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The dangers of making learning so safe and so easy it lacks any real sense of challenge. When we do this we deny our learners the opportunities they need to learn from mistakes and grow their minds. 

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.

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?

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. 

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. 

Despite this being a 'thinking' conference, despite us all being advocates for structured and scaffolded models of thinking, not one group had applied any thinking routines, utilised a collaborative planning protocol or talked about applying an inquiry model or design thinking cycle. It wasn't that we didn't know about them. It wasn't that we don't know how to use them. It wasn't that we don't value them. We had all the knowledge we could desire on the how to and the why of a broad set of thinking tools and anyone of these would have enhanced the process, but we did not use any of them. Why was this the case and what does this reveal about our teaching of these methods to our students?

This week I spent three days in Brisbane attending the Australian Association of Mathematics Teachers' national conference. The theme of the conference was "Why Maths?" and along with 500 other mathematicians, we looked to find inspiring answers to this provocative question beyond the classroom. Here are my key takeaways from this event. 

What might it take to ensure students choose to be in our courses because the value of the learning achieved through mindful attendance is such that they would not want to be anywhere else?

Our language choices communicate both intended and unintended messages. In the choices we make, in the subtlety of these choices, lies a truth more powerful than that conveyed by a literal reading of our words. When we look closely and critically at our use of language, we begin to see particular patterns which reveal much about what we genuinely value and expect from our learners. 

Reasoning is at the heart of mathematical thinking. It is what mathematicians do. But how do we teach it?

Powerful learning begins with the perfect provocation. Creating, refining and skilfully presenting the perfect provocation is an essential capability for teachers hoping to engage their class in rich dialogue. Claims that the percentage of students engaged by their learning declines from 75 percent in fifth grade to 32 percent by eleventh grade suggests a need for a more provocative environment. 

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.

For teachers in Australia, the long Term Three is drawing rapidly to a close. Indeed as I write this just ten days remain before a two-week break. This is the perfect time to consider a holiday reading list. Just enough time to raid the school library or place an order with your favourite book store. Here is what's currently occupying space on my nightstand. 

I have just had the opportunity to spend the weekend learning alongside a large group of mathematics teachers. After a day and a half of talking and thinking about mathematics teaching, I am excited to get back to school and try out some new ideas. There were also some key takeaways for me that I share below. These are the questions or wonderings that my mind wandered to while listening to the numerous talented speakers over the past two days.

Adults love to ask "What if...?" questions too. It is a model that can be a catalyst for change when used in the right way and when combined with some other questions. 

It's interesting how threads emerge from the books we read. An idea springs out at you from one book and then occurs again in another or a link is found between the two. When it turns up a third time in a different place and from an alternate perspective you really take notice. I have had this experience with the concept of emotional or psychological safety.

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.

A common challenge for students and teachers is how to develop a great idea for a piece of writing. Too often students struggle with the process of finding inspiration for their writing. They have a vague idea for the story they hope to tell, but all too quickly it transforms into a list of events with little or no detail. The goal here is to provide our students with a process to use during the planning process. The hope is that by identifying the type of thinking required during the early phases of ideation and to focus their attention on details, that the stories our students subsequently compose will be more enjoyable to read. Hopefully, this process helps.

In this time of COVID19 and remote learning or emergency distance learning the value of encouraging students to investigate their questions should not be forgotten.