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

One of the thinking moves that we hope our students will confidently engage with is centred around the disposition of uncovering complexity. As we endeavour to shift our students towards a deeper understanding, the capacity to uncover complexity is a vital step. However, the ability to uncover complexity is itself complex and an excellent example of a skill that is best achieved when considered as a disposition. 

What becomes clear, as you dive further into the emerging research that connects what we know about learning, mindsets, dispositions for learning and the development of mathematical understandings, is that a new approach is required. We need to move away from memorisation and rule based simplifications of mathematics and embrace a model of learning that is challenging and exciting. We can and should be emerging all our students in the beauty and power of mathematics in learning environments full of multiple representations, rich dialogue and collaborative learning. 

For educators, parents and learners Carol Dweck's research on the benefits of a Growth Mindset is naturally appealing. Those who have a growth mindset achieve better results than those who don't, are more resilient and accept challenge willingly. After two years of incorporating a growth mindset philosophy we are finding that the reality of shifting a student's disposition away from a fixed mindset and then maintaining a growth mindset is significantly more complex than at first imagined.

Rather than expecting to be immersed in learning that shines a light on the path forward the notion of searching for driftwood that suits the learner's needs is very empowering. It requires an imagining of learning as a very active process where the learner is aware of their context, their current understanding and what they might need to move forward. It demands a conscious practice of reflection and a disposition towards taking charge of one's learning. It is a very agentic view where learning is something that you do, not something that happens to you. 

If we are to cultivate the dispositions required in these times of postnormality and post-truth we need to establish cultures in our classrooms which will allow them to thrive. 

A common question is how do we facilitate the development of independent, self-regulating learners. With an increased focus on the development of dispositional models for learning where the skills and mindset of the learner are crucial, how do we ensure that our learners move from requiring external regulation to a model of internal regulation?  

When schools communicate, and share strategies they are using to develop mindsets, dispositions and competencies with parents and when parents adopt these strategies and elements of a metalanguage for learning and thinking, our students are better able to integrate the desirable attributes. 

We live in a time of chaos, complexity and contradiction. (Sardar, 2010 [1]) Where rapid changes and transformations through technology, politics, globalisation and the climate, conspire against normality (Friedman, 2016 [2]) These times demand a fresh approach to education, one that provides learners with the thinking dispositions they need to turn challenges into opportunities, to connect their learning to their passions and emerge from their years of formal education as self-navigating life-long learners. 

Our collective ability to learn and by doing so, adapt to changing circumstances through the acquisition of new skills and dispositions is what Edward de Bono refers to as EBNE; Essential But Not Enough. - What then might education need as it develops a response to times of rapid change?

In "Factfulness", Hans Rosling shares a valuable insight into why we must question our assumptions. In times when we are bombarded with information, when false claims abound, having a disposition towards scepticism seems vital. Rosling urges us to not only question the facts we are presented with but the internal biases which influence how we interpret these facts.

Our goal might be to support Deep versus Surface Learning, but what does this mean in practical terms. What are the beliefs and dispositions which support teaching for deep learning, and what are the implications of this in terms of the pedagogy we adopt?

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

When we are young, we are naturally curious. We ask many, many questions. As we encounter the world, our consciousness is bombarded by a plethora of opportunities for curiosity. And at this early stage of exploring and discovering the world we inhabit, there is no filter between our sense of curiosity and our expression of our it. If we are curious, we will be asking questions and heaven help anyone close enough to be a potential source of answers. - At school, our relationship to both curiosity and inquiry changes.

Sometimes, it seems everyone who ever went to school is an expert on education and has a plan to make it better. Actual teaching experience, years of professional learning and formal training are all easily swept aside. The result is an ongoing dialog around what schools should do, what teachers need to do more of or less of and how the academic success of the nation is linked to strategy x or y.

As we move towards this brighter future with the fear of a global pandemic somewhat alleviated, what might be our next steps? How might we apply the lessons learned so rapidly, and brutally during this past twelve-month period? Might COVID be a catalyst for the reinvention of education that so many have been calling for?