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.

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.

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."

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

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, Gelman & 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.

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

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

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

"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

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

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

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


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.

Rethinking Time to see Education as a Lifelong Journey - Lessons from Blueback

“Blueback" by Tim Winton is a beautifully written story from which much can be learned. It is a simple tale of a young boy growing into adulthood and discovering his place in the world. Winton’s literary style invites the reader to journey with the books lead character, Abel as he experiences the ebb and flow cycles of life. Through joyous moments befriending the giant blue groper Blueback, through the challenge of moving away from his isolated home where he lives with his mother, to confronting ruthless business men whose greed threatens the natural beauty of the environment, to his growth into manhood, a career pursuing his passion for the ocean, to finding love and starting a family of his own the reader travels with Abel. Like waves passing over a reef, Abel’s life is a series of events which arrive with the possibility of tension and harm but pass leaving him subtly changed and stronger than before. Throughout his life, is the constancy of the ocean and the faithful companionship of Blueback.

“Abel and his mother slid down into the deep again and saw the fish hovering then turning, eyeing them cautiously as they came. It twitched a little and edged along in front of them to keep its distance. The big gills fanned. All its armoured scales rippled in lines of green and black blending into the dizziest blue. The groper moved without the slightest effort. It was magnificent; the most beautiful thing Abel had ever seen.” - Blueback by Tim Winton

Blueback is a beautiful metaphor for life and particularly of the life we live in schools. When looked at close up, with an eye on the details, the experience of school is one of passing and recurring cycles. When looked at from a distance, with an eye on the whole, there are elements of constancy, the throughlines which bring meaning to our experience and which have as their consequence the residuals of education.

There are the daily cycles that begin with the breakfast table discussion of the day ahead, travel routines to school, daily lessons, lunch-breaks, more travel and home-learning all punctuated by times with peers negotiating the social milieu of our relationships. There are the weekly cycles of subjects, specialist teachers, sports days, music lessons, assemblies and co-curricular. There are the longer-term cycles of units of learning; the annual introduction to grammar, the unit on fragile environments, the history project on settlement, another maths unit about fractions and why they matter. There are the annual events, the camps, the musicals, the sporting carnivals the excursions and the special community days such as Mother’s Day, Easter with the traditional hat parade and of course the many events with which we conclude each year.

School seems to be about fitting as much as possible in the short periods of time into which we divide our school life. Ask any teacher and they will tell you, they are forever short on time, that the days seem to never have enough hours for all they need to hold. Each week seems to race by and as quickly as one ends, the next begins. It seems we are just gaining traction with the grammar unit when it is time to move on to persuasive writing. Our students are just grasping why our environment is fragile, when we must change direction for the electricity unit. Our amazing plan to finally teach our students why they should care about fractions, has once again been foiled by the annual art excursion which seems to come around sooner each year.

Our day is divided ever so neatly into one hour (or there about) blocks of time. For the student, the day is a procession of discrete lessons; of introductions, middles and ends. Looked at on this small scale, the daily life of a school student has much more in common with an anthology of short stories than with the epic novel that it should be. Read just any single chapter of Blueback and you will discover a nice story but entirely miss the point, never see the part it plays in the whole. For the teacher trapped in the moment with a looming deadline and an ever-expanding to-do list it is a challenge to shift perspective and see beyond the next few pages of the story they are writing with their students.

We measure the passing of time in Weeks and Terms and Years. Time in school seems to be all about beginnings and endings. We must start the history unit in Week Three of Term, it must finish in Week Eight, the assessment is in Week Nine. The fractions unit occupies just four lessons before the term ends, next term we must begin the geometry unit on time. Each year is a fresh beginning, a new start, but is it a new book when what we need is the next chapter?

From Kindergarten to Year Twelve, our students have spent thirteen years, or three quarters of their life at school. Looked at from this more expansive perspective we see that our students have a great deal of time in which to develop the dispositions they will need for success in their post-school lives. There will be many, many lessons along the way which they forget. There will be excursions they remember because the bus broke down rather than for the physics exhibition it had taken them to. These are the chapters of Blueback, the cycles that washed over Abel's life, but they are not the whole story. We might never finish the unit on fragile environments, but our students may learn from this and the history unit and their persuasive writing lessons, that they have the capacity to drive change. After years of struggling with fractions and geometry and grammar, they may learn that persistence is the key to success. Through the musicals, and the science projects and the art show and the hat parades they will discover that they are indeed creative, and confident. From countless projects, debates, tutorials, presentations and even home-learning they will develop the skills required for collaboration and communication. They will leave our doors ready to write great stories of their own; to discover their "secret of the sea".

If we insist on looking at education on a small scale, lesson by lesson, unit by unit, we are doomed to see it as an endless cycle of chasing our tails and of never having as much time as we might wish for. If we step back and consider the throughlines, the big understandings, the essential dispositions which can only be developed by time measured in years, through the culmination of many connected and related experiences, we have a hope of seeing the greater success that education is capable of achieving with and for our students.

By Nigel Coutts

Winton, Tim. (1997) Blueback. Penguin Group Australia.

Letting how we choose to learn inform our teaching

Think of a time when you were completely immersed in a learning challenge. A time when you became aware of the need to master a new skill or concept. A situation that took you outside of your comfort zone, when there were times that you became frustrated, when you thought of quitting, downed tools and walked away, but came back time and time again. Maybe it was a problem you had to solve. Maybe it was a challenge you wanted to overcome. Perhaps it came with a significant payoff but perhaps it was just one of those things you had to accomplish. 

This learning challenge may push you into a state of Flow as described by Mihalyi Csikszentmihalyi, but at the time it is more likely that you are focussing on the growing feeling of frustration, the moments of elation when you sense a breakthrough and the subsequent despair when it doesn’t quite work. What aligns with Csikszentmihalyi’s description of ‘Flow’ is that time flies, the world fades into the back ground and that cup of coffee you had hoped might reenergise your thinking goes cold on the desk beside you. 

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

True learning is and should be a challenge. The moments when we are pushing our cognitive limits are the times when our brains grow. A cognitive challenge should have much in common with a physical challenge. If mountaineering is your thing you will choose the steep and winding path over the tourist cable car option every day. As you struggle your way towards the summit, your legs aching with each step you may long for the climb to be over, but you don’t want to be rescued and robbed of the achievement. 

Think of the actions you take along the path of your learning journey. Do you stop and stare into space as you wait for your mind to process a new idea? Do you frantically jot down ideas only to toss them in the bin moments later? Do you turn to the internet, a book, a video, an instruction manual for guidance? Maybe you ask a friend how they would approach the problem or maybe you plod along in splendid isolation knowing that the answer is somewhere inside. Do you stop and go for a walk, or wander through the house hoping to be struck by inspiration?

True learning is messy, non-linear, difficult to plan for, complicated, frustrating and intrinsically rewarding. As we seek to build an understanding of new ideas either through formal learning such as may occur in a classroom, or through informal learning that we self-direct, we take many twists and turns. The path that one person takes from incomprehension to understanding is not guaranteed to be the same as another even when the learning experiences along the way are the same. We build new understandings on top of those we already have, and this will powerfully influence how we learn and how we value what we learn.

Think also of the conditions which block your learning. Few of us choose to engage with challenging new concepts in an openly public environment where we are exposed to the scrutiny of our peers. Collaborative learning can be powerful but if we are the only one in the group struggling with a new idea and we do not feel safe, we are likely to invoke protective measures to insulate our egos. Without an emotionally safe environment in which we feel accepted and where risk-taking and mistake-making are accepted we are likely to stick with ideas that we have already mastered. 

Think of the physical environment that you choose to learn in. Are you able to adjust the temperature, the lighting, open a window? Can you get up and move around? Can you stop, do something else for a time and go back to your learning? Do you have access to refreshments whenever you feel the need? Do you have a choice of where you sit? Do you need to sit at a desk, in a comfy chair, on a lounge, or maybe you prefer to spread your things out on the floor? Can you take a toilet break when you need to? Are you able to block out distracting noises or do you like to have some background sounds? Are you able to switch off from external distractions or do you find task switching a useful way of overcoming the tedium of focussing on one thing?

The point is, learning is something we do in different ways and under different conditions. We are more likely to be fully engaged with learning that matters to us, that has a clear and meaningful purpose and that we have some control over. We learn best when we feel safe and when the conditions are right, we will persist with learning even when it is challenging; doing this is what makes us human and is what has allowed us to survive as a species. How we learn is also unique to us.

The value to us as teachers in taking time to stop and think about how we learn, is that it should encourage us to reflect upon the conditions which we create for our students to learn in? The potentially painful questions that need to be asked are “Could you learn something genuinely challenging in your classroom and would you want to?”, or “If you were confronted by a fiendish problem, would you choose to solve it in your class?”

By Nigel Coutts

Mihaly Csikszentmihalyi (1997). “Finding Flow: The Psychology of Engagement with Everyday Life”, Basic Books

Why we fear data and how our perception can change.

Data occupies a somewhat curious place within education. Mention it to teachers and you tend to get one of two responses. One group will roll their eyes and with great sarcasm how data is "so exciting”. The other group responds with something akin to “actually I quite like data” indicating that experience has shown them that they are members of a small group. The question is why do some people find data to be a useful and fascinating tool while others see it as a good method for inducing sleep?

Much of it is to do with the way in which we experience data. Long lists of numbers, highly confusing charts and extensive presentations that show how one factor can be clearly shown to have a loose correlation with another. One half of the audience is fascinated, wants to see the underlying data and looks forward to a chance to dissect the numbers later in their own time. The other feels like they are being asked to make sense of an optical illusion; one of those where if you squint just right an image of zebra appears. The presenter has obviously spent a great deal of time crunching the numbers and are convinced there is a story to be told, but most people are not seeing it. Too often the capacity to analyse data is not accompanied by the ability to transform it into a compelling narrative.  Instead of a riveting moment between the lead characters of a film we have an extended scene of Jar Jar Binks. 

Data shows that 86% of people are more likely to believe any claim that includes reference to a compelling statistic, a figure that rises to an astounding 92% if the claim indicates an effect size and the sentence “according to research”. Disappointingly only 7.1% of people recognise that the previous sentence, and this one are both entirely fictional. This use of data to add weight to any argument has become so widespread and so frequently proven to be flawed, erroneous, blatantly false or almost immediately contradicted by another equally confusing data set, means that the use of data has for many lost all impact. Indeed, while some are happy to believe anything with a good data set behind it, others immediately question any piece of data and search for the lie as soon as they hear it. 

In education data is all too often used to support a claim that the claimant already believes to be true. Not always, but often, data is used to support a plan already well under way. A new writing programme in a school is more likely to be embraced if data is found to show it is needed. Rather than looking for the story in the data and from there exploring the consequence of the patterns which emerge, data is used to build a case in support of an argument. This reversal of the intended role of data is perhaps why many people so quickly turn off when data is introduced to the debate. It is not that they are disinterested, but that they know what will follow is a compelling demonstration of why the plan they are being asked to contribute to is a foregone conclusion. 

Data in education is closely connected to assessment and to the type of assessment that is easily reported in numbers. There is a growing awareness that much of the high-stakes assessment movement has more to do with command and control than it does with student success. Traditionally assessments such as NAPLAN, PISA, TIMSS, & PIRLS have measured what is easy to measure and the data has then been used to argue for more of a certain style of teaching and learning that might prepare students for more of this style of assessment but offers them little value beyond their school years. This use of data is so compelling that teachers come to question their own professional judgement. Although a teacher may see his/her students learning on a daily basis, engage in dialogue with them about where they are with their learning and where they need to go next, even though they may gather copious artefacts of learning that demonstrate achievement, many teachers feel that they require something in the form of numbers to justify their decisions. 

It is our negative experiences with data that prejudice against its better uses. Data should be a tool that allows us to better see what might be. Through the thoughtful use of data, powerful stories can be revealed. When data is allowed to speak, when it is handled respectfully and with a desire to use it to reveal a truth that might otherwise remain hidden, it is a powerful tool. When it is communicated in ways that make its story plain and understandable by all it becomes a tool that invites dialogue and shared understanding. With access to great quantities of data and the computing power required to make this information accessible, data should be viewed as a great asset rather than as something of a black-art of which we should be sceptical. 

By Nigel Coutts

Towards a pedagogy for life-worthy learning

Particular patterns of pedagogy can be seen to influence much of the debate in education, particularly those that shift the focus from what the teacher does to what the students do, individually or collectively. In traditional pedagogical models the emphasis has been on the manner in which the teacher organises curriculum elements, presents these to their learners and assesses what has been retained and can be applied by the student. In a sense pedagogy was the script that evolved for the teacher’s presentation of content to a group of learners as a result of the teacher’s knowledge of the curriculum and the theory of how this content is made most digestible by the learner.

This model of pedagogy had much to do with systems of management. Many of the teaching moves or classroom routines were clearly linked to managing and constraining the behaviour of the students. The organisation of the daily schedule, the physical layout of the classroom, the expectations for behaviour of both students and teachers all point to a system that was designed so that one person may impart the maximum possible knowledge to as large a group as possible. The dominant pedagogical debate beyond questions of how to best manage students was associated with the presentation and ordering of content; how do I present this information to the learner such that it is most likely to be retained?

In the contemporary classroom, there is much greater consideration of what the learner does in partnership with their teacher so that they develop the capacity to learn. Classroom routines and structures are designed to engage the learner in a rich process of dialogical learning.

With this shift comes an emphasis on understanding how students learn and with this knowledge in mind developing learning experiences that will allow the learners to develop their skills and disposition for learning. It is meaningful to speak of learners as problem finders, a role that was once very much the sole preserve of the teacher. Further the curriculum is often negotiated or a consequence of a dialogue between the teacher and the student. Assessment once the preserve of the teaching professional, now involves opportunities for self and peer-assessment and the teacher plays a role in facilitating this process. Where once the teacher’s expertise lay in their ability to teach, now we find a growing emphasis on their ability to model learning.

This pattern comes out of the emergence of a number of elements impacting education. One is the rise of ICT and the shift that this brings to the importance of content knowledge. When access to knowledge was scarce, the teaching of content knowledge was an important role for teachers. The emphasis was on the transfer of knowledge from the teacher to the student and teaching was about how effectively this transfer could take place and how this transfer may be measured. The student’s role in this process was relatively passive and entirely receptive. Now that access to content is ubiquitous the value of pools of knowledge stored in long term memory has declined. Memory alone is not sufficient for success. Today the emphasis is on what students are able to do with this knowledge. (Wagner & Dintmarsh 2015) The challenge confronting teachers is how we might prepare students to locate and use information relevant to the problems they identify, recognise the skills they may require and then work creatively and collaboratively to create a unique solution.

We also have a much better understanding of what learning is like from a neurological perspective. We know for example that emotion plays a significant part in establishing the conditions necessary for learning. 'It is literally neurobiologically impossible to build memories, engage complex thoughts, or make meaningful decisions without emotion.’ (Immordino-Yang. 2016) We know that all learning is a consequence of thinking and that the consequence of this is an understanding that learning is an active process requiring the participation of the mind of the learner. We better understand what it means to understand and know that to achieve this level of competence with concepts requires opportunities to use what we have learned in novel situations. Our classroom practice can be informed by research that describes, the factors which result in intrinsic motivation (Ryan & Deci. 2000), the conditions necessary for creativity (Csiksgentmihalyi. 2013), the development of a growth mindset (Dweck. 2006) or a culture of thinking (Ritchhart. 2015)

For pedagogy the consequence of this is that we shift towards a student centred learning model in which the students are empowered to be learners. Seeing students as creators of works, finders of problems, metacognitive learners and global connected collaborators brings a shift in the role of the teacher to one of guide and mentor. (Loughran 2013) Much is made of measuring who does most of the talking in classrooms and the shift is towards a classroom dominated by the student’s voices. (November. 2012). We set up scenarios in our classes that allow students to fail and in doing so explore iterative learning cycles of trial and error through which students learn ‘grit’ and expand their ability to grapple with complex ideas and solve ‘wicked problems’. Assessment for learning in these classrooms is more interested in evaluating the processes of problem-finding/solving, inquiry or creative and critical thinking utilised by the students rather than the recall of content.

The difficulty experienced by those implementing this shift in pedagogy arises from the fact that neither the curriculum or the ‘High Stakes Testing’ of NAPLAN, HSC, SAT or PISA has kept pace with the change. While teachers struggle to adapt their pedagogy to better fit this new model they do so with a narrow, content heavy syllabus, in a climate of testing that focuses on base skills across a limited and disconnected curriculum. That compliance with the curriculum and student performance on standardised tests are measures of school and teacher success, makes the task of delivering a student centred pedagogy more difficult.

Our students are confronted by a conflict in the three message systems that play the most significant role in prioritising education; curriculum (the what might be taught), pedagogy (how teaching and learning is delivered) and assessment (what is valued by its measurement). The result is we have students who are engaged by learning that focuses on their long-life skill development and challenges them with meaningful learning experiences linked to their interests and real world problems and yet they are measured against a curriculum that overemphasis specific content knowledge and tested in ways that do not allow them to use their skills for creativity, collaboration and connectedness. Our students very quickly learn to play the game and through their experience of the realities of schooling develop a clear understanding of what truly matters. So long as the teacher says that they value thinking and creativity but assess students on memorisation and recall, students will know where to place their efforts and what learning truly matters.

If there is a positive message attached to all of this, it is that the development of dispositions essential to success as a life-long learner are also excellent preparation for tests with an emphasis on memorisation and recall. A learner who possess a deep understanding of fundamental concepts within a discipline, who is a creative and critical thinker, who can find and solve problems, is also able to achieve when the test requires less of them. Our challenge is to show our learners that their path to success is not a short-cut to knowledge, but a winding path towards understanding and life-worthy capabilities.

By Nigel Coutts

Dweck, C. (2006) Mindset: The new psychology of success. New York: Random House.

Immordino-Yang, Mary Helen. (2016) Emotions, Learning, and the Brain: Exploring the Educational Implications of Affective Neuroscience (The Norton Series on the Social Neuroscience of Education). W. W. Norton & Company.

Loughran, J. (2013). Pedagogy: Making Sense of the Complex Relationship between Teaching and Learning. Curriculum Inquiry. 43, 1, 118-141.

Mihaly Csikszentmihalyi (2013) Flow: The psychology of happiness’ and creativity: The psychology of discovery and invention. New York; Harper Perennial.

November, A. (2012) Who owns the learning?: Preparing students for success in the digital age. Solution Tree Press; Bloomington IN

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

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.

Wagner, T.& Dintmarsh, T. (2015) Most likely to succeed: Preparing our kids for the innovation era. Simon & Schuster; New York

How might we confront the challenges of time and "the system"?

Speak to teachers the world over about what they want for their students and you find clear patterns emerging. Key dispositions, capabilities and attributes emerge from the conversation. There are the traits of kindness and empathy which allow our students to become caring stewards of the world, its animals, its people, its biomes, its history and its future. There are characteristics which allow them to be productive problem finders and solvers imbued with capacities for creativity, critical thinking, collaboration and communication. They are respectful of diversity, open to new ideas, flexible in times of change and aware of their place in the world. They are happy in their own skin, aware of their limitations but always aware of their potential for growth. They are agentic and desire to take action for a better world with an understanding of their role within the collective citizenship of the planet.

Dig a little deeper and you find that these teachers have a reasonable imagining of what is required for our young people to achieve these goals. An education which values and enculturates these dispositions is essential. Teachers the world over understand the part that they can play (alongside families and the broader community) in providing our young people with the foundational experiences they require to emerge as young adults ready for the challenges which lay ahead. While the methods required to achieve this may vary the goal is clear and we are blessed with a highly professional collective of educators who are driven by a desire to meet this challenge with their energy and passion.

What then stands in the way?

Two forces seem to present the most significant obstacle to educators hoping to achieve these illustrious goals for and with their learners. The first is time, the second is “the system”. Together these two factors act as a bulwark to change; the constraints within which progress is able to occur but only to the point that it strikes against the seemingly immutable obstacles.

Time, as Bilbo Baggins exclaims is what we always need more of. Our greatest plans and hopes seem to be dashed by the limited time that we have in which to make them real. Teachers want more time to understand the needs of their learners, more time to collaborate, more time to explore the details, time to spend on detours from the curriculum, time to reflect, review and redo. We work within the limitations of time all of the time. We make plans spread over multiple years to give ourselves the time required to implement our designs and yet we know that the students before us now will have moved out of our care before our plans are fully realised. Our limited time causes all manner of pressures and tensions. We seek a semblance of work life balance and strive to give time to all that matters to us across all the spheres of our life. We need and want to spend time with family and friends, we hope to find time to take care of our health (physical and mental) and we desire to learn and enrich our lives with arts and culture. We see that our days are often occupied with the minutia of our roles and sense that we are not spending our time on that which has the greatest impact on our quality of life or that of those who rely on us.

We may have no control over the amount of time that we have but we must at least strive to take charge of how that time is used. Only by taking stock of how we utilise our time and value it as the limited and irreplaceable commodity that it is might we hope to allocate it and our energy more wisely. This is no small task but it is one we cannot hope will be done for us.

The other great tension felt by educators looking to better serve the true needs of their learners is "the system”. Individual teachers function within schools, which function within the boundaries and demands of larger organisations which serve the needs of governments driven by a desire for reelection by a citizenry that may well be misinformed of what is required to build a future-focused education system. The legacy of the past, the incessant pressure of the now, the structures which are imposed, the processes which constrain action, the poorly applied proxies of success which measure only what is easily measured act in combination to restrict and limit teacher agency.

For the teacher within this system it can be near impossible to imagine a way to enact change in the face of such an overwhelming entity. The system takes on the proportions of Hobbesian “Leviathan” acting with malicious intent to stifle and suppress our best intentions. We come to see the system as either an unassailable foe or as great authority figure to whom servitude is required. As meek individuals within this system our role in its functions is erased by the inky completeness of our adversary. And yet it is a truth that the system is us and we are it. We choose to see it as that which authorises us to maintain the status quo even where we see it failing our learners or to see it as that which binds our hands. Change has never had its roots within the system but always within the minds of those who seek it out.

As we confront "the system” we make choices about the path we shall take. One is to accept that it exists and that we must be content with acting within its constraints and hope that in a brighter tomorrow that it may change and allow us greater freedom. Another path is to take what action we might, to bring about change where we can and push against the limits of the system where it constrains us. Others will confront the system head on, question its authority and demand change.

In all of this we must not turn away from the promise of our own agency. Time is short but we can choose how we use it, the system is mighty but we are a part of it and can act to maintain it or to change it. In the end, we can choose to let the world happen to us, or we can let our voice be heard.

By Nigel Coutts

The messages we send about learning

I am a dog person. I am one of those people who can’t help but smile at any dog I walk past and I greet the dog before its owner. I have two Jack Russell terriers and they are absolutely my babies. A few years back one of them developed the habit of becoming extremely timid of any other dog that we would pass. She would dig her feet into the ground and it would have been easier to continue walking if the anchor to the Queen Mary was on the far end of the leash instead of a small brown and white ball of fur. The answer to the dilemma came from the world of TV via Cesar Millan, “The Dog Whisperer”. It was not her causing the problem, it was me. 

Cesar explains how the lead becomes a conduit for the emotions of the human on the end of it. Subconsciously I was conveying my uncertainty down the lead and she was reading these signals and responding with fear. I needed to change my mindset and convey calm confidence as we welcomed other dogs on our ramblings. Today she greets other dogs with a wag of the tail and her head held high but I know it is not that she has changed, she is getting positive messages through the lead. 

We send our students many messages about learning, growth, ability, potential. . . Sometimes we are sending these messages deliberately, such as when we talk about growth mindset and the rewards of effort, persistence and risk taking. At other times the messages we send are accidental, incidental and unplanned; these are often the strongest messages we send. 

Students are very adept at learning what ‘school’ is about. They see past the pretty posters, the motivational speeches and the rhetoric about learner attributes. They read the hidden message with great skill. The routines of the day send strong messages about what truly matters; lining up, walking silently to class, listening while the teacher tells you what to do. Assessments are another tool that tells a message about learning. We may say that risk taking and creativity matter but that message is sunk by the assessment that shouts at the students ‘there is a right answer and you need to know it’. 

Mathematics provides a good example of the contradictory messages we send to students. On one level, we invite them to be creative, to think deeply about their solutions, to collaborate with their peers and ask questions when they are unsure. We say that we embrace mistakes as the path to learning and tell our students to have a growth mindset. We tell them that mathematics is beautiful and that mathematicians are finders of patterns.

But then we give them timed drills of mathematics facts. Speed and accuracy become the measures of mathematical fluency. We give tests with one right answer and repeated examples of near identical questions. We create blatantly artificial ‘real world scenarios’ in word problems designed to conceal the mathematical thinking required in much the same way that riddles hide their meaning. We teach prescribed methods and reduce mathematics to a sequence of steps to be blindly followed. We begin the exploration of mathematics with a broad array of concrete materials which allow us to see and touch numbers but as the concepts become more complex these are removed and we are left alone with only formulas to guide us. We understand little but know much. Recall of information becomes the visible substitute for understanding and the assessments we take require little else. We may pass the tests but we know that mathematics is not for us; we are not maths people.

Two approaches to teaching number facts but two vastly different stories about mathematical thinking.

No teacher sets out to send such messages. We do not want our students to perceive maths as a subject that is beyond their abilities or is only to be attempted by a certain type of student. We know that mathematical thinking is of great value and in a world that is increasingly shaped by data is a much needed disposition. Sometimes we are unaware of the messages we are sending, after all a five-minute quiz on Kahootz is just a little fun. We fail to notice that this quick quiz aligns perfectly with the mental image that our students have constructed in response to countless similar quizzes; that mathematics is a subject where success is measured in terms of speed and accuracy. At other times, we believe we are saving our students by providing them a quick and easy way to solve a complex problem. Why bother with the complexities of dividing fractions when you need only "invert and multiply”. Sadly, we should not then be surprised when our students don’t ever really understand fractions and are unable to contemplate an approach to any problem that is not dressed in its usual coat and hat. 

We need to become whisperers of our own messaging systems. Only by being aware of every message that we send our students can we hope to change their narrative of what it means to be a learner. When we acknowledge that their story of learning is the one we are telling them, we can take steps to shift the narrative. 

By Nigel Coutts

The power of powerful ideas shared simply

Some statements stand out in your memory for the power with which they resonate through you mind. I recall the first time I encountered the question posed by Alan November “Who owns the learning?” on the cover of his book of the same name. In four words, Alan poses a question that strikes at the heart of education and encourages us to re-think our approach. If we believe that the learner should own the learning, what are the implications of this for our teaching? Like a stone dropped on the surface of a calm pond, the ripples from a powerful idea spread, expand and gain strength.

Warren Berger’s thinking has a similar effect. His work is around the power of questions as a catalyst for creativity and innovation. Ask the right question, in the right way and the effect can be profound. Warren tells the story of innovators who have taken the time to fully understand the situation and found that the answer came from re-imagining the questions that were being asked. The stone that Berger drops in the pond is the title of his book “A more beautiful question”. We ask questions all of the time but for most of that time our energy is spent on finding an answer to the question we have asked. Berger asks us to give more time to finding our beautiful question. When we shift our thinking from a mindset that values answers to one which appreciates the power of a question we open ourselves to new possibilities.

Some statements bring their authors great fame. They immediately grab the attention of their audience with their bold, unapologetic challenge to the status quo. In 2006 Sir Ken Robinson dropped a virtual bombshell on the world of education in what has come to be the most watched TED Talk of all time with over 53 million views on the TED site alone. “Do schools kill creativity?”. Framed any other way Robinson’s query may have disappeared into the ether. Delivered with the perfect mix of humour, charisma and passion, Robinson’s question continues to impact our vision for what education should offer.

The title of a 2014 article by Andy Kiersz is similarly bold in its approach to the teaching of mathematics. “Everything About the Way we teach Maths is Wrong”. There is nothing subtle or gentle about the headline and in the body of the article the author tells his reader about the writing of Paul Lockhart and his book “A Mathematician’s Lament”. Read the full text and explore Lockhart’s writing and you will question why we do not teach a more beautiful model of mathematics. Lockhart writes, "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.”

In 2015 I had the privilege of hearing Lane Clark speak in Bilbao at "ICOT 2015” on the power of real learning. Among many gems is Lane’s essential challenge to how we approach learning; “Now you know it, So What?”. The challenge here is to teach more than knowing and provide our students opportunities to make practical use of the information with which we fill their heads. Lane is not the first to pose this style of challenge. In 2013 Sugata Mitra shifted our thinking about the value of knowledge by asking "Could it be that we are heading towards or maybe in a time when knowing is obsolete?”. For educators the world over, the idea that knowledge could be obsolete was either liberating as it opened the door to learning that focused on dispositions, or was hugely confronting and potentially dangerous. While Mitra’s thinking comes from his observation of the emergence of the internet and his research into the learning potential of an internet connected computer, revealed through his “Hole in the Wall” project, the idea is not new. Those who are advocates of the thinking of John Dewey will know that the teaching and valuing of disconnected or discrete knowledge has long been questioned. “Only in education, never in the life of farmer, sailor, merchant, physician, or laboratory experimenter, does knowledge mean primarily a store of information aloof from doing.”

I share these ideas because I find in considering viewpoints such as these an opportunity to reflect on the manner in which things are done. By confronting ideas that challenge the “way we have always done things” we allow us to either better value what is good in what we do or begin the search for a better story. In their bold and challenging presentation, these ideas force us to think and that can only ever be a good thing. If a bold claim leads to rich and healthy debate, then it has served a powerful purpose; after all the status quo is best imagined as the point where our questioning begins.

I finish with what has become one of the most significant ideas I have toyed with in recent times. It is an idea captured in a single word coined by David Perkins "Lifeworthy; that is, likely to matter in the lives learners are likely to live.” In a single word Perkins challenges his readers to focus their efforts on learning that will matter in the lives that their learners are likely to lead. In a world where there is so much to learn, amidst curriculums which are massively overcrowded, the idea of teaching that which is Lifeworthy has great power and invites fresh dialogue around what we imagine education should provide those who own the learning.

What idea has shifted your thinking?

By Nigel Coutts

Who owns the learning? Preparing students for success in the digital age by Alan November 


The title alone is worth pondering, ‘Who does own the learning?’ If the best learning occurs while the unit is being programmed, if the students have little say in the direction their learning takes then how are we preparing them for their learning futures. Alan has a solid understanding of the implications of technology for learning and combines this with student centred pedagogical approaches to describe a model of education that empowers young learners to take charge of their learning. For teachers the challenge is to get out of the way of the spectacular learning that their children are capable of.

Future Wise: Educating our Children for a Changing World by David Perkins 


How do you answer the 'uppity question’ from a student who wants to know why they need to learn what you are teaching? Do you reply that they need it to do well in the test or are you confident that it is learning they will need to do well in life? In this book Perkins examines what we teaching in schools and makes recommendations for a shift in focus. A key idea introduced early and unpacked throughout the book is the idea of ‘LifeWorthy’; learning that is 'likely to matter in the lives learners are likely to live’. Future Wise is jargon free and a great book to share with colleagues, it will help you rethink what you spend time on in class and clarify how you see the role and purpose of education.

Visit “A More Beautiful Question”

Read “Everything about the way we Teach Maths is Wrong”

Listen to Sir Ken Robinson’s TED Talk “Do Schools Kill Creativity”

Listen to Sugata Mitra’s TED Talk - “Build a School in the Cloud”

Find out more about Lane Clark and her approach to inquiry and real learning.