The professor returns the jar to the table and takes a second bag from under the table. Delicately and with some shaking of the jar to facilitate the process the professor now empties the contents into the jar. Out of the bag tumbles a stream of gravel which fills the spaces between the larger rocks already in the jar. Again the jar is held aloft, and the question asked, “Is the jar full?” and again the answer comes, louder this time, “Yes!”.

The professor’s face reveals little emotion as a third bag is pulled from beneath the table. This time fine sand is poured into the jar and with some gentle shaking encouraged to fill the small spaces between the rocks and the gravel. A faint smile is evident on the professors face as the jar is once more held up for review, and the students are asked, “Is the jar full?”. The students respond with a resounding and confident “Yes!” suspecting that the professor must surely be close to beginning the serious work of the lecture.

The now heavy jar is placed delicately back on the bench. The professor pauses for a moment, takes a small sip from the coffee cup which has sat as always on the bench beside a large pile of papers. He pauses as though distracted by some thought of times long past, before pouring the nearly full contents of the cup into the jar before repeating the process with a second cup from beneath the bench. A grin moves across a wise face as the jar is once more held aloft, and the professor proclaims triumphantly “Now the jar is full!”.

The message is now unpacked for the class. The jar represents our lives, and the challenge is to decide what we will fill our lives with. The large rocks represent those things which matter most in our lives. The gravel and sand the small things which occupy our time and keep us from what matters most. If we place the gravel and sand into our jar first, if we attend to the little things first, we have no space for the large rocks. The cup of coffee shows that no matter how full our lives might be, there is always time for a cup of coffee with a friend.

It is an essential story for educators to ponder as we decide not only what fills our lives but what fills the lives of our learners. It is a story that requires its audience to stop and ponder what are their “Big Rocks”, what are the things that truly matter. When we consider what we emphasise in our teaching the question needs to be asked, are we focusing on what we believe will truly matter in the lives that our learners are likely to live? Too often we spend time and energy on tasks which are not well aligned with what matters most to us and to our learners. The daily minutia of being a teacher pulls us away from the actions which we value most. Our students are required to engage in tasks which result in them developing a false view of what school and learning are about. We allocate our time and their time to activities which we know are low impact even when we know this is not what matters most. We remain in what Stephen Covey describes as the realms of the not important and fire fighting.

CoveyMatrix_gcu_time-matrix.png

Engaging with the process of identifying our big rocks is well worth the time but that it should only be the first part of the process. Once we determine our big rocks, how will we make sure that our actions and the messages we send to our students, our team members and ourselves align with these ideals and move us closer to achieving our goals? It is always hard to move out of the zone of the urgent, low order tasks and move our thinking into the more strategic realm. In a recent article, Jeff Bezos of Amazon reflected that his role required him not to do lots of work but to make one or two significant decisions a day. The hard part is making the right decision. Maybe if we consider the magnitude of the impact that each action we take might have on our learners and on our school, we will gain a better understanding of how we allocate our time and make better decisions. 

By Nigel Coutts

Local Wisdom versus Global Assessments

A significant shift continues to occur within global education markets. It is signified by the manner in which it makes sense to speak of a global education market. It is driven by neo-liberalism and the expansion of markets into all aspects of our lives and it is made possible by manipulation of the third messaging system within the educational triad of curriculum, pedagogy and assessment. It is a drive towards accountable, comparable and productive education systems fine-tuned to maximise the return on investment and provide industry with the workforce it desires. What must be asked is how does this trend impact students and are these the forces that should be driving change in our education systems?

The concept of an International Education market has its origins in the emergence of global testing initiatives. Without measures for meaningful comparisons between national systems, the very idea of a market remained abstract. With the emergence of international tests such as PISA (Programme for International Student Assessment), it has become possible for direct comparisons of national education systems to be made using a score and with that ranking tables. Assertions such as 'We are falling down the international rankings and our students are performing at a lower level in some subjects than they were a decade ago, according to the OECD’ (Jensen, Hunter, Sonnemann & Cooper 2014 p3) become possible, and nations compete to out-educate each other.

PISA brings with it an interest in particular aspects of educational systems through its manipulation of the messaging system of assessment. What PISA measures is given value and focus but the true breadth of PISA is rarely discussed while the traditional domains of reading, writing, mathematics and science take the limelight. This narrow focus on select disciplines results in a narrowing of the curriculum and the logic behind this focus needs to be analysed.

While reading, writing and mathematics have always been considered of importance the emerging STEM (Science, Technology, Engineering and Mathematics) discipline is easily seen as a response to emerging trends in industry, a trend that predates PISA. 'The role of schools has become increasingly regarded as being to supply appropriate human capital to serve the needs of business and industry.’ (Angus 2009 p38) Imaginings of national prosperity are increasingly linked to the quality of graduates in the STEM fields as seen in reports from Australia’s Office of the Chief Scientist which state ‘Australia is now the only country in the OECD not to have a current national strategy that bears on science and/or technology and/or innovation.,’ (Chubb. 2014 p10) and PwC suggests a focus on our capacity for innovation linked to OECD reporting 'But we need to lift our game; the OECD recently rated Australia as only ‘average’ in its competency and capacity to innovate.' (PwC 2015 p13)

In 2018 PISA added an evaluation of students’ global competence and an optional assessment of financial literacy. For 2021 an assessment of creative thinking is planned and work on developing appropriate measures for this are underway. It will be interesting to see how the results of these assessments are reported by the mainstream media and the influence that they might have on educational policy. Will we see a renewed emphasis on global competence and creativity fuelled by reports that nations are slipping on these dimensions compared to a new global education elite?

The influence that PISA has on education is profound, and many of the problems it creates are outlined in an open letter written to Dr Andreas Schleicher, director of the OECD's Programme for International Student Assessment by a group of concerned academics. Chief amongst their concerns is that PISA brings a focus on the use of quantitative data and with that an emphasis on aspects of education which are easily measured. 'By emphasising a narrow range of measurable aspects of education, Pisa takes attention away from the less measurable or immeasurable educational objectives like physical, moral, civic and artistic development, thereby dangerously narrowing our collective imagination regarding what education is and ought to be about.’ (Letter to OECD)

That PISA is a product of an organisation whose focus is on economic development is also seen as problematic. 'But preparing young men and women for gainful employment is not the only, and not even the main goal of public education’ (Letter to OECD). The writers go on to state that 'OECD's narrow focus on standardised testing risks turning learning into drudgery and killing the joy of learning’ (Letter to OECD). The globalisation of education that PISA allows for sets an agenda that sits divorced from local issues and stands separate from cultural traditions and values. Driven by economic forces and linked to growth targets as it is, PISA shifts our thinking of what is important for education in one specific direction.

In this trend towards globalisation, the place that schools and education play within local communities is lost, replaced by national and global imperatives, 'the policy framework within which schools now work is characterised by new public management, top-down leadership, performativity and remote ‘standards’ (Angus. 2009 p37). In this market economy, 'Students and teachers are expected to turn themselves into the kinds of people demanded by ostensibly ‘high performing’ and ‘effective’ schools that succeed in market competition.’ (Angus 2009 p38)

The realities of how this transformation may occur are less clear and it is apparent from the dialogue that it is the responsibility of the individual to transform. PISA and NAPLAN create a setting in which ‘highly effective’ schools, teachers and students are believed to thrive and those who do not achieve success are the deviant minority. 'This minority has to be cajoled or coerced into being achievement-oriented, industrious, self-helping and properly trained for the workforce, and this is the strategy to overcome social exclusion.’ (Connell. 2013 p5) This blaming of individuals ignores the clear research that assesses the effect size of various influences on educational outcomes and reveals '85% of the effect being due to family circumstances’ (Angus. 2009 p38) What truly works or does not work for any individual child, or even any particular community is not easily measured and surely cannot be measured by one assessment.

The complexity of international comparisons is given little attention in the mainstream press. Where this complexity has been analysed and studied a more complete picture of what is working for some nations but also why this might not transfer to another system emerges. In ‘The Smartest Kids in the World’ Amanda Ripley (2013) looks at the education systems of some of the reportedly high-achieving nations including Finland, Germany, South Korea and Poland. Through this analysis, it becomes clear that each education system is a reflection of the culture in which it functions. While there may be some lessons to be learned and applied from one system to another, it would not be possible or effective for Australia to wholesale adopt another nations systems and process for education. It is deeply flawed to believe that such a move would be positively transformative and so one needs to ask what purposes are achieved through simplistic comparisons of national systems.

If one approach from international systems must be widely adopted, perhaps it should be the one that seems to deliver positive results with greatest consistency across multiple systems. Identified by the OECD and discussed in depth by Jensen et al, (2014) it is a commitment to professional learning programmes for teachers. The consistent features of such programmes are that they give time for teacher development, collaboration, mentoring, feedback and teacher driven research. Such programmes have the power to transform schools for the betterment of all. However, if such programmes are not allowed to develop in response to locally identified needs and are not driven by teachers and researchers working within local communities, they are bound to produce limited results.

Globalisation and market forces will not improve the educational success of all students. 'Broadly, we know how to make schools work even in environments of poverty: build up local experience, develop relevant curricula, create social solidarity and mutual help, put in serious resources’. (Connell 2013 p6). For education to thrive, we need a more honest discussion of what our schools need, one driven by richly complex and humanistic data and understandings, not global test scores.

by Nigel Coutts

Angus, L. (2009) Problematizing neighborhood renewal: community, school effectiveness and disadvantage Critical Studies in Education Vol. 50, No. 1, February 2009, 37–50

Chubb, I. (2014) Science, Technology, Engineering and Mathematics: Australia’s Future. Office of the Chief Scientist; Australian Government, Canberra

Connell, R. (2013) Why do market ‘reforms’ persistently increase inequality? Discourse: Studies in the Cultural Politics of Education

Jensen, B., Hunter, J., Sonnemann, J. and Cooper, S. (2014), Making time for great teaching, Grattan Institute

Jensen, B & Sonnemann, J. (2014) Turning around schools: it can be done Grattan Institute

PwC (2015) A smart move: PwC STEM Report April 2015 (Accessed online April 2015) -https://pwc.docalytics.com/v/a-smart-move-pwc-stem-report-april-2015

Ripley, A. (2013) The smartest kids in the world: and how they got that way. New York; Simon & Schuster Paperbacks