Contemplating questions of work life balance

Visit the Apple website and have read of their “Jobs at Apple” page and you will be enticed by an organisation is all about creating the conditions where people can engage in work with impact.

Do more than you ever thought possible. Have more impact than you ever imagined. - This is where some of the world’s most passionate people create the world’s most innovative products and experiences. Join us and you’ll do the best work of your life — and make a difference in other people’s lives.

It sounds like the perfect description for a teaching role. After all, is this not how we see our roles as educators and is this not the sort of person we hope to have leading the learning of our children. As educators we are in the very special position of being that person with the opportunity by actions to shape a life, to lay a foundation upon which a lifelong love of learning is built and to empower the next generation. Surely this is a position that even an Apple engineer would be envious of.

Oddly lately I have been pondering how schools responds to the question of a work life balance. Let me try to explain my thinking. I am still trying to clarify my thinking here, so please bear with me.

I think it is a positive step that the question of work life balance is regularly an agenda item. The hero narrative of the teacher giving there all for the good of their students has probably served no one well. Claims that teaching is a calling and not a profession seem to undervalue the importance of professionalism and give permission for the deeply thoughtful and reflective practices of educators to be devalued. We should be proud of our profession and value what our professionalism brings to the care and nurture we provide to young people.

And we need to have conversations about how we take care of ourselves and how we meet our needs. This is where the question of work-life balance is of importance. For ourselves, for our families, for our students, our employers and all who rely upon us, our health and well-being matters. I wonder though if the current work-life balance agenda is based on a somewhat limited interpretation of what it means to achieve a work-life balance. I wonder how the work-life balance mix that is typically advocated for in this current agenda might be misaligned with the life-goals of some.

Don’t get me wrong, for many people the dialogue around striking a balance between life and work is important. Any move away from workplace cultures that place unceasing demands on time and availability, an always on lifestyle where sleep deprivation and constant business is a badge of honour, is a positive thing. Messages that it is ok to turn the phone off, disconnect from email and take a lunch break are all positive and necessary. I just wonder if we have perhaps have adopted a restrictive one-size fits all imagining of what it means to strike a work-life balance?

In our search for a happy work life balance, maybe we approach this goal from the wrong direction. At the core the concept is that individuals have their work which occupies a large amount of their time and energy and almost diametrically opposed to this their life which includes family and friends. Striking a work life balance becomes a balancing act between time at work, time with family and friends, between doing what we have to do for work and doing what we enjoy. And this is important for many people, but has the pendulum swung to far and are we now creating cultures where individuals confront pressure if their lives do not align with the traditional imagining of work and life.

Maybe the traditional approach to work and life does not serve the needs of all and ignores that for some of us the questions around work and life require a different perspective. Phil Libin the former CEO of Evernote, the popular cloud based solution for note-taking. When interviewed for Traingulation by Leo Laporte, Phil provided the following insight to this question of balance in life and work:

"If you think of it as life as being separate from work, then you’re going to have this conflict, if you think of them together and you try to have a job that’s sufficiently epic that you want to spend more time, that no matter how much time you spend at it you want to spend more then its great."

Astronaut Chris Hadfield echoes this sentiment in these words, “Decide in your heart of hearts what really excites and challenges you… Don't let life randomly kick you into the adult you don't want to become.” And these thoughts seem to fit with the sort of people who read the Apple jobs page and think, “yes, that’s where I want to be”, putting a ding in the universe. The challenge is how might we create cultures in our workplaces that give those who need it permission to switch off while also providing those who want to ‘do more than they ever thought possible’ the conditions they need to do just that.

It seems it is about empowerment and agency. If we are in control of our work and our life then we can make choices that provide us with the balance we require, whether that be through switching off or powering on. When our choices are restricted through policy or culture we will find balance a struggle but where we have control and can act strategically for our own well-being true balance becomes achievable.

By Nigel Coutts

Growth = Mindset + Action

"Sometimes people overcomplicate things”

It was this line in a Growth Mindset video that made me stop and take notice. It has a truth to it that we can easily miss. It directs our thinking in a new way, towards what lies at the heart of the matter. In this case it shines a light on what we do if we have a growth mindset and what we should be doing when we have a fixed mindset. 

The uncomplicated version of the story goes like this: Belief leads to Action, and Action leads to Growth. If I believe I can do something I am more likely to take action to achieve my goal. I am more likely to practise, more likely to persist with a challenge, more likely to listen to feedback and more likely to incorporate feedback into my actions. If I am taking actions that are likely to result in growth, then I am more likely to see growth than if I don’t take action. My mindset or the beliefs which underpin it, when backed by action make growth possible. The opposite is also true, if I believe I can’t grow or learn, I am less likely to take action, less likely to persist and less likely to listen to feedback. I will fail to take action if I believe that my innate talent means I don’t have to try and without action I will fail to grow. 

Henry Ford was right, "Whether you think you can, or you think you can’t, either way you are right.” 

Having the right mindset is alone not sufficient for growth. I might talk the talk about a growth mindset and believe I can learn a new skill but unless I back that belief with action, it is just talk. Indeed, I probably need to look at why I am not taking action to achieve new learning, maybe I have a false growth-mindset. If I am not willing to take the risk involved in trying something new, if I am unwilling to begin a learning journey, if I talk about potential but avoid demonstrating it, I am using the language of a growth mindset to protect or hide my fixed mindset. 

Taking action alone is also not enough to ensure growth. There are many ways I can practise at achieving the perfect golf swing but there is a very good chance that my unguided efforts will go to waste. Practising a flawed method ten thousand times can only result in failure and build habits which will be hard to unlearn. If action is to result in growth and success it needs to be the right type of action and my chances of achieving this increase if I seek support in my learning from an expert. But hours spent in the company of an expert is also never going to result in growth. At some point I need to do the work, take the action, practise and practise some more. If I do this and take on board feedback that will refine my actions than I have a chance of achieving my goal. 

If I am a school interested in student growth through the adoption of a growth mindset programme, but I only target a part of this process I am likely to achieve little success. Many schools have adopted strong beliefs about the value of a growth mindset. Their beliefs are evident in the posters and slogans adorning their walls. “F.A.I.L = First Attempt in Learning”, “The Power of YET”, “Everything is hard, before it is easy”

All of this can be good but advocating for a growth mindset alone is not going to result in a change. Unless the belief that we can all grow is coupled with action that is designed to achieve that growth we will remain where we are.

What can be remarkably powerful is to apply the behaviours we adopt in our growth mindset contexts to those that trigger a fixed mindset. If I can recognise a context where my thinking is fixed but then apply the behaviours I bring to my growth mindset contexts I open the door to growth. Maybe I believe I can learn a new piece of software, but I can’t learn to play the piano. Instead of giving up on the piano, I apply the actions I would take to learn a new piece of software. I seek expertise, I give time to the task, I persist when it gets hard, I adjust what I am doing, I practise and practise some more. I know these actions work for learning software so I shouldn’t be surprised when they work with the piano. I also remind myself that one of the biggest obstacles is my mindset. Instead of trying to change that and then take action, I begin by taking the action I would take if my mindset was different. Actions are much easier to change than mindsets. 

So, by keeping things simple and focusing on beliefs, actions and growth I can achieve my goals and tackle new challenges and I have an approach to apply where my mindset lets me down by believing in the power of taking action towards a goal. 

By Nigel Coutts

Watch the video that inspired this.

The Curse of False Expertise

A growing body of research reveals details of the “Curse of Expertise” in which it is shown that as an individual’s level of expertise increases, their ability to communicate their knowledge to a novice declines. The extent to which an expert assumes information to be common knowledge can be so large that they fail to see the gaps which exist in the understanding of a novice. The take-away is that the expert needs to consciously think like a novice and be deliberate in seeking an understanding of where the novice’s knowledge of a subject strikes its limit.

Physicist and author, Richard Feynman could be considered a master at overcoming the curse of expertise. He understood that the best indication of a truly deep understanding of a concept was revealed in one’s capacity to describe it to a child. His advice: "When we speak without jargon, it frees us from hiding behind knowledge we don’t have. Big words and fluffy “business speak” cripples us from getting to the point and passing knowledge to others.” Feynman understood that his expertise would prove to be a barrier to his students learning and that as such he would need to take actions to ensure his knowledge was accessible; something all educators should do.

But what if our expertise is imagined or false. What if what we think is so, just ain't so. This might be more common than we care to admit, and it is worth considering the source of this difficulty and its implications.

Not just what we were taught but also the way that we were taught things in school shapes our beliefs about what matters, and these messages can be hard to undo. Consider the average mathematics class that the typical teacher experienced when they were forming an understanding of what mathematics is all about. The emphasis was almost certainly on accurate calculations and application of prescribed methods which would result in the correct solution. Today that teacher is likely to believe that mathematics demands this sort of knowledge and that an expert mathematician is one who can quickly and accurately perform calculations. The trouble is this is false expertise as revealed by comparing these beliefs with the way that maths is described by a modern syllabus; "Mathematics is a reasoning and creative activity employing abstraction and generalisation to identify, describe and apply patterns and relationships….The study of mathematics provides opportunities for students to appreciate the elegance and power of mathematical reasoning and to apply mathematical understanding creatively and efficiently.” (NESA, 2017) In place of speedy and accurate calculation the syllabus speaks of “enjoyment”, active participation” and “challenging and engaging experiences”.

The same is undoubtedly true of other disciplines. If you spent time in a typical Science classroom you would likely believe that the work of a scientist revolves around correctly filling in a science lab report. The emphasis of the learning is on accurately filling in the template and a knowledgeable scientist would know the template by heart. In History the lessons seemed to revolve around remembering a list of dates, names and places and expertise could be measured by the number of facts which one might recall on demand. Somehow this does not fit with the rationale for the study of History according to the syllabus: "History is a disciplined process of inquiry into the past that helps to explain how people, events and forces from the past have shaped our world.” And if Geography is a “rich and complex discipline" that “build(s) a holistic understanding” and "is the study of places and the relationships between people and their environments”, how does it get reduced to knowing where you find Muscat on a map. False Expertise.

The implication of this unquestioned false expertise is that it becomes self-repeating. We believe that our knowledge base and underlying beliefs about the disciplines we teach are sound. Our teaching methods are founded upon this knowledge and these beliefs and so we present our students with a view of learning within these disciplines which is aligned with them. We perpetuate false expertise.

We must unlearn and relearn what we know and in doing so question the beliefs upon which our expertise is constructed. We need to examine closely the rationales for what we teach and understand deeply the concepts our students are needing to learn. We need to ask always, What will students actually do with the skills and knowledge they are acquiring and what underpins my belief that this learning will matter in the lives they are likely to live.

By Nigel Coutts

Learning From the Feynman Technique

The Curse of Expertise

NSW Educational Standards - Curriculum and Syllabuses

In Postnormal Times our Students need to be Brave

In contemporary times, we understand the importance of creativity, imagination and ideation. We are living in times shaped by chaos, complexity and contradiction where we confront ‘wicked problems’ such as climate change, globalisation, rapid technological transformations. These are times of rapid accelerations and ‘post normality’. The patterns of action and the organisational structures which served our needs in the past no longer apply and we are constantly confronted by challenges for which we do not have ready-made solutions. Only through the deployment of our most creative and innovative dispositions will we think our ways forward. 

“In an uncertain and often volatile world, successful organisations and their leadership must embrace ambiguity, disruptive change, risk, and the exponential quickness of the digital 4th industrial revolution.” (Jefferson & Anderson, 2019)

In “Normal” times, we had action stories which served our purposes well. In schools, these action stories revolved around the transfer of knowledge and skills from one generation to the next. Normality was normal because we had a clear understanding of what was required for young people to participate in the world of adults. There was an obvious body of knowledge and set of skills which would serve the school leaver well. Reading, writing and arithmetic, combined with a knowledge of some history, world place names, an understanding of some basic science and solid interpersonal skills mostly centred on following social norms was sufficient for a citizenry in normal times. The structures of our schools served these needs sufficiently well and our exit slips provided future employers with the evidence they required to determine which of our students would be the most suitable candidates. 

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. (Sardar, 2010)

But now we are in Postnormal times and what once worked is at best no longer sufficient, at worst it is outright dangerous. The skills our students need to develop are centred around dispositions not readily learned in a teacher directed classroom. Creativity, critical thinking, collaboration, communication, problem-finding, ideation, hypothesising, and innovation are now critical skills where but a short time ago they may have been viewed as the innate properties of certain individuals. Each requires that students are learning within environments which provide frequent opportunities that demand these skills. Each is learned not through direct instruction but through immersion in a culture where thinking in all its forms is the norm. 

“We need to transform our schooling system from a predominantly test-driven transmission model of learning to a place where creativity, collaboration, communication and critical reflection are central to learning.” (Jefferson & Anderson. 2018)

Coupled to this drive towards creativity and innovation is an understanding of the importance of individual and collective agency. In these times of volatility and chaos it is easy to see the world as something that happens to us and turn towards despair. The postnormal era is also the Post-truth era and it is easy to lose faith in the institutions in which we once placed great trust. Our politicians seem to play games with the truth, science is openly questioned and painted with the same brush as opinion. 

‘Our beliefs come first; we make up reasons for them as we go along. Being smarter or having access to more information doesn’t necessarily make us less susceptible to faulty beliefs.’ (Brotherton, 2019)

Empowering us against despair is our sense of agency; the degree to which we are able to imagine our capacity to influence and shape events towards our purposes. Where the individual full of knowledge and possessing a pre-defined set of skills achieved through a traditional education may find themselves lacking in times of rapid and volatile change, the creative and agentic innovator will see opportunity and new possibilities. 

“agency,” is the ability to make choices and direct activity based on one's own resourcefulness and enterprise. This entails thinking about the world not as something that unfolds separate and apart from us but as a field of action that we can potentially direct and influence. (Ritchhart. 2015)

If we are to cultivate the dispositions required in these times of postnormality and post-truth we need to establish cultures in our classrooms which will allow them to thrive. As we strive to do so it is likely that we will recognise the need for a classroom culture that is safe and where risk-taking and mistake making are not only tolerated but embraced. As we move towards a valuing of creativity we move away from notions that there is a right or wrong answer. There is not a known method and it is unlikely that success will be achieved on the first attempt. In building this culture we seek to eliminate messages that are likely to restrain or limit thinking and we value the creative process at least as much as the creative product. 

In this drive towards the provision of environments which are safe and risk-tolerant there is a danger that we might go too far. We have done this in the past when in an effort to create safe playgrounds, we removed every possibility of risk. The result is a generation of children whose safety is ensured by the structures in which they spend their days but who have not developed the ability to evaluate risks. 

Creative, innovative, agentic thinking demands bravery. If, in our efforts to provide environments which support risk-taking we remove all risk or deny the bravery demonstrated by individuals who take risks with their thinking, we do our students a disservice. Rather than removing risk, we need support all learners to take risks and to be brave. We need to acknowledge brave thinking as a step towards learning. We need to ask our students to be brave in their imagining, their questioning, their appraisals of truth, their confronting of power and their agentic actions. We need to show that we are brave and that bravery is a part of our lives. As Nelson Mandela shares "I learned that courage was not the absence of fear, but the triumph over it. The brave man is not he who does not feel afraid, but he who conquers that fear."


By Nigel Coutts


Rob Brotherton (2016) Suspicious Minds: Why We Believe Conspiracy Theories. Bloomsbury Publishing.

M. Jefferson & M. Anderson. (2019) Transforming Organizations: Engaging the 4Cs for powerful organisational learning and change. Bloomsbury Publishing.

M. Jefferson & M. Anderson. (2017) Transforming Schools: Creativity, Critical Reflection, Communication, Collaboration. Bloomsbury Publishing

Ritchhart, R. (2015) Creating cultures of thinking: The eight forces we must truly master to transform our schools. SanFrancisco: Josey-Bass  

Sardar, Z. (2010). Welcome to postnormal times.Futures, 42(5), 435-444. 

A Conceptual approach to Big Understandings and Mathematical Confidence

Contemplating the effects of traditional mathematics in "A Mathematicians Lament", Paul Lockhart wrote

"If I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done - I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.”

The traditional pedagogy of Mathematics encourages students to see the discipline as one that requires them to memorise and recall on demand a set of procedures and isolated facts. Speed and correct answers are overemphasised at the expense of understanding and genuine number fluency. As students focus on learning the procedures they fail to make a connection with the logic behind the methods they are using. They develop fundamental misconceptions and develop a narrow and shallow mathematical knowledge.

Retention of information through rote practice isn't learning; it is training. (Ritchhart, Church & Morrison. 2011)

This traditional pedagogy results in students developing a negative attitude towards mathematics. Many develop a mathematical phobia and believe that they are not a "maths person". When confronted by challenging mathematics they retreat and have no or only poor strategies with which to approach new ideas. This all leads to a decline in the number of students pursuing mathematical learning beyond the years where it is compulsory.

Fortunately there is a growing body of research that shows there is a better way.

This approach to mathematics is structured around a set of core ideas and practices. Each element works with each other element to build Mathematical Confidence for the learner. Mathematical Confidence is achieved when the learner believes that they are able to reason, communicate and problem solve with mathematical concepts. Mathematical confidence requires a deep level of understanding, adaptive expertise, fluency and a growth mindset when confronted with mathematical challenges.

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Through Number Talks students develop a rich Number Sense, a capacity to manipulate, de-compose and re-compose numbers, notice patterns and communicate mathematical ideas. By visualising, playing with and investigating "Big Ideas" students develop their understanding of essential concepts in mathematics. Strategies from "Visible Thinking" provide structures for student thinking and make this thinking observable to their teachers. Engagement in real-world, open-ended problems provide students with opportunities to apply their mathematical skills and reveals the relevance of mathematics beyond the classroom. By employing a "Teaching For Understanding" framework to their planning and pedagogy, teachers ensure the focus of mathematics is on developing adaptive expertise and ensures students experience opportunities to demonstrate and refine their understanding. The result is Mathematical Confidence defined by ones ability to bend their mathematical knowledge to new situations, to incorporate new concepts into their existing scheme and embrace challenges with a growth mindset.

Where to begin? Understanding the impact of our instructional order

Typically, the lesson begins with the teacher presenting the required method to the students. The teacher begins with step one being demonstrated on the board. Once step one is complete, the teacher demonstrates step two, and then step three and sometimes steps four and five. With triumphant zeal the teacher indicates the correct answer with a flourish of whiteboard marker and perhaps a double underline for effect. In phase two the students copy the process they have been shown with the teacher looking on to ensure the steps have been followed accurately. Naturally there are some bugs and errors that require correction. By the end of the lesson most students are able to accurately follow the steps and arrive at a desirable answer even if some of the numbers are changed.

Compare this to how a computer is programmed. The ‘coder' determines the steps to be completed and enters them into the machine ensuring accuracy; this equates closely to phase one of our lesson although with our students the coding occurs visually and aurally rather than via keyboard. The coder then runs the code on the computer and looks for bugs in the code which may cause unwelcome results; this is phase two of our lesson. Finally, having checked the code and feeling confident that it is bug free and fit for purpose the coder releases their programme into the world where it runs on a range of subtly different systems and with a mix of inputs; a very near comparison to phase three of our lesson.

The focus is on mimicry and memorization rather than deep mathematical thinking and understanding, flexible use of mathematical concepts, communication of mathematical arguments and justifications, and developing a positive disposition that values connections between mathematics and students’ identities beyond the classroom. I think it is important that mathematics teachers use instructional routines that not only build procedural fluency through conceptual understanding but also support strategic competence, adaptive reasoning, and productive dispositions. (NCTM President - Robert Berry)

There is a better way, one that supports conceptual understanding.

The alternative approach is to present content in a sequence that allows students to develop their number sense while also engaging in exploration of concepts or Big Ideas (through visualisation, play & investigation), with opportunities to problem-solve and problem-find as ways of strengthening their capacity for working mathematically. At the point of need in this cycle, new content including mathematical methods can be taught through targeted instruction with the goal to always build understanding.

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This approach to organising the presentation of content is built on three research based beliefs:

1. Mathematical understanding requires students to engage first with concepts rather than procedures.

2. Engagement and learning is increased when students see a need for the methods they are being taught

3. Instructional sequences which begin with problem solving allow for learning through 'productive failure'

1. Unless mathematics is to be viewed as a discipline defined by rules, where success is determined by how accurately one follows those rules, learning must begin with the underlying concepts (Big Ideas). This is backed by research from Australia's Chief Scientist that examined the approach taken to mathematics in 619 Australian schools achieving significantly above expected growth. "87% of case study schools had a classroom focus on mastery (i.e. developing conceptual understanding) rather than just procedural fluency."

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2. We are more likely to engage with new ideas when we see how they will help us achieve a short term goal. Telling students you will need this in the future, or worse, you will need this for the test is unlikely to increase motivation. When what we are learning has immediate relevance, when we are clear on the purpose of what we are learning our intrinsic motivation is triggered according to Daniel Pink, author of Drive. (Learn more about 'Drive' in this Video)

Jo Boaler et al., shares the following research that reveals the power of teaching mathematical processes at the point of need, rather than in isolation of need and in advance of application to contexts that matter to the learner.

A really interesting research study (Schwartz & Bransford, 1998) showed that students learned more when they worked, using their intuition, on problems that needed methods, before they learned the methods. They did not learn the methods until they had encountered a need for them. This caused the students' brains to be primed to learn them.

Boaler, Munson, Williams. (2018) Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 5 (p. 249). Wiley.

This approach of teaching to big ideas and teaching smaller ideas when they arise, has the advantage of students always wanting to learn the smaller methods as they have a need for them to help solve problems. (Boaler, Munson, Williams. What is Mathematical Beauty? Teaching through Big Ideas and Connections YouCubed )

3. Manu Kapur describes an instructional order "that reverses the (traditional) sequence, that is, engages students in problem solving first and then teaches them the concept and procedures. (He) call(s) this sequence of problem solving followed by instruction productive failure". Kapur's research shows that "Productive failure students, in spite of reporting greater mental effort than Direct Instruction (DI) students,significantly outperformed DI students on conceptual understanding and transfer without compromising procedural knowledge". (Kapur)

The aim is to ensure students develop the number sense, capacity for working mathematically and mathematical confidence they need along with an understanding that mathematics is a visual and beautiful subject.

By Nigel Coutts

This post has been adapted from ‘Global Cognition’ a site that is being developed by the author of this blog to support teachers implement this approach in conjunction with their use of the ‘Mindset Mathematics’ series by Boaler, Munson & Williams and the NESA Mathematics Curriculum.

Aligning assessments with the purposes of our teaching

Imagine a daily scene at your typical sporting facility designed to meet the needs of athletes across many different sports. Each day three particular athletes arrive for their routine training session. Each athlete is committed to success and trains hard. They have recruited expert coaches and seek guidance from specialists in sports medicine to ensure that their daily training schedule and overall healthcare plan aligns with their goals. They are equally passionate about their sports and this is plain for all to see in their approach to training.

Alex is into athletics and in particular is training in the hope of making the Olympics. Alex likes short to middle distance events and is focussing currently on training for the challenging 400 metre event. Alex spends time working on starts, running corners and accelerating hard over the last 50 metres to ensure the line is crossed at full speed. Alex’s coach has set up a training routine that ensures every muscle in Alex’s body is finely tuned to this task.

Bobbie is into Football (Soccer) and considers it to be the one true sport. Bobbie trains hard and is working on endurance and speed as areas of growth. Bobbie also spends time on drills to enhance ball control and passing. Bobbie hopes that all this effort will ensure a full game can be played with fitness left for the final ten minutes of play. Bobbie knows that improvements in strike rate come from a combination of skill with the ball, speed in open play and endurance.

Charlie is into weightlifting and has a training regimen designed to increase power and build muscle. Charlie is keen to find the limits of human strength and is continually increasing the weights lifted. Charlie spends long hours hoisting steel into the air and likes to feel the burn that comes from pushing muscles to new limits. Charlie’s coach works hard to ensure that the limits are not exceeded too rapidly and builds rest and recovery time into the schedule. The untrained onlooker could easily overlook the science behind Charlie’s training schedule.

After many weeks the three athletes are asked to participate in an assessment of their training methods. The researcher wants to find out which training method works best and will use this to inform coaches nationally of the method with the greatest research based effect size. The assessment is designed to be easy to administer and provide clear quantitative data. A few days later, Alex, Bobbie and Charlie are lined up on the starting line for a quick run around an oval, the time each records will reveal which athlete has chosen an effective training regime and who has been wasting their time.

With the assessment over each athlete is given their score. Alex is very happy. Bobbie is pleased. Charlie is devastated, clearly all that effort has been for nought.

In this example, the folly of the scenario is plain to see. Alex’s preparation was ideally suited to the assessment and the result achieved was as might have been expected. Bobbie’s training schedule was also sound preparation for the assessment; although the time spent on drills is probably the cause of a result that was less than what Alex achieved. Charlie’s preparation probably hindered performance and although it has built a powerful body, it is clearly a slow moving one. But in this situation the assessment is clearly not aligned with each athletes differing purposes. It suited Alex very well. It failed to reveal that Bobbie still has limited ball control and it gave no indication of Charlie’s immense strength.

The trouble is that we do this sort of thing all of the time. We rely on an assessment measure without taking a close look at what it is measuring and we obfuscate the information we need to evaluate the utility of these measures by reducing the results to numerical values.

Take as an example an assessment of learning in the sciences. One set of students participate in a classroom where direct instruction is the norm. They are presented with detailed information over a number of weeks. They transcribe information from texts and teacher instruction into their books, they study their notes at home and in small groups. They take mock exams and revise information that they missed. In another classroom a group of students is approaching similar content through an inquiry process. They understand that their goal is to master the process of scientific inquiry. They ask lots of questions, design experiments to test their hypotheses and share their results. Their teacher guides them through the inquiry process, models how a scientist works and provides feedback on the methods they are using. Both methods have their place in learning, both have value.

The complication comes when the student’s learning is assessed. If the test is based on recall of knowledge then the first group is more likely to succeed. The method of instruction they experienced is aimed at achieving the type of learning that the assessment measures. If the assessment requires students to design an experiment that will test a hypothesis, the second group has a clear advantage as their learning has prepared them for this exact task. The problem becomes significant when the assessment is used to endorse claims that one teaching method is more effective than another without any reference to what was assessed.

It is easy to point the finger at standardised assessments but the problem is more expansive than that. We all have a certain concept of what a summative assessment should look like and of the sort of items that belong within one. The biases that stem from our experience with tests and from the relative ease with which we assess recall of facts compared to creativity, critical thinking and problem finding/solving result in assessments that overvalue particular modes of teaching.

We need to consider the purposes of our teaching, the goals that we hope to achieve with and for our learners and in each instance, what success might look like. Only when we ensure that the assessments we value align with the learning we hope to engender, will we begin to have an accurate perception of what works and what does not. Until then Alex will be very happy, Bobbie will be blindly pleased and Charlie will be mightily devastated.

by Nigel Coutts

Taking time to design programmes for understanding

Identifying what our children need to learn is one of the most important processes within education. For the teacher this is the question they engage with as they design their teaching and learning units. By no means is this an easy task and the teacher must balance multiple factors to ensure that the programmes they design provide their students with the learning they require. Even the most effective sequence of lessons is of little value if what it sets out to teach has little importance in the lives our learners are likely to lead.

Often when we tackle the programming process we spend much of our time designing the learning experiences with which our children will engage and through which they will acquire and demonstrate new learning. We plan a sequence of activities, find or create resources, identify success criteria and plan assessments along the way and at the conclusion. This process takes a great deal of time, collaboration and a solid understanding of pedagogy. The trouble is that sometimes, we are teaching the wrong thing. Sometimes the focus of all our efforts is on learning that neither truly builds on where the child is with their learning nor drives them towards the sort of understanding they genuinely require.

One might think that the curriculum should provide us with the information we require for this task. In part it does, however looked at from another perspective we see that the curriculum serves a slightly different purpose. The typical curriculum document is a long laundry list of items which when combined into a whole represents the knowledge and skills which comprise a discipline. These parts are important and at some point they require our attention and inclusion within our plans but we should not lose sight of the fact that they are merely parts. What we require is a more conceptual approach. Our teaching should be guided by our knowledge of the understandings which will matter most to our students; of the concepts that are at the heart of our disciplines and learning areas.

Many teachers have found the answer to this challenge in an approach known as Teaching For Understanding. In this research based approach to planning learning experiences the educator is asked to begin by considering the essential understanding goals that they wish to achieve for their learners. This represents a fundamental shift in thinking and requires also that extensive time is allocated to the process of identifying and clarifying the understanding which we hope to achieve; what they are and how they will be taught and what evidence we might see to indicate we have been successful.

In Teaching for Understanding, teachers and learners focus their attention on the essential concepts within our disciplines, topics and ideas. Understanding Goals take us beyond superficial knowledge, require us to act strategically with what we know and empower us to be problem finders and solvers. Understanding Goals require learners to take a broader view, to engage with multiple outcomes and utilise knowledge and skills collectively in unique and original contexts.

"The fullest representations of humanity show people to be curious, vital, and self-motivated. At their best, they are agentic and inspired, striving to learn; extend themselves; master new skills; and apply their talents responsibly." Ryan & Deci (2000)

The Teaching for Understanding framework is the product of a five-year Harvard research program that sought to develop students’ understanding rather than simply knowing. It stresses in-depth learning and provides teachers with a language and structure for planning their curriculum and for discussing ways of promoting deep understanding with their colleagues, students and parents.

"Project Zero’s research on Teaching for Understanding helps educators to answer two essential questions: What does it mean to understand something? And what kinds of curricula, learning experiences, and assessment support students in developing understanding? The Teaching for Understanding framework that was developed through this research helps educators take students beyond the simple mastery of facts to being able to apply knowledge flexibly in unfamiliar contexts.” (PZ Website)

Teaching and learning can be aided by having a commonly shared language about learning itself (sometimes referred to as a meta-language). Through this common language teachers can discuss what it is that they are doing in planning, delivering and assessing the curriculum; teachers can discuss with students the learning process itself, and students can engage in peer conversation about their learning. Teaching For Understanding is part of the foundation of this common language of learning and is evidenced in the resultant pedagogy, planning and the students experience of learning.

Teaching for Understanding is built upon a performance perspective of understanding. "The performance perspective says, in brief, that understanding is a matter of being able to do a variety of thought-provoking things with a topic, such as explaining, finding evidence and examples, generalizing, applying, analogizing, and representing the topic in new ways.” (Blythe, 1988)

As teachers plan, a series of questions are utilised to develop four elements of a Teaching for Understanding unit as detailed below. These question ensure attention is given to identifying; what is most important for students to learn, the experiences which best scaffold this learning, how students will extend and demonstrate their developing understanding and the understandings to be achieved.

TfU Planning Guide - Questions to ask as we plan for understanding. Source - Tina Blythe

TfU Planning Guide - Questions to ask as we plan for understanding. Source - Tina Blythe

This planning process creates a learning journey that is typified by the diagram below. At the highest level teachers identify overarching understandings which are essential to the discipline or subject such as ‘Fair testing is at the heart of the scientific method’. Generative topics establish the significance of the learning and provide an indication of the scope of the unit. Essential questions are those defined by McTighe & Wiggins (2013) "as essential for students to continuously examine so as to 'come to an understanding' of key ideas and processes”. The authors of Teaching for Understanding use the term ‘Performance of Understanding’ to describe the opportunities students engage with as they develop, apply and test their understanding. Students "might acquire pieces of knowledge from books and lectures, but without the opportunity to apply that knowledge in a variety of situations with guidance from a knowledgeable coach, they will not develop understanding. Performances of understanding, or understanding performances, are the activities that give students those opportunities.” Within a Teaching for Understanding framework a series of performances of understanding serve the purposes of 'Assessment for Learning’ (Black & Wiliam, 1998) and provide the learner and their teachers with evidence of where they are with their understanding and what is required to drive their learning forward. Culminating performances of understanding are those placed at the end of a unit of learning and are those which allow learners to demonstrate their achievement towards the Unit Long Understanding Goals, understanding of the generative topic and overarching understandings.

Key elements of Generative Topics:

  • Generative topics are central to one or more domains or disciplines.

  • Generative topics are interesting to students.

  • Generative topics are interesting to the teacher.

  • Generative topics are accessible.

  • Generative topics offer opportunities for multiple connections. (Blythe, 1988)

All of this can be quite challenging at each step of the process. It requires a rethinking of what matters most and a shift to teaching in a more conceptual way. For teachers who are used to teaching an assemblage of parts, processes or blocks of knowledge this takes time to adjust to. Teaching the concept of multiplication is very different to teaching the multiplication facts or the vertical algorithm and yet students are unlikely to have the knowledge they require to understand multiplication if they do not experience it conceptually. Change is an important concept in many disciplines but it one that is often lost among a sea of examples of change. When an understanding of the concept becomes our goal we begin to seek experiences which allow our learners to engage with these in their true form instead of through proxies for them.

Einstein famously stated that “It’s not that I’m so smart. But I stay with the questions much longer”. Teachers can greatly enhance the quality of outcome that they achieve with and for their students by applying this sort of advice and spending much more time in determining what their students need to understand and less time on the activities they will perform along the way.

By Nigel Coutts

Black, P & Wiliam, D (1998), Inside the Black Box: Raising Standards through Classroom Assessment, School of Education, King’s College, London.

Blythe, T. (1998) The teaching for understanding guide. San Francisco, California; Jossey-Bass Publishers

Johnston, P. (2004) - Choice Words: How Our Language Affects Children's Learning. Maine; Stenhouse Publishers.

McTighe, J. & Wiggins, G. (2013) Essential Questions: Opening doors to student understanding. Virginia; ASCD

Ryan, R., & Deci, E. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. American Psychologist, 55(1), 68-78.

When designing student learning, what questions guide us?

We ask lots of questions as we plan for our student's learning. Some of the questions we ask are about where they are with their learning. These are the questions that we answer with information from assessments combined with our professional judgement and our interactions with our students. Some of the questions are about what our students need to learn next. These are the questions where continuums such as those described within the curriculum provide us with guidance. We combine this prescribed continuum with our knowledge of learning and learners to decide where we hope to take our learners in their learning journey. Some of the questions we ask involve our understanding of the world beyond our classrooms and our thinking about the skills and dispositions which will be of most value to our students in their tomorrows.

But perhaps we miss one important question along the way. Maybe we should be asking questions about how our students will apply what they learn?

David Perkins describes the ‘uppity question’ that students ask; “Why do I have to learn this?”. Often the answer is something along the lines of ‘it will be on the test’ or ‘you will need this as an adult’. The truth we know is that much of what we teach is at best infrequently used and while it may be on the test, the students would be right to counter our argument with ‘why is it on the test?’. The typical response to this line of thinking is to reconsider what we are teaching so that when we tell our students 'that this learning will matter in the lives they are likely to live’, we are confident that it will be.

But maybe we can strive to avoid the question altogether. Maybe we can plan for learning experiences where the utility of what is taught becomes self-evident.

Some of the learning situations that our students engage in have such clear relevance that the question ‘why do I have to learn this?’ is never asked. Consider a situation where a student is developing a solution to a problem that matters to them. Maybe the student is making something through a design thinking methodology. From developing an understanding of the problem, through a process of ideation and prototyping the student’s efforts are clearly linked to a problem that matters to them. Along the way they undoubtedly find themselves requiring new skills and knowledge in areas which may not be immediately associated with the problem they set out to solve. Perhaps they need to budget for resources, communicate their ideas with collaborators, research related concepts and phenomenon. This secondary learning has meaning because of the part it plays in the primary task.

Other learning tasks reveal their relevance in other ways. A teacher who reveals their passion for a subject invites their students to share in that interest. When we find a topic engaging, beautiful, powerful and share our emotional connection to the learning with our students we remove the sense that it is merely content to be learned for its future utility. Learning that is situated in a context of social connections and relationships takes on a meaning that brings immediate relevance.

Another path is to reveal the empowerment that comes with a new skill or understanding. Telling our students that 'knowledge is power’ will not suffice, they need to be shown how the knowledge and skills they acquire empowers them. Learning to analyse poetry so that one can write an essay on the evolution of the sonnet has little meaning but being shown how poetry serves to ignite powerful emotions in the reader or provide an avenue towards self-enlightenment might spark an interest. With the right start, the learner can be invited to participate in a process of evolving and fine tuning their skills and expanding their repertoire such that they are increasingly empowered by the knowledge they possess.

Increasingly in contemporary times we understand that our students need not wait for adulthood before they apply their learning to real-world purposes. The young entrepreneur who transforms and idea into a business reveals the presence in society of new opportunities. Innovative ideas no longer require the backing of big-business to succeed. Small-scale, grass-roots projects baked by crowd funding and low-volume manufacturing techniques or purely-digital solutions allow anyone with an idea to capture new markets. Social media brings new avenues and youth activism is revealing itself as a powerful agent for change. Young people are not waiting to achieve voting age before finding their political voice. When students learn about global issues such as climate change, poverty or gender inequality they are able to take action and discover their agency. Education needs to keep pace with these trends and recognise that it has a part to play in training both political actors and the next generation of industrialists to use their power in responsible ways.

These new opportunities for students to apply their learning immediately bring with them new challenges. Once, education was like filling a bucket with water in the hope that it may one day be used to fight a fire or nurture a garden. Today our students are using their knowledge, skills and dispositions to solve problems and achieve goals that were once the preserve of adults. It was sufficient in the past to teach the skills of persuasive writing and leave learning about the consequences of its use in achieving political goals for later. This is no longer a safe strategy and we have seen repeated examples of young people who have found themselves in the midst of a political storm for which they have little or no preparation. What are the understandings children need to navigate these waters and what opportunities might schools provide for students to experiment safely in this new territory? Clearly there is a new set of questions to be asked about what we might teach our students.

By Nigel Coutts

What meal would your team be?

What makes a team truly great? What are the qualities which allow some teams to perform at a high level while others seem trapped? One approach to this question is to consider a team as though they were a meal. Thinking metaphorically, we ask what are the ingredients that make a great team and how might we combine them to produce the best results?

Some teams are like a stew. Each member of the team has their unique qualities, their particular strengths and peculiarities. A good stew combines diverse ingredients into a single pot with the result being a meal that always tastes exactly like stew. The mixing and blending of flavours in a stew is so complete that it becomes difficult to see the contribution of individual ingredients. Teams are like stews when the individual differences melt away and the team becomes a heterogeneous blend. There is minimal tension, very few arguments, no conflicting opinions and everyone seems to be working from the same page. Such a team can be a pleasant place to work. It can be very supportive and individual weaknesses are blended over by the cohesion of the team.

A team that has morphed into a stew is the sort of place where innovation goes to die. New ideas seem to sink down into the stew and disappear with little evidence to be seen in the overall flavour and texture. New members are inevitably indoctrinated into the “way things have always been”. Fresh perspectives and voices that challenge the status quo have little hope of transformation. Stew like teams are dangerous in times of rapid and uncertain change. They lack the flexibility required to adapt as circumstances change and new opportunities emerge. So deeply ingrained is the flavour of a stew that it is perhaps easier to throw out the whole pot and start again. If that is not possible, then maybe the only solution is to consistently add more and more of the one transformative ingredient until its flavour begins to overwhelm the otherwise inescapable last of stew.

Some teams are like a freshly tossed salad. Such teams are almost the complete opposite of our previous example, the stew. In a salad, each ingredient stands on its own. The contribution of each ingredient is clearly evident. Each ingredient adds its unique personality to the salad and as you add fresh ingredients to the mix the possibilities widen. Salads are adaptable and can be easily remixed and rearranged in new combinations. In a team that is like a salad diversity is evident, many perspectives are shared and the voices of individuals are heard.

A team that is like a salad can be a great place to work. The culture of such a team can be very dynamic and responsive. Individuals are able to find their place and with little need to “fit in” that individuality is readily expressed. Arguments can be difficult to deal with and tensions can be left to fester or frequently explode as there are few normative pressures. A salad like team can be a place that generates new ideas in abundance but is unable to move from divergent ideation to convergent transformation. Everyone has an idea but no one is willing to give an inch to achieve consensus. A salad can also be a place where there is little support for individual weaknesses. The observation that one bad egg can ruin a salad applies also to teams that are salad like. It is also too easy for one ingredient to dominate. A single overpowering ingredient in the team or too much of one type of ingredient can result in an imbalance that is difficult to address.

Some teams are like “meat and two sides”. A good simple meal with minimal fuss and easy preparation. The standard fair of pubs and clubs the world over. A team becomes like “meat and two sides" when it is centred on one talented and dominant member. In teams like this the ideas, thinking and bulk of the work is done by one member. Take that one member away and you are left with an almost empty plate, a vacuum that needs to be filled. Without the meat on the plate the two sides have little to offer, they were always secondary to the main show and merely basked int its glory.

A team that is like “meat and two sides” will only be as strong as its dominant member. It will be for the most part well managed and will get the job done. In the right circumstances where the challenges of the day fall within the areas of strength of this dominant individual the team will run smoothly. The two sides add a certain something and so long as they know their place and are content with playing along with the dominant team member disputes will be avoided. When the challenges are beyond the scope of the dominant member, even if they may have been addressed by one of the sides moving into a more substantial role the team is unlikely to succeed.

Of course the range of meal which we might select as a metaphor for our teams is endless. The trick is to know what type of team we have and what type of team we might need. Just as there are times when our culinary needs are well served by a tasty stew there will be times when a team with stew like properties fulfils our needs; unless change is likely. There will be times when a salad is perfect while at other times a good serve of fish and chips might be best. By closely scrutinising, understanding and valuing the team we have; by knowing each individual ingredient and the combinations made possible we begin to plan a successful meal (team).

By Nigel Coutts

Lessons from Schrödinger's Cat

There are some ideas which seem to translate nicely into fields of thought far from their point of origin. These are ideas which shine a metaphorical light on concepts and allow us to develop a deeper understanding of that concept once we see it from a fresh perspective.

Schrödinger's cat is a concept within quantum physics; a field that is far from the day to day functioning of the typical (non-science) educator. It is a thought experiment developed by the Austrian physicist Erwin Schrödinger in 1935 to help explain quantum superposition. For those who do not spend their days contemplating quantum physics, the ponderous circumstance that Erwin’s cat is placed in is a response to an article that "highlighted the counterintuitive nature of quantum superpositions, in which a quantum system such as an atom or photon can exist as a combination of multiple states corresponding to different possible outcomes." (Wikipedia)

Schrödinger proposed a scenario in which a cat is placed inside a box with a vial of poison which at a random point in time is broken open resulting in the cat’s tragic death. With no way of seeing into the box the observer does not know if the cat is alive or dead. Schrödinger proposed that we can thus think of the cat as both alive and dead up to the point where we break the box open and confront either an annoyed and very much alive cat, seeking vengeance for its confinement or find ourselves in need of a shovel.

What might this radical oversimplification of a great physicist's work have to do with education?

Consider a typical unit plan or sequence of lessons. Students are introduced to a concept or idea. The teacher guides them through the material essential for them to learn. There might be a lecture, perhaps a stimulating video. Most likely the students will be asked to read something related to the topic before the teacher spends time in class discussing the parts of greatest importance. New methods will be introduced to the students. There will be modelling of the process by the teacher, followed by an opportunity for the students to practice the new method. New vocabulary will be introduced and as the unit draws to its logical conclusion the teacher will artfully draw the many pieces together.

The last piece of the puzzle is the final assessment. Maybe it is a class assessment or maybe it is a high-stakes standardised and formalised assessment such as the Higher School Certificate or the SAT. In this final summative assessment the quality and depth of the students learning as a consequence of their engagement with the learning process and the teachers skill in making the concepts and understandings is put to the test. The result of this assessment is a clear numerical statement of the success or not of the whole learning endeavour.

The final assessment of the student is somewhat similar to opening Schrödinger’s box. Only at this point do we know if the student has mastered that which we set out for them to learn.

When we draw a parallel between Schrödinger's cat and our learning sequence as described above we see a fundamental flaw in our design. While Schrödinger’s sealed box serves a purpose in his metaphor, the educator is much better served by a box with a window. We want to be able to observe our students at every point in their learning journey and should their metaphorical vial of poison break, we want to take immediate action. And yet when we rely heavily on summative assessments as the measure of learning we create a situation where we only discover gaps in learning long after the point where we could have taken appropriate action.

The clear antidote to this scenario is to rely upon formative assessments and strategies to make our students thinking and learning visible; to us and to them. By constantly gathering and acting on evidence of where our students are in their learning journeys and by enabling them to be observers and drivers of their own learning, we set a window into Schrödinger’s box. Our goal is to drastically shorten the time between noticing that a student has misunderstood a concept, is not mastering a new skill or has missed a key connection and the implementation of actions we collectively take to remedy this.

To stretch a metaphor perhaps too far, we want to know when the vial breaks open, we want our cat to notice it too and together we want to find a way to avoid an unfortunate ending.

By Nigel Coutts

Curiosity as the edge of knowledge phenomenon that drives learning

We are driven by curiosity. It is an innately human quality that has driven us to explore, ask questions, investigate, wonder why and search for a deeper understanding. In a very fundamental way curiosity is the driver of all self-directed learning. It is our desire to find out more, unlock new knowledge and answer our questions (big ones and little ones) that compels us to learn.

Sir Ken Robinson famously and provocatively asked “Do Schools Kill Creativity?”. The same question might be asked about curiosity.

There is some evidence that this might be the case. Numerous studies have reported that the number of questions asked by a child steadily declines as they grow. From somewhere around the 300 per day mark at age four this declines to less than 100 by the time the child is nine years old. This is of course linked to a steady increase in what the child has achieved sufficient knowledge about and a decline in the number of new encounters in their daily exploration of the world and yet it remains as a point of concern as there are potentially other factors at play here.

As students experience what school is about they quickly learn that what matters most to their teachers, and for their success, is right answers. The patterns at the heart of education send powerful messages about what learners are supposed to do. Spend a little time in the average classroom and you see that the dominant pattern is typified by the teacher asking a question and the student providing an answer. Indeed, an alien visitor arriving with no knowledge of “who is who” would be forgiven for assuming that the teacher is the curious one and the students are the keepers of humanities knowledge.

Some students might miss the unsubtle messaging that exists within the dialogical structure of the classroom but they surely will not miss it when the time comes for their learning to be assessed. Few if any assessments offer marks for questions that the students may have at the end of a learning module, even in environments that claim to value curiosity. If we are to value curiosity and seek to encourage it surely it would be one of the dispositions that we assess. Unfortunately the disposition most commonly assessed is recall of knowledge followed closely by the ability to communicate that knowledge in the prescribed method of an essay.

Recently there has been debate about the place that curiosity plays in learning and its relationship with knowledge. The claim is that for a learner to ask quality questions about a field of knowledge they must first possess a sufficient level of knowledge. This line of thinking is used to argue for a pedagogical model that begins with teacher to student transfer of knowledge and moves opportunities for questions and curiosity to the latter parts of the learning journey. This raises some interesting questions.

It is reasonable to agree that a degree of knowledge is required before an individual is likely to arrive at meaningful questions that might drive an inquiry. Before I wonder what is on the other side of the door I need to become aware of the door. Before I am curious about a phenomenon in physics I need some exposure to that phenomenon. The question is do I require knowledge or does an engaging prompt that stimulates curiosity enable my mind to generate relevant questions at a novice level and then as I acquire knowledge ask more complex questions typical of an expert.

Mihaly Csikszentmihalyi’s description of how the creative process is sparked parallels the role that curiosity plays in sparking a desire to learn:

The creative process starts with a sense that there is a puzzle somewhere or a task to be accomplished perhaps something is not right somewhere there is a conflict a tension a need to be satisfied. The problematic issue can be triggered by a personal experience by a lack of fit in the symbolic system by the stimulation of colleagues or by public means. In any case without such a felt tension that attracts the psychic energy of the person there is no need for a new response therefore without a stimulus of this sort the creative process is unlikely to start.
(Mihaly Csikszentmihalyi)

Curiosity exists at the edge of knowledge. For this reason even the most wise person has a point where the extent of their knowledge is reached; what they do at this point is what makes them wise. With this in mind rather than extinguishing curiosity learning should shift the point at which we rely upon our curiosity ever deeper into our learning journeys and further from the point of what is known. Curiosity is the driver of learning for the novice and the expert.

There is a real advantage in including curiosity inducing learning into our routines. Research by Gruber, German & Ranganath reveals the power of curiosity for learning in the moment and its benefits to learning in other contexts. As reported by Jackie Gerstein of “User Generated Education”:

The study revealed three major findings. First, as expected, when people were highly curious to find out the answer to a question, they were better at learning that information. More surprising, however, was that once their curiosity was aroused, they showed better learning of entirely unrelated information that they encountered but were not necessarily curious about. 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. Second, the investigators found that when curiosity is stimulated, there is increased activity in the brain circuit related to reward. Third, when curiosity motivated learning, there was increased activity in the hippocampus, a brain region that is important for forming new memories, as well as increased interactions between the hippocampus and the reward circuit.

So if it is agreed that curiosity is an effective driver of learning and has an important role to play in enhancing the effectiveness of our learning, what opportunities do we offer for students to demonstrate curiosity? How do we move curiosity from being something teachers exhibit while planning a unit to one that is at the heart of our learners experience of school? How do we shift the narrative of education from one that values right answers to one that values curiosity and the search for answers.

By Nigel Coutts

Related:

Questions at the Heart of Learning

The Questions that Matter Most

Helping Students to Become Problem Finders

More than Knowing the Right Answer

Mihaly Csikszentmihalyi (2013) Creativity: Flow and the psychology of discovery and invention. New York; Harper Perennial.

Matthias J. Gruber, Bernard D. Gelman, Charan Ranganath. States of Curiosity Modulate Hippocampus-Dependent Learning via the Dopaminergic Circuit. Neuron, 2014

Educators as Agents for Educational Policy

Education exists in an uneasy domain and the teaching professional is forced to navigate between a multitude of conflicting tensions. Our education systems are dominated by abundance of voices all shouting for attention and offering a solution to the problems they have diagnosed. Each individual claims expertise and insights gained from years as a student is sufficient experience to allow one to speak with authority.

Politicians know that education is an election issue and politicians exist to give their public what they want. Henry Ford knew that had he sought the opinion of his customers they would have requested a faster horse. Henry listened to other voices instead and delivered the Model T. Henry was not a politician. The political take on education is one developed mostly from a distance. It reflects a belief that education needs fixing and that the blame for its current state lies with teachers. It relies on limited data, that is oversimplified, misinterpreted and packaged to suit the predetermined message. It plays to false dichotomies which in a two party system of democracy neatly allows one side to offer the opposite solution to that recommended by their opposition. Opinion polls drive policy but the opinion of those most likely to offer truly useful information is largely ignored or given equal credence to that of the masses.

The media in its present form exists to sell advertising in competition with Google and Facebook; the pretence that they are in the business of selling papers or attracting viewers has passed its use-by. A headline that proclaims consistent progress or an article that offers an in-depth exploration of the complex nature of educational decision making is unlikely to achieve as many Ad views as one proclaiming that the system is broken. Every journalist has an opinion and celebrity counts more than expertise. Why seek the opinion of an educator when that of a half-baked entertainer is available. Truly deep journalism, that explores complexity and is aware of context is a risky enterprise and one that is unlikely to increase impressions. Only on the fringes does one find a more rounded view where educator voices are included and respected for the expertise they bring but this is not where the mainstream public finds their news.

With little access to a more nuanced view of education the general public has a limited perspective. If you are a parent you will have some insights into what occurs in schools but an understanding of why it happens and a picture of the greater complexity behind the scenes is likely to be lacking. Reporting of assessment results rings alarm bells. Reading that Australia’s results on international assessments leads to calls for inquiries into schools and teachers rather than for a close accounting of what the assessments measure or their inherent validity. Little mention is made of the geographic distribution of underachievement or the link between NAPLAN results and ICSEA ( Index of Community Socio-Educational Advantage) scores. Everyone who has been to school has an opinion on the subject and debate continues with little reference to research or genuine expertise. Dichotomies abound and issues are oversimplified. Back to basics is the answer unless you advocate for 21st Century Skills. Follow Finland or maybe Singapore; their results are stellar. Rely on the judgement of an education professional; no thanks.

In the middle of all this sits the professional educator. Armed with years of training, a broad knowledge of research, experience from the classroom and an understanding of learners and learning. Teachers understand the complexity of education. They use their professional knowledge to plan learning experiences that meet the needs of their students. They balance multiple demands on their time while complying with seemingly contradictory policies and curriculums. They enact multiple dictates from a polyphony of interest groups all while ensuring that the needs of their students come first. They know that test scores are just one measure of their achievement and understand that the success attained by many students thanks to their care, is not reflected in any of the standardised measures.

In modern times more than ever though, being an exceptional educator is perhaps not enough. If education is to rise to the challenge of a rapidly changing world, if we are to ensure our students are prepared with the skills they will require in times of uncertainty and volatility, educators will need to find their voice and become agents for change. Teachers need to understand that education is shaped by political forces and that excellent classroom practice needs to combine with advocacy for education as a respected profession that takes collective control of its future. Policy must be something driven by educators, not something which happens to educators.

As in so many aspect of education, John Dewey had the measure of the situation,

It is . . . advisable that the teacher should understand, and even be able to criticise, the general principles upon which the whole educational system is formed and administered. He is not like a private soldier in an army, expected merely to obey, or like a cog in a wheel, expected merely to respond to and transmit external energy; he must be an intelligent medium of action. John Dewey, 1895.

By Nigel Coutts

The Eight Cultural Forces - The lens & the lever

Schools are busy and complex places. Whenever you bring several hundred people together for an extended period of time on a regular basis complexity is likely to thrive. One way to consider the complexity involved in the average school might be to map the connections and interactions which exist. Start the process with one person, consider all of the factors and experiences which make this person who they are. Now connect this person to one other and make note of the interactions which occur between these two people. Be certain to consider all of the factors and experiences relevant to this second person. Repeat this process again and again and again until you have mapped the interactions and intersections of everyone directly involved in the school. Then keep going, you need to consider all of the people on the periphery of the school and so far we have only considered the people; don’t forget the environment of the school and its community, the culture of the place, its history, its place in the world. Now that you are almost finished, go back and start the whole process again, things have changed since you started.

Education is inherently complicated and any attempt to reduce it to simple terms is likely to fail. The tendency to simplify things to one or two easily addressed factors is behind much of the frustration that teachers experience whenever they listen to politicians or the media offer a soundbite on the state of education. Teachers know how complex things really are, after all they spend much of their time in schools and large chunks of their day thinking about what goes on inside schools. Politicians and the media make short visits or rely on memories of their school days. When a new plan is announced to re-focus education in one way or another it is almost inevitable that it will fail to address most of the complexity that occurs in schools. Those in the know are hardly surprised.

This unavoidable and irreducible complexity means that schools are challenging place to study, to understand and to manage change within. Even for the teacher who spends everyday inside the school there is so much going on that unguided observations and the plans based upon them come with no guarantee of success. This is a fundamental tenet of complexity theory. Complexity theory points towards the importance of exploring the interactions between the intentions and effects of agents within organisations and reveals that the exponential scaling of these connections brings greater degrees of complexity than may be managed.

Perhaps the closest that complexity theory comes to a positive statement on the outlook for managing complex systems is that ‘despite complexity theory’s relative inability to predict the direction or nature of change, by implementing at each constituent level changes whose outcome we can predict with reasonable confidence, we are at least influencing change in the appropriate direction’ (Mason, 2008 p46) This points us in the direction of a lens that enables a clear perspective of what occurs inside schools; a lens that allows us to retain our perception of the whole while permitting us to then influence that whole by targeting its more manageable parts.

Such a lens is offered by the ‘cultural forces’ as identified by the research of Ron Ritchhart and colleagues at Harvard’s Project Zero. In the cultural forces, we find a set of naturally occurring factors which are present in all schools, all classrooms and between all members of a learning community. From an extended observation of schools engaged in the business of education the cultural forces emerged as the factors which have a significant impact on the culture of the organisation. The cultural forces are present without any deliberate action and they are either exerting a positive force or heading an organisation in the wrong direction. While the cultural forces occur across all settings, how they are expressed varies immensely.

Source - Worldwide Cultures of Thinking Project, 2015 Ron Ritchhart, Project Zero at Harvard University.

Source - Worldwide Cultures of Thinking Project, 2015 Ron Ritchhart, Project Zero at Harvard University.

Ritchhart identified eight cultural forces; opportunities, time, modelling, language, environment, interactions, routines & expectations. The teacher armed with an awareness of these cultural forces seeks to ask questions to uncover how each force is currently experienced within their sphere of influence and linked to a particular goal. As Ritchhart was seeking to understand how we might build a culture of thinking questions such as ‘What opportunities am I providing for my students to engage in critical thinking?’ were common. In a different context with a focus on building capacity for positive social learning one might ask ‘How might I offer more opportunities for students to apply their new social skills?’.

As lenses, the cultural forces encourage a focus on actionable items that influence the culture of a school or classroom. For example, by looking at and asking questions about how ‘Time’ is allocated in schools we gain a perspective on what matters most and often find that much time is spent on items which have little to do with our core purposes. Through the lens of ‘Interactions’ we see how the connections between people (teachers, students, the community) are either supporting or hindering learning that matters. Are we focused on interactions that support collaborations and responsible risk taking or are we focused on aspects of command and control? Do we provide our students with effective “Modelling’ of the habits of an effective learner or do they only see their teachers as pre-formed experts? Each cultural force provides us with a fresh perspective and we can then move to how we might make changes to how that force is expressed so as to move us towards a desired state.

The cultural forces do not remove the complexity that exists within schools but they do allow us to see what is there and to see it in manageable chunks. Having used the cultural forces as a lens for understanding what is there, a school might decide to focus on tweaking just one of the forces as they work their way towards their goals. A teacher might notice that her students have difficulty settling after time in the playground and decides to implement a new ‘Routine’ to help the students re-focus at these times. While all eight of the forces are in action all of the time, there is no need for us to address them al at once.

Daniel Wilson of Harvard’s Project Zero speaking in Melbourne noted that designers achieve greater success with complex problems than others. Designers have a capacity due to their thinking dispositions to cope with complexity and to adapt solutions as needed while working towards a vision or shared goal. Daniel indicates that complex situations, such as those which schools increasingly confront as a result of rapid change and previously unencountered challenges, require emergence as a path to solutions. A bubbling forth of ideas which may be transformed into plans and drivers of change from all areas within an organisation is seen as the best approach to change where solutions have not yet been found and cannot be passed down from above. Ewan McIntosh indicates that much of the success that the Designer has is a result of their use of a design thinking process. Their capacity to generate, apply and evaluate ideas is a result of an approach to problem solving that is flexible enough to enable creativity yet provides sufficient structure to avoid complete divergence. ‘You need the box to think in’.

The great strength of the cultural forces as an approach to problem finding and solving in schools is that they provide educators with enough structure while being adaptable to all contexts. The cultural forces do not constrain or describe the solutions that might bubble forward. The change leader in a school is merely offering their team a lens with which to see, a common language with which to discuss it and a lever with which to move things. Armed with the cultural forces a school can allow great ideas to bubble up and to be acted upon purposefully.

By Nigel Coutts

Mason, M. (2008). What is Complexity Theory and what are its implications for educational change? Educational Philosophy and Theory, 40(1), pp. 35-49

Ritchhart, R. (2015) Creating cultures of thinking: The eight forces we must truly master to transform our schools. SanFrancisco: Josey-Bass

A pedagogy for Cultural Understanding & Human Empathy

"For us, we are all very different, our languages are very different, and our societies are very different. But if we could extract ourselves from our point of view and sort of look down at human life the way a biologist looks at other organisms, I think we could see it a different way. Imagine an extrahuman observer looking at us. Such an extrahuman observer would be struck precisely by the uniformity of human languages, by the very slight variation from one language to another, and by the remarkable respects in which all languages are the same."

- Noam Chomsky

How we see ourselves, how we describe ourselves reveals a great deal about how we see ‘others’. In May of this year, speaking to the audience of the International Conference on Thinking, Bruno Della Chiesa invited us to consider how we might approach the question of "who we are?”. In responding to such a question, what list of affiliations do we invoke to define ourselves? Do we attribute our identity as belonging to a particular culture or nation? How important in our self-definition is our membership to one or more of the subgroups of humanity?

Bruno shared that the cumulative impact of his study of language and of languages is a re-imagining of his identity to one that is defined primarily by his ‘humanity’. With each additional language that he mastered his perception of his place in the world was altered. He moved from a one-dimensional perspective of the world to what he describes as an n-dimensional perspective; an understanding of cultures not in isolation but as a richly interconnected whole. As we learn additional languages we develop an understanding of language from the interferences between them. Each additional language is easier to learn as we see beyond the differences to an understanding of the fundamental constructs which are near universal. The same pattern occurs as we experience and learn multiple-cultures from our engagement with languages. We become open to a cross-fertilisation of ideas resulting in a philosophy of language and with this and through exposure to multiple cultures we develop a philosophy of culture. This philosophy of culture allows us to see ourselves (us) and ‘others’ as members of a global culture defined by our humanity rather than our nationality.

How we construct our identity defines how we see “others”. Human history is marked by the often ugly and bloody interactions between a powerful ‘us’ and new and frightening ‘other’. Too often we see the world in terms of ‘us’ and ’them’ and this perception of ’them’ of otherness has allowed the worst of our inhumanities. It is this perception of ‘others’ as something to be frightened, mistrusted, as unworthy, uneducated or uncivilised which has allowed us to engage both in war and to turn our backs on those in need. But, if we begin by defining ourselves as humans, the notion and power of and negative responses towards ‘us and them' relations is diluted. When we see our commonalities before we see what makes us unique we remove the greatest barrier to a better world.

Recent events locally and globally reveal that despite all our efforts; the rise and rise of democracies, the normalisation of global transactions, of the daily blending of cultures in increasingly multi-cultural societies, of the historical analysis of our past failings, we must never turn away from the threats posed by the perception of ‘us’ and ‘others’ as a relationship which must be dominated.

One day, maybe, we will have a world where the division between ‘us’ and ‘them’ has dissolved. Where our capacity for human empathy and understanding eclipses our capacity for hate, but such a time will not happen without our efforts and as Paulo Freire reminds us, education has a powerful part to play.

"But the humanist, revolutionary educator cannot wait for this pos­sibility to materialize. From the outset, her efforts must coincide with those of the students to engage in critical thinking and the quest for mutual humanization. His efforts must be imbued with a profound trust in people and their creative power. To achieve this, they must be partners of the students in their relations with them." - Paulo Freire

When we encourage our students to learn another language so they may better understand themselves and their neighbours, when we encourage them to study another culture not to know how ‘others’ live but to explore what links us all, we make possible a new definition of ourselves, not derived from our place of birth but from our undeniable humanity. We need a pedagogy that allows our students to see 'the very slight variation from one culture to another, and by the remarkable respects in which all cultures are the same'.

By Nigel Coutts

For those about to make a resolution

With the year rushing to a close, this seems like the right time to set goals for the year ahead. To pause and consider what next and make some personal promises.

The trouble is that the history of setting New Year Resolutions is littered with failures. It is so easy at this point in time to make commitments for change and then just a few weeks later to have forgotten what they were. Guilt sets in and what was a positive process now seems like an exercise in futility. By making a New Year’s Resolution we merely set ourselves up for an inevitable failure.

Change is by no means an easy process and it is one that surely begins with wanting to change. It is our desire to change combined with the pressure of the season that leads us to engage with this process of making a New Year's Resolution. But change requires so much more than desire and if we are resolving to change because it is “that time of year” there is a good chance we are not truly ready to commit to the change.

Understanding that change is a process and not a “resolution" allows you to approach it with a better understanding of what it will require. There is a definite benefit in knowing what it is you hope to achieve. If there is a common element in all of the “change manifestos” it is that a clear and powerful vision of the desired state post change is a critical first step.

It also needs to be a vision that is owned by the people who will be most impacted. In the case of a New Year’s Resolution those people are ‘you’. If the resolution you set is a response to what you think others believe you should do or be or become, then you are headed in the wrong direction. This is surely part of the reason why so many New Year’s Resolutions fail, the person making the resolution did not truly want the change, they merely wanted the approval that might have come from others had they achieved it. Once you realise that those you were planning to impress as a result of your new resolve are too caught up with their own issues to notice, you see how your efforts were for naught.

Should you arrive at that point of knowing what you truly hope to achieve and have a clear understanding of why it is of great personal significance, you are ready to start the process of changing. It is one thing to decide you want to climb a mountain; it is an entirely different task to actually do it. One requires an idea and a couch on which to have it, the other involves a whole lot of focused and persistent action.

At some point in the whole process of imaging a change you have to work out exactly what you need to do to achieve it. The mountaineer who only makes plans for how they will hang their flag on the summit will never get as far as the first camp. Success is only likely if you are clear on what you must do, what the first step is, the second and so on. It might be said that the journey of a a thousand miles begins with the first step, but the second and third and every subsequent is as important as the one which starts it all.

Now that you are on your way you will undoubtedly come up against more than a few roadblocks and speed bumps. No change that is worth something as lofty as a New Year’s Resolution can be achieved with ease. The greatest hurdle is likely to be that of habit. The way that we have always done things, the things we do and barely notice that we do them, the habits that are part of who we are become the biggest obstacle to change. Habit is also perhaps the best strategy with which to achieve your goals. Rather than leaving change to chance, make the little steps along the way to success a part of a new habit, one that precludes the old ways you are wanting to avoid. Spend too much time checking email in the morning, change your schedule to include a power walk, not just to clear the head but to get you away from the emails.

The choice to set a New Year’s Resolution should not be taken lightly and if you do and you want to succeed it at it you must commit to the journey. The choice you make on Monday night should be something that you are wanting to live with for a very long time, if not maybe just let New Year’s Eve be a chance to enjoy what might be best described as "scare the wits out of your dog day”.


Source -  The Oatmeal

Source - The Oatmeal


By Nigel Coutts

Holiday Reading - Christmas 2019

With the Christmas Holiday’s finally here this is the perfect opportunity to catch up on some of that reading which has been delayed while more pressing matters are dealt with. Here are the top items on my holiday reading list. With a project underway that explores a conceptual based approach to teaching mathematics there is a bias in that direction.

1. In the Moment: Conferring in the Elementary Math Classroom by Jen Munson

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In this book the idea of a mathematics conference is unpacked and made practical. By conferencing mathematical understanding students are invited to move beyond knowing and develop deep and flexible knowledge. Teachers gain valuable insight about how their students are processing mathematical concepts and where they might need to intervene. - “A conference is a shared opportunity for teachers and students to learn together in the moment”

2. Making Number Talks Matter: Developing mathematical practices and deepening understanding by Cathy Humphreys & Ruth Parker

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"Number Talks" is an approach to the teaching and learning of Number Sense. Rather than relying on the rote-memorisation of isolated number facts achieved through drills of "table-facts", Number Talks aim to build confident, number fluency, where learners recognise patterns within and between numbers and understand the properties of numbers and operations. Number Talks are a "mind on" learning task that engages students in an active learning process as they search for patterns, decompose and recompose numbers and develop a flexible understanding. It is achieved through direct instruction methods and facilitative dialogue with the teacher or between groups of peers who have had experience with the number talks methodology. It becomes one of the routines of a classroom focused on mathematical reasoning.

Number sense is important because it encourages students to think flexibly and promotes confidence with numbers. . . . The fact is, students who lack a strong number sense have trouble developing the foundation needed for even simple arithmetic, let alone more complex mathematics. A large body of research has shown that number sense develops gradually, over time, as a result of exploration of numbers, visualizing numbers in a variety of contexts, and relating to numbers in different ways. (Keith Devlin)

Making Number Talks Matter is a great introduction for teachers looking to make thinking with and about numbers a routine part of their student’s learning.

3. Yes, But Why: Teaching for understanding in mathematics by Ed Southall

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As teachers of mathematics we all know the maths we need to teach? A more challenging question is do we truly understand it? If we are looking to change how we teach mathematics because we realise that the methods used in the past did not build understanding we might have a problem if we learned our maths by these same methods. In this book author Ed Southall dives into the details behind the mathematics. This is the perfect book for the mathematical thinker who wants to understand the ‘why’ of mathematical concepts, who needs to know their origin story and who enjoys looking at things from a slightly different perspective.

4. Flip the System Australia: What matters in education edited by Deborah M. Netolicky, Jon Andrews and Cameron Paterson

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The third book in the Flip the System series turns the focus to Australia and its unique context. This is a book by teachers for teachers with a clear goal; challenge the current hierarchy and seek to explore ‘What matters in education’ rather than following global agendas and a ‘what works’ paradigm. The authors draw on their experience from inside the profession and their knowledge of the conflicting pressures that our modern education system faces. "This book does some talking but is ultimately about listening to the wisdom of the profession and engaging them at system level. We hope that by amplifying diverse but collective voices, this book can be part of a move to a world in which similar voices are sought out and valued by those traditionally at the decision-making peak of the education system.”

5. Developing Tenacity: Teaching learners how to persevere in the face of difficulty by Bill Lucas and Ellen Spencer

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The growing trend in terms of curriculum design is characterised by a tension between advocates of a capabilities or disposition driven curriculum and those advocating for a focus on knowledge. There is no shortage of opinion and research around what the capabilities or dispositions are that our young people will need for success in their futures and Lucas and Spencer have added their voice to that discussion. In this series, which started with ‘Developing Creativity’, the authors move the conversation to the practical point of describing what classroom routines and pedagogies might we implement if we want to develop these capabilities.

6. Calling all Minds: How to think and create like an inventor by Temple Grandin


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Written by an inspiring and creative thinker who loves to tinker and apply her knowledge of engineering combined with her capacity to visualise ideas to create solutions to problems. This book combines insights into the mind of a world-renowned maker with practical projects which get the reader involved in tinkering. This is a book that challenges a singular view of intelligence as a limited set of cognitive capacities and reveals that it is a much more expansive concept. “There is no better way to start than by making things of your own design. All the projects I made when I was young contributed to the inventions I’ve made throughout my life. And they have given meaning to my life.” If we seek to enable a generation of creative problem solvers who will transform the global challenges we face into opportunities, we need to get them inventing before they leave school.

By Nigel Coutts

Teaching mathematicians shouldn't be like programming a computer

Traditional methods of teaching maths have more in common with how we programme a computer than what we might do if we wanted to engage our students in mathematical thinking. We shouldn’t be overly surprised then when our students consider mathematics to be all about learning a set of rules that they need to apply in the right order so as to output the correct response. But is there a better way?

The product of most computational thinking, an algorithm is in essence just a step by step list of instructions that can be followed by a human or machine. An algorithm is defined by Google as "a process or set of rules to be followed in calculations or other problem-solving operations, especially by a computer". This result was returned as a result of the very special and complex algorithm that is deployed by Google to make sense of my search and deliver results that are likely to meet my needs. Google also provides me with a nifty graph revealing the frequency at which the word ‘algorithm’ is used. It shows a rapid increase in the words use beginning around 1960; the sort of growth curve that corporations dream of. The rapid rise in our use of the word algorithm reflects that it is increasingly normal for students to learn to code and in doing so create a list of instructions that are followed by a machine/computer.

Most algorithms are much simpler than the one that powers Google and the algorithms we deal with in most school mathematics lessons are many orders of magnitude more simple. Indeed, it may be because of this lack of complexity that we do not recognise that so much of the mathematics taught in a traditional maths lesson could easily be translated into an algorithm to be followed by a machine. We may not even notice that the methods we use to teach maths to our children are painfully similar to how we would programme a computer.

Typically, the lesson begins with the teacher presenting the required method to the students. The teacher begins with step one being demonstrated on the board. Once step one is complete, the teacher demonstrates step two, and then step three and sometimes steps four and five. With triumphant zeal the teacher indicates the correct answer with a flourish of whiteboard marker and perhaps a double underline for effect. In phase two the students copy the process they have been shown with the teacher looking on to ensure the steps have been followed accurately. Naturally there are some bugs and errors that require correction. By the end of the lesson most students are able to accurately follow the steps and arrive at a desirable answer even if some of the numbers are changed.

Compare this to how a computer is programmed. The ‘coder' determines the steps to be completed and enters them into the machine ensuring accuracy; this equates closely to phase one of our lesson although with our students the coding occurs visually and aurally rather than via keyboard. The coder then runs the code on the computer and looks for bugs in the code which may cause unwelcome results; this is phase two of our lesson. Finally, having checked the code and feeling confident that it is bug free and fit for purpose the coder releases their programme into the world where it runs on a range of subtly different systems and with a mix of inputs; a very near comparison to phase three of our lesson.

If you have some awareness of the limitations of a computer that result from the strict manner in which it follows rules, you are not surprised when a piece of software fails completely when asked to perform a task it was never intended to perform. Even the supposedly ‘intelligent' software that outsmarted Chess master Gary Kasparov would not have been much use to the staff of Pixar Films as they animated Toy Story and for the most part we are not surprised by this. What does surprise is when our students are unable to apply their mathematical knowledge to new situations even though they have been ‘coded’ in the same way that a computer is, one logical step after the other.

What our students lack as a result of their mathematical programming is a true understanding of mathematics. The manner in which they have been taught instils a belief that mathematics is a discipline of rules and procedures to be followed accurately so as to produce the correct answer. Errors occur as a result of missed or inaccurately followed steps. Without an algorithm to guide them they are lost in a sea of numbers and a forest of symbols with no rules to show them the way.

This approach to teaching mathematics as a set of rules to be memorised is reflected in the thinking of mathematical educators such as Ed Southall who writes:

Mathematics gradually became a mysterious entity, whose rules and steps I was expected to unquestioningly memorise – which I dutifully did. However, the process of storing numerous algorithms and their quirky properties became increasingly tedious, and I fell out of love with the subject that once intrigued and excited me. (Southall, 2017 p1)

Fortunately, Ed persisted and has searched for the understanding that his mathematics lessons failed to provide. Many students do not persist and turn away from mathematics as soon as they have the opportunity. It is sad that many of the teachers who have presented mathematics as this dry, sterile subject of rules and procedures believe that they are doing their students a service by sharing methods that make maths easy.

What is needed is a fresh approach, one that begins with an exploration of essential ideas or concepts. Students need opportunities to play with numbers, create visualisations of what might be going on, search for patterns and ask questions. When we approach mathematics as a discipline full of creativity and inquiry we also provide our students with opportunities for true mathematical thinking. We build number sense and flexible fluency where students understand that numbers can be manipulated, decomposed and recomposed. We build with our students an understanding of the effect that mathematical operations have and why a particular process produces a given result. In doing so we teach to the intent of the curriculum. For those in New South Wales this means that we teach our students to ‘wok mathematically' as follows:

Students develop understanding and fluency in mathematics through inquiry, exploring and connecting mathematical concepts, choosing and applying problem-solving skills and mathematical techniques, communication and reasoning . . . As an essential part of the learning process, Working Mathematically provides students with the opportunity to engage in genuine mathematical activity and develop the skills to become flexible and creative users of mathematics. (NESA)

This delightful description of mathematical learning may not apply where you teach but it is not an uncommon declaration of what curriculum planners see as a most vital element of instruction. In the Common Core State Standards, mathematical understanding is valued and the "NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections” are included as the first of mathematical processes and proficiencies.

When the moment is right, we may still teach students a particular process, after all there is a great deal of mathematical knowledge on which we can build. What we change is the place that learning procedures has in our curriculum. Rather than being the starting point for our mathematical instruction we teach the processes at the point of need. In a mathematical exploration where students arrive at the point where a procedure is required we teach the method. We unpack it, pull it apart, visualise what is going on, play with moving its parts around and in the end our students have a new tool with which to think and an understanding of its utility.

By Nigel Coutts

Southall, Ed. Yes, but why? Teaching for understanding in mathematics (p. 1). SAGE Publications.