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Experience shapes our understanding of the world and our responses to it. Our past influences our decision making and constrains our imaginations of what is and is not possible. understanding this is a crucial step towards change; a first step towards discovering a better way to do things. Until we understand how our experience is limiting our imaginations we will continue to be restrained by the way things have always been done. 

There is an understandable interest in deep-learning, after all, who wants their students to have a superficial understanding of the content. Read the marketing of almost any school and you are likely to find some statement about the deep-learning that is achieved as a result of their excellent teaching and learning platform. Likewise, ask any teach about their philosophy of teaching and you will hear how they engage their students with learning that promotes a deep-understanding.

The shift away from teaching for the rote memorisation of prescribed methods requires teachers to rethink their approach to the discipline. With this new pedagogy comes a need to understand the processes of mathematical thinking in ways not previously required. When we require our students to be able to reason and problem-solve through unique challenges we also require our teachers to have an understanding of the mathematical moves that their learners are likely to call upon.

Understanding the "Why" of any initiative should be a key step prior to implementation. Without a clear Understanding of our "Why" how are we to judge the success of what we are implementing. How will we know which steps take us in the right direction if we have no concept of why we are journeying. In our implementation of ICT (Information & Communication Technologies) and now Digital Technologies, a lack of clarity on the matter of "Why" has often been the most significant challenge to success. 

Of all the subjects that our students engage in, mathematics is the one most requiring an injection of learner agency. What is it about mathematics that engenders it to modes of teaching that are so heavily teacher-directed? How might this change if we seek to understand the place that learner agency plays in producing learners who will emerge from our classrooms with a love of mathematics and a deep understanding of its beauty?

Recently I have been contemplating how we might define inquiry. Like many terms in education, it is often used in multiple contexts and has a range of meanings attached to it. Coming to agreement on what inquiry is, requires negotiating seemingly divergent understandings. If we are to avoid oversimplifications and dichotomous thinking, we need to explore these multiple perspectives and find a balance point.

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. 

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?

James Tanton shattered my understanding of the vertical algorithm. More than that, he helped me to see how poorly I understood place value and that many of my students function with the same misunderstanding. What made the experience more humbling was that it took him less than two minutes to do this.

With our goal of deep-learning in mind where do we begin and what learning opportunities might result in this? Having clarified our key terms of understanding, learning and deep, we can turn to a set of questions which might be of use as we plan the learning our students will engage in along their way.

The Australia-Indonesia BRIDGE Project aims to increase knowledge and understanding between Australia and Indonesia through school-to-school partnerships that link students in both countries.

The CETL(NI) has developed a Hybrid Learning Model which can be used to describe learning activities as a series of understandable and universal set of learning events where the teachers and students experience and roles are clearly defined at each stage. The strength of this method is its transparency, use of plain English and its potential in breaking down effective complex learning activities into a generic, re-usable format so that good practice can be disseminated, reapplied and evaluated easily.

it is an easy-to-understand and engaging slide show, which probably could be adapted to use for beginners training or for an overview session for LMS

Our learners will never now a world where Digital Technologies are not the norm. Using solutions developed within this space and with this mindset is already their normal. Unless they are to be slaves to this technology we must also empower them to be creators of digital solutions. To do this we must begin with recognising the challenges that a curriculum built around mastery of Digital Technologies brings to our teachers and seek to understand the supports they require.

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 one such idea.

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.

Being wise is about so much more than knowing the right answer. Indeed, it can be argued that knowing the right answer can be an obstacle to learning and understanding. As we move further into times where knowledge is ubiquitous and yet truth is increasingly hard to find, merely knowing the right answer can be an impediment. 

All learning is a consequence of thinking. I have these words printed and posted on the wall above my desk. It is a reminder of what I believe is a vital understanding. The consequences of this one statement are quite profound. They fundamentally shape what I do as an educator and the experiences I hope to create for my learners.