Making Learning Stick

This year, the Faculty of Mathematics at my school has been focusing on increasing what TeacherToolkit (in one of his famous ‘5 Minute plans‘) calls ‘stickability’ of learning.

I have an ongoing and passionate interest in how the brain works and have been following, with increasing interest, the connections made between neuroscience and education. In a space where there is considerable debate as to what constitutes quality learning and how to attain same, it is important that any strategies employed in the classroom are based on a firm, well-researched evidence base.

We are coming to the end of term break here in Australia and I have taken the headspace time over this break to read two books that explore what quality learning looks like from different perspectives and offer advice for teachers, as professional learners, to better promote quality learning in their classes.

(1) Make It Stick: The Science of Successful Learning by Peter Brown, Henry Roediger III and Mark McDaniel (Harvard University Press, 2014)

(2) Learn to Teach, Teach to Learn by Catherine Scott

Learn to Teach explores the most up-to-date findings on how children learn, to help teachers create effective learning environments and plan for teaching.  It covers the purpose of education; socio-cultural approaches to human cognition; attention and intelligence as cognitive tools; and the role of mindsets, memory and language in learning. It promotes the idea that the mind is a cultural product and that education is best understood as fostering the development of valued cognitive tools appropriate for the twenty-first century.

In Make It Stick, the authors make the point that learning is an acquired skill and that the most effective strategies in learning are often counterintuitive. The main points of the book are:

Learning is deeper and more durable when it is effortful.

We are poor judges of when we are learning well and when we are not. When the going is harder and slower, and it doesn’t feel productive, we are drawn to strategies that feel more fruitful, unaware that the gains from these strategies are often temporary.

Rereading text and massed practice (concentrated study in one period of time) of a skill or new knowledge are by far the preferred study strategies of learners but they are also among the least effective. These give rise to feelings of fluency that are taken to be signs of mastery but for true mastery or durability (‘stickability’), these are largely a waste of time.

Retrieval practice – recalling concepts or events from memory – is a more effective learning strategy. Retrieval strengthens the memory and interrupts forgetting. A single, low-stake quiz after reading a text or listening to a demonstrated example produces better learning and remembering than rereading a text or looking over notes. While the brain is not a muscle that gets stronger with exercise (better take that slide out of my next presentation to the Year 9s!!), the neural pathways that make up a body of learning do get stronger, when the memory is retrieved and the learning is practised. Periodic practice arrests forgetting, strengthens retrieval routes and is essential for hanging onto knowledge.

When you space out practice at a task and get a little rusty between sessions, or you interleave the practice of two or more things, retrieval is harder and feels less productive but the effort produces longer lasting learning and enables more versatile application of this learning later on.

Trying to solve a problem before being taught the solution leads to better learning, even when (or perhaps because of?) errors are made in the process.

When you are adept at extracting the underlying principles that differentiate different types of problems, you are more successful at picking the right solutions in unfamiliar situations.

We are all susceptible to illusions that can hijack our judgement of what we know and can do. Testing (low-stake) helps calibrate our judgements of what we’ve learned.

All new learning requires a foundation of prior knowledge. To learn trigonometry well, you need to remember some algebra and geometry.

Elaboration is the process of giving new material meaning by expressing it in your own words and connecting it to what you already know. The more you can explain about the way your new learning relates to your prior knowledge, the stronger your grasp of the new learning.

Putting new learning into a larger context helps learning. If you are trying to learn an abstraction, like angular momentum, it’s easier if you ground it in something concrete that you already know.

People who learn to extract the key ideas from new material and organise these into a mental model and connect that model to prior knowledge show an advantage in learning complex mastery.

Every time you learn, you change the brain. We start life with the gift of our genes but we become capable through the learning and development of mental models that enable us to reason, solve and create. The elements that shape our intellectual abilities lie within our control. This involves understanding that when learning feels hard, you are doing important work. And that striving and setbacks are essential if you want to surpass your current level of performance toward true expertise. Making mistakes and correcting them build the bridges to advanced learning. Grit, resilience and persistence.

(Pages 3-7, Make It Stick)

I found these two books to be enriching and affirming of what we have been trying to achieve in our journey within the faculty, and the broader school. In the analytic domain, we have been working on gaining the brain’s attention by engaging students, determining essential learning, focusing on prior knowledge, teaching for understanding, formative assessment to check for understanding, providing more opportunities for students to articulate their reasoning and make thinking visible and making more connections between concepts to strengthen neural pathways. In the affective domain, we have been deliberately focused on resilience, grit, persistence, the importance of having a growth mindset, the instructional benefits of error-making and talking to students about how learning something new is challenging and may feel discomforting. There are always ways we can improve, but it is heartening to know we are heading in the right direction.

The rich evidence base, that these two books are embedded within, is also worthwhile emphasising. It is this academic authority that should support any decisions made about teaching and learning in any school.

Highly recommended reading.

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Engagement in, as and for Learning

What if all students were engaged in their learning in all classes and realised their own power in improving this learning?
What would that look like? How can we make it happen more often?


This year, I have been fortunate to be involved in AITSL’s Learning Frontiers project. Learning Frontiers (Australia) grew out of Learning Futures (UK). Valerie Hannon of the UK’s Innovation Unit is heavily invested. You can hear more about the UK’s project here and read about the Australian one here.

The above questions are the guiding questions for my school’s investigation into improving students’ cognitive engagement. Cognitive engagement can be understood as a student’s psychological investment in their own learning, how actively engaged they are in what they are doing, how invested they are in it.

This is the hardest to detect from behaviours alone – it is “not just students doing things but it is something happening inside their heads”. When cognitively engaged, students concentrate, focus on achieving goals, are flexible in their work and cope with failure. This is different from high performance: a student who is performing well may still be disengaged if they are coasting and not motivated to exert themselves more than is necessary to get by.

Students are absorbed in their activity: anyone witnessing a young person playing, say, on-line role playing games will know what this looks like. Researchers from the University of Western Sydney have described the difference as being ‘in-task’, not just ‘on-task’.

Other indicators of high absorption would be students wishing to continue beyond the end of lesson, or not even noticing the lesson had ended – what Csikszentmihalyi has described as being in ‘Flow’. Students display persistence, even in difficulty: a deeply engaged student becomes confident in their own ability to succeed, through persistence. As one Learning Futures student put it:“’ve got to figure it out for yourself ‘cos if people just told you, you’d just find it an easy life, but life is full of obstacles and stuff, and you’ve got to work through them yourself and make your own mistakes”

Students’ learning ‘leaks’ out of school: a student may frequently choose to continue with their task or project beyond school – in their homes, either with friends, or alone. Students are able to positively ‘connect’ their learning : deeply engaged students often display ‘expert’ characteristics – especially if they are engaged in project or enquiry learning.

Students begin to think and act, like scientists, or engineers, and can independently ‘join up’ learning from one context to another. In the words of another interviewee: ‘I make links between everything, so I can tell a story, or relate it to something that happened, and that’s how I really learn’. This adaptive competence, the ability to construct and contextualise their own learning, is in sharp contrast to the ‘bite-size’ knowledge acquisition, that typifies much of current conventional pedagogy.

We want our students to be more cognitively engaged in their learning, not only compliant learners. Compliance engagement is if students:

  • Attend regularly
  • Conform to behavioural norms
  • Complete work in the manner requested and submit on time
  • Are ‘on-task’
  • Respond to questioning

 Notes From Nina is a blog that I follow and a recent post has also pursued an engagement theme that is well worth reading here. She has titled it Engaging Students in Learning, not just Schooling. In this post she writes:

The learning process has two components that must be integrated for deep learning to happen: interaction (with the materials and peers) and acquisition of the content (Illeris, 2009, p. 9).  A successful integration of content and interaction leads to personal construction of understanding, i.e. deep learning, because the student has situated the new knowledge into her/his existing understanding.  Another student, who is just engaged in schooling not learning, may miss out the both components, and just be physically present in the classroom. Yet in today’s world, more than ever before, we must help students to become lifelong learners, who learn because they want to, not because someone tells them to do so….

In addition to the two components of learning process, we also want to think about the dimensions of cognition, emotion and environment (Illeris, 2004, p. 82), because they create the frames of each individual learning experience.  In school settings the focus of learning is too often very narrow, and only aims to transfer the content knowledge. But the way we acquire the content  has a straightforward effect on how durable the resulted learning is.  Shallow learning aims to passing the class or just getting out of it. Deep learning aims for understanding, and using the learned content in the future. What is problematic, is strategic learning, which aims to have good grades, without any interest in the content itself.

Christopher Bantick’s recent article  describes what he believes quality schooling looks like. “Truly great schools focus on academic success” he writes. In Australia, this is evidenced by NAPLAN results (national tests in literacy and numeracy) and ATAR rankings (a summation at the end of secondary schooling based on final year exams) . He goes on to state that “Parents want their children to have access to the best possible teaching to gain access to desirable universities”.

So what is a quality education? Is ‘schooling’ equivalent to ‘educating’? Is the only purpose of a secondary education to provide access to university? What does ‘academic success’ look like? Does it look the same for every student? For every school? Should we look to China as an exemplar on how to improve academic success?

We know that there is, what Pasi Sahlberg, amongst others, has termed GERM, the Global Education Reform Movement. A movement that has, as its key elements:

  1. Standardising teaching and learning
  2. A focus on literacy and numeracy
  3. Teaching a prescribed curriculum
  4. Borrowing market-oriented reform ideas
  5. Test-based accountability and control[1]

Many of these elements have an economic rational basis, especially the use of standardized tests.  “The fault is not with the mathematics, or with the importance attached to what the tests are attempting to measure. It is in the way we are reducing our sense of accomplishment in education, as we do in economics, to ‘equations, graphs, numbers and formulas’. [The fault] is in the reduction of the worth of education to mathematics”[2]

Michael Fullan has led those who have analysed the effectiveness of GERM in driving educational change and has come to the conclusion that these are, in fact, the wrong drivers to produce effective and sustainable change that improve learning outcomes for students. In his 2011 seminal paper on ‘wrong drivers’ versus ‘right drivers’ [3], Fullan describes a ‘right driver’ as one that achieves better measurable results for students. He suggests four criteria to judge a driver’s effectiveness. Does it

  1. foster motivation of teachers and students;
  2. engage educators and students in continuous improvement;
  3. inspire team work; and
  4. affect all teachers and students?

The key to success is to place educators and students at the centre. This means aligning the goals of any change agenda and the intrinsic motivation of participants.

Last year I attended the launch of the book by Brian Caldwell and Jim Spinks called The Self-Transforming School. The authors and their team have looked at the research on education coming out of 11 countries throughout the world and explored the experiences that are shaping educational theory and practice, in addition to systemic practices, including resourcing arrangements, of various governments. They use this research to point towards the trends and practices they see developing in education for the next 25 years and then discuss how we can ensure significant, sustained and systematic change that will secure success for all students regardless of school setting.

They ask the question: What beliefs and practices will produce the best outcomes for students?

The authors qualified the use of the term ‘outcomes’. In education, this is not equivalent to ‘endpoints’ such as Y12 results (or similar). It is the difference between starting points and endpoints. So, I would argue that ‘academic success’ is defined by this difference. In fact, I would argue that ANY learning can be defined by this difference, including that of professional learners like teachers.

What are the outcomes we want for our students? Are we reducing our idea of the worth of education by focusing on results in isolation of other metrics of growth – such as the development of an increased capacity to unlearn and then relearn, learn through the instructional design of mistake-making & deal with challenge or the dispositions to think critically and creatively? In our quest to attain best, and then ‘next’, practice, I would posit that we endeavour to see beyond the somewhat short term and contained (perhaps even ‘containing’?) metrics of test performances and look to aspects of education that place educators’ and students’ learning at the centre.

If Australia wants to position itself as a ‘self-transforming’ nation and aim, not merely for ‘best practice’ but ‘next practice’ then I would suggest that our focus should be more on the elements of teaching and learning that develop and support quality learners, both in our teaching and our learning. Caldwell and Spinks write, we need to ‘see ahead’, ‘see behind’ (honouring and extending accomplishments in the past), ‘see above’ (understanding the policy context and the evidence-based global perspectives), ‘see below’ (demonstrating a deep understanding of the needs, interests, motivations and aspirations of its students and staff),‘see beside’ (networking professional knowledge to take account of best practice in other schools and settings) and ‘see beyond’ (seeking out what aspects will lead to ‘next practice’)[4]

Yong Zhao writes in the introduction to his latest book, Who’s Afraid of the Big Bad Dragon: Why China has the Best (and Worst) Education System in the World :

The Chinese national educational system has won high praise as an efficient system with national standards, a national curriculum, a high states test (the college entrance exam), and a clearly defined set of gateways to mark students’ transitions from one stage to another[3]. Admirers note that every Chinese student has a clear and focused goal to pursue; Chinese teachers and parents know exactly what to do to help their students; and the government knows exactly which schools are doing well. What those admirers ignore is the fact that such an education system, while being an effective machine to instill what the government wants students to learn, is incapable of supporting individual strengths, cultivating a diversity of talents, and fostering the capacity and confidence to create.

I wrote this book to show how China, a perfect incarnation of authoritarian education, has produced the world’s best test scores at the cost of diverse, creative, and innovative talents. I also tried to illustrate how difficult it is to move away from authoritarian thinking, by showing how China has struggled to reform its education for over a century. The book is intended to warn Western countries about the dangerous consequences of educational authoritarianism.

Readers may also want to read the blog post by Anthony Cody here on Zhao’s book.


Speaking at the ACEL (Australian Council of Educational Leaders) conference this week, Richard Gerver said “”Australia seems to have lost confidence in what it had, which was essentially an enviable vision for the future of education”. (See this article for more). He decries looking to other countries as exemplars. Further, in this recent post, the author, asks “Who decided schools are broken?” Who, indeed.

As leaders of learning, we need to ensure our voices are heard in this space. Another recent post on Notes from Nina‘s blog  talks about the importance of leadership in education. She writes:

My favourite definition of leadership is this:

Leadership is about leading others towards an imaginary future.

It is not easy, because we don’t actually know what is there.  But, by having sufficient knowledge and data, we can make educated guesses about it. Effective leadership in education is about engaging the whole team to improve educational outcomes

The other hard, but oh so important step in leadership is to move the focus and action from what is urgent to what is important. In classroom this means teaching and learning for life, not for test (this also can be seen as engaging indeep learning).

A major part of my daily work is about my attempts to provide leadership and  empower my students to step up on the plate and be in charge of their own learning and meaning-making.

So, Team Australia, what do we want for our nation’s future? Let’s take an educative, lighthouse stance, celebrate what we are doing well in educating young people to have agency and the capacity to create their future and shine our light for all to see.

[1] Finnish Lessons, Pasi Sahlberg, Teachers College Press, 2011, p 103

[2] The Self Transforming School by Brian Caldwell and Jim Spinks, Routledge, 2013, p 97



[4] The Self Transforming School by Brian Caldwell and Jim Spinks, Routledge, 2013, p 115


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Getting Teacher Evaluation Right

The University of Melbourne Graduate School of Education has a series of Dean’s Lectures and I attended one on January 30 to hear Linda Darling Hammond speak on the title of this post.

She started by asking “Why is there so much attention to teacher education reform?” and her belief is that the mission of 21st century teaching is different to what was before. It’s no longer good enough for teachers to ‘know their content’ and deliver it. It’s more of a co-learning role now where teachers, and their students, are expected to be on learning journeys, where teachers should know about learning and how to better engender that learning in their students.

“Why has it been problematic?”

1.  Lack of:

  • clear standards of practice
  • time
  • expertise
  • links to professional development

2.   Little attention to student learning

3.   Unwieldy processes for making decisions

“How we might make matters worse”

1.   focus evaluation entirely after entry to teaching

2.  creating systems that focus on ranking teachers versus improving teaching

3.  making decisions substantially based on value-added test scores

4.  putting all of the weight on school principals

5.  designing systems that cannot be implemented

“What do effective teachers know and do?”

  • engage students in active learning that builds on what is known about their prior learning
  • create intellectually ambitious tasks
  • use a variety of teaching strategies
  • assess student learning to adapt teaching to student needs
  • create effective scaffolds and supports for language and content learning
  • provide clear standards, constant feedback and opportunities for revising work
  • develop and effectively manage a collaborative classroom in which all students have membership

Darling Hammond made the point that the above listed qualities of what effective teaching looks like are all embedded in the AITSL standards for the performance and development of Australian teachers.

So, if we now know what effective teachers need to be able to do and know, how do we develop teachers to reach these standards of practice?

Darling Hammond made the point that systems created for such a purpose need to combine evaluation with the creation of a standards-based teacher development process, and that this process should be educative (not punitive). And that this MUST (her emphasis, based on the research evidence) be concomitant with the training and development of the leadership group (otherwise the professional learning of teachers will go nowhere).

Within the development process should be opportunities to show integrated evidence of:

  1. practice
  2. professional contributions
  3. student learning

Multiple measures are required to reflect practice. Lesson observations used as part of the evidence platform need to be standards-based and performed by experts who have been trained in evaluation and ideally in the same content area.

What is your school doing in relation to the professional learning of all who work within it? One of the biggest dangers I see is that of too broad a palette. Look again at that list of what makes an effective teacher. Is the professional learning program at your school aimed at these elements of practice?

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The Self-Transforming Teacher

It has been a long while since I have written a post. Apologies. It has not been due to lack of interest, or material. Just a very diverse and challenging year.

I have gained much from Twitter this year. Thank you to all I follow for your thoughts, insights and, perhaps most importantly, your links to blogs, reports, news stories from around the world, that are related to education. One of the most recent blog posts that struck a chord was by Margery Evans, the CEO of AITSL (Australian Institute for Teaching and School Leadership). It is here. In this post she writes:

“If there is one persistent truth about teachers, it is the dedication that leads us to live and breathe our profession. It is part of each one of us, embedded in and expressed through our personal values and world views, a constant focus of our attention.

The membership of our community is ever changing as new graduates enter the profession and experienced educators retire. We evolve as new research about teaching and learning informs our practices and the understanding of what it takes to be an excellent teacher grows. We create and re-create our profession constantly, but some qualities endure, foremost of which is our focus on providing the best possible education for all students and the very personal way in which we exercise our professional responsibilities.

The core medium of the teaching process is and always will be the individual human being.

This is what makes the act of teaching so very personal, complex and enduringly difficult to capture in theory and policy documents. Our diversity as teachers is what makes our profession strong, but it also poses challenges….We all understand that the quality of teaching is a key factor in determining educational outcomes for students, and that school leaders set the tone and tempo that enable excellent teaching to flourish……..what we are doing is establishing the traditions that will help our profession to endure and remain focused on excellence, as it constantly changes and evolves. We are creating the frameworks that bind the family of educators together and help us to recognise, share and develop the professional qualities that we value in ourselves and each other …”

Apart from bringing a tear to my eye, it made me wonder about the traditions we have as individual teachers, as the discipline groups to which we belong, as schools and as broader educational systems. Are all of these traditions ones that “will help our profession to endure and remain focused on excellence”?

As Margery notes in this post, it is what we bring as individual human beings to this dynamic that will influence how the system behaves. We need to drive the profession. No longer passengers along for the ride. We need to set the agenda, set the parameters around the discussions and, above all, lead by example.

One of the most inspiring events I attended during 2013 was the launch of the book “The Self-Transforming School” by Brian Caldwell and Jim Spinks. In the Foreword, Dame Pat Collarbone writes that

“….in order to bring about systemic transformation, we need to develop the capacity to lead that change at a local level rather than introduce more and more measures and bureaucracy……..a command-and-control culture has cascaded down through the system for decades so that many people now do not know what it means to take up their own authority. A dependency culture creates not only inefficiencies but, all too often, low morale……it is often very hard and painful for people to discard ways of working that they have developed over many years and that have served them well in the past……..the way in which leaders lead or resist change, and how they engage with their staff, sets the climate of a school that either promotes trust and innovation or reinforces rigidity and resistance……..senior leaders usually have a sound knowledge of the theory of change, are able to visualise where they want to take their school, but find it hard to distribute leadership whilst retaining accountability. ….transformation [requires] …a higher level of professionalism of teachers, leaders and those that support them.”

So, how do we reinvent ourselves and our schools to better create an education with a better fit for the children of today and tomorrow?

We need to start with ourselves.

One of the chapters in the book is titled “Innovation Everywhere”. It speaks of the need to ‘see ahead’ (future-focused), ‘see behind’ (honouring and extending past accomplishments), ‘see above’ (understanding the policy context in which we operate), ‘see below’ (deep understanding of the needs, interests, motivations and aspirations of students and staff) , ‘see beside’ (networking professional knowledge and looking at what other schools are doing) and ‘see beyond’ (to what research points at, looking at best practice in other fields). The authors write of the need for schools ‘to do well in what they are currently expected to do’ but also ‘keep an eye on promising innovations and future possibilities’ using a ‘split screen approach’.

Michael Fullan is quoted on Page 127, that with respect to transforming learning,

“No matter how you cut it, we are not making progress…the goals are too vague, having a glitzy attraction. When [we look at] specificity, the focus is on standards and assessment (which does help with clarity), but the crucial third pillar – pedagogy or fostering actual learning – is neglected”

In my opinion, the focus on pedagogy should be the cornerstone of every teacher’s development as an educational professional. How do we make learning better? We need to look closely at what we are doing in our classrooms. Take notice of who is learning and why, who is not and why not. What are the essential elements of our disciplines young people should be learning and why? How do we teach people to be better learners? To know more about themselves as learners and learn how to better unlearn and then relearn? How to motivate themselves to learn. How to be persistent and persevere when challenges arise. How to be ‘grittier’ as Angela Lee Duckworth says in her excellent TED talk. (You may also like to read the US government’s report on Promoting Grit, Tenacity and Perseverance and this blog post). These are the skills that will matter for the future.

But all of this noticing and reflecting needs to be done with a weather eye on what is already known about learning. It needs to be informed and grounded by research. Not just affirmed by peers or past experience or intuition. Not what makes us feel good..or what makes our students feel good. Does what we do improve learning? How do we know?

This is why we need to engage with developing our own professional learning journeys and driving ourselves on that journey. It should not be someone else’s call. If we want our students to be autonomous learners, we need to be as well. If we want our schools to be self-transforming, we need to be too. We need to be the change we want to see ‘above’ and ‘below’.

So, at this time of the year that is full of tradition, I will take some time over the break to consider the traditions that inform and guide my practice as a teacher. And develop some new ones. Ones that will embrace constant and considered transformation. Ones that will focus on pedagogy and improving learning for me, my students, my school and the system in which I teach, “framing what it takes to grow, develop and be successful in our profession” (from Margery Evans’ post again).

How will you frame your professional growth and development for 2014?

Posted in Pedagogy, Students, Systems, The profession, Vision | 1 Comment

Evaluating the Quality of Mathematics Instruction

I recently discovered the existence of this fantastic tool, developed by Harvard Graduate School of Education in 2010.

It is specifically aimed at teachers of mathematics and gives a list of aspects of the mathematics classroom that should be in evidence in order to be described as ‘quality instruction’. I can see it being used as the starting point for conversations between teachers for classroom observations. An evaluative tool designed to develop instructional quality, not specifically for teacher evaluation but looking at improving the mathematical learning experienced in classes.

Additionally, Dylan Wiliam recently tweeted about some research that has looked at the link between the use of this tool and student outcomes. That research paper is here.


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Finnish Lessons

I spent some time today reading Pasi Sahlberg’s Finnish Lessons – What Can the World Learn from Educational Change in Finland?

Some quotes follow:



  • has developed and owned its own vision of educational and social change connected to inclusiveness and creativity, rather than renting a standardised version
  • relies on high-quality, well-trained teachers, with strong academic qualifications who are drawn to the profession by its compelling social mission and its conditions of autonomy and support
  • has developed teachers’ capacity to be collectively responsible for developing curriculum and diagnostic assessments


The intense individuality of the Finns blended with low hierarchy and traditional willingness to work with others has opened pathways to endless creative potential

p17 should aim at educating young people to realise themselves as holistic individuals, possessing intrinsic motivation for further education


..three phases {of educational change]:

  1. rethinking the theoretical and methodological foundations
  2. improvement through networking and self-regulated change
  3. enhancing efficiency of structures and administration


[Common themes for Prof Development of teachers included]  “Conception of Knowledge”, “Conception of Learning”, “About Possibilities of School Change”. These contained questions like “What is knowledge?”, “How do pupils learn?” Discussions on conceptions of knowledge and learning has clearly affected how teachers talk about learning and teaching. Earlier discourse … was replaced by [that on] critical thinking, problem solving, and learning how to learn.

p 51, referring to why mathematics results in international testing improved dramatically

  1. mathematics teaching is firmly embedded in curriculum design and teacher education in Finnish primary schools
  2. most primary schools in Finland have professionals who understand the nature of teaching and learning- as well as assessing – mathematics
  3. education of maths teachers in Finland is based on subject didactics (pedagogical content knowledge) and close collaboration between the faculty of mathematics and the faculty of education. This guarantees newly trained teachers has a systemic knowledge and understanding of how mathematics is taught and learned


Teachers at all levels of schooling expect that they are given the full range of professional autonomy to practice what they have been educated to do: to plan, teach, diagnose, execute and evaluate.


Finnish teacher education is now ‘academic’, meaning it must be based on and supported by scientific knowledge and be focused on thinking processes and cognitive skills needed to design and conduct educational research…systemic integration of scientific educational knowledge, didactics and practice to enable teachers to enhance their pedagogical thinking, evidence-based decision making and engagement in the professional community of educators.


Particular attention is devoted to building pedagogical thinking skills, enabling teachers to manage instructional processes in accord with contemporary educational knowledge and practice.


Teacher-education curricula are designed so that they constitute a systemic continuum from the foundations of educational thinking , to educational research methodologies, and then on to more advanced fields of educational sciences.

p84 Key principles of teacher education

  1. Teachers need a deep knowledge of the most recent advances of research in the subjects they teach. In addition, they need to be familiar with the research on how something can be taught and learned
  2. Teachers must adopt a research-oriented attitude toward their work. This means learning to take an analytical and open-minded approach to their work, drawing conclusions for the development of education based on different sources of evidence coming from the recent research as well as their own critical and professional observations and experiences
  3. Teacher education in itself should also be an object of study and research


[Teacher prof development] has shifted from fragmented in-service training towards more systemic school improvement that builds better ethical and theoretical grounding for effective teaching


Authorities and most parents understand that teaching, caring and educating children is too complex a process to be measured by quantitative metrics alone.

Pedagogical leadership is one of the key areas of professional school leadership in Finland. Teachers rely on their leader’s vision and the principal understands teachers’ work.


Professionalism as the main characteristic of teaching requires that teachers are able to access and follow ongoing development of their own profession and that they can freely implement new knowledge within their own instructional work.

p102 On the GERM (Global Educational Reform Movement)

Michael Fullan…speaks about ‘drivers of change’, such as education policy or strategy levers, which have the best chances of driving intended change in education systems. “In the rush to move forward”, writes Fullan, “leaders, especially from countries that have not been progressing, tend to choose the wrong drivers”. ‘Wrong drivers’ include accountability (v professionalism), individual teacher quality (v collegiality), technology (v pedagogy) and fragmented strategies (v systems thinking). These ineffective elements of education reform that resonate closely with the aspects of GERM have fundamentally missed the targets and continue to do so..

p105 Referencing the Fourth Way, characterised by Andy Hargreaves

The Fourth Way is a way of inspiration and innovation, of responsibility and sustainability. The Fourth Way does not drive reform relentlessly through teachers, use them as final delivery points for government policies or vacuum up their motivations into a vortex of change that is defined by short-term political agendas and the special interests with which they are often aligned. Rather, it brings together government policy, professional involvement and public engagement around an inspiring social and educational vision of equity, prosperity and creativity in a world of greater inclusiveness, security and humanity.


..if people work or learn in an environment where avoidance of mistakes and fear of failure are dominant, they typically don’t think for themselves.Fear of failure does not engender creativity.


..teachers cannot create and sustain contexts for productive learning unless those conditions exist for them

LOTS to think about in this book. And a fantastic way to begin the new academic year. Courageous leadership is needed …from me, from my school and from my nation.

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Algebra Summit

Everyone seems to be having a summit these days so I thought…why not teachers of mathematics?

Today marked the start of our ‘meeting week’, a week without students in which staff meet to reflect and review on the academic year about to end and to plan for the one ahead. All teachers of secondary mathematics in our school met today to look at algebra across these year levels.

Our goals were:

  • —To develop a common understanding of the purpose of algebraic processes and thinking
  • —To develop a common language to be used
  • —To explore and compare personal beliefs regarding the teaching of certain aspects of algebraic thinking and processes
  • —To reflect on these and compare them to available research
  • —To develop a coherent thread of algebraic thinking and processes from Y7 to Y12 as much as possible

There were specific ‘rules’ for the environment in which this was to happen:

  • —One of professional respect
  • —One of respectful challenge, rather than mutual endorsement. Expect to justify what you say in terms of how it contributes to improved student learning. All voices need to be heard.
  • —One that accepts that you will not always get what you want but one of continuous capacity building; of each teacher and of the faculty
  • —Where we consider ‘our’ students rather than just ‘my’ students

Teachers worked within small groups of 4 or 5. We started by articulating the meaning for the common algebraic processes of expand, factorise, simplify and solve. This brought out a few misconceptions and helped to build a common understanding of the language we use.

Participants were then asked to think about what algebraic thinking involved and looked like. Then everyone was asked to respond to the following – with respect to expansion, factorisation, simplification and solving.

  • —What mistakes are typically made by students when expanding?
  • —How do you/ would you teach expanding?
  • —How does the way you currently teach expanding relate to how it is taught at other levels?
  • —How could you develop your teaching of expansion to deliberately address algebraic thinking?

Following this, teachers compared approaches as to how they would teach students to factorise a particular quadratic trinomial, solve an equation involving two algebraic fractions, complete the square etc. The catch cry became “think back, think forward” how does this process relate to what students already know and how will it link to what they will experience in the future?

We briefly looked at how the CAS calculators can be better used to develop algebraic thinking by allowing students to experiment, get answers, look for patterns, generalise, predict.

A really collaborative, open discussion that I think will set the scene for professional dialogue to come.

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