I recently had the opportunity to speak with a group of parents whose children are transitioning into a new phase of their learning. I used this as an opportunity to share some key messages for successful learning and thought I would briefly unpack these here.

Our beliefs about mathematics play a significant role in how we approach learning within the discipline. These beliefs are established by the nature of our early engagement with mathematics and are difficult to change once established. For many people mathematics is viewed as a subject that is not for them. Indeed the situation is so bad that many people will say that they are not a maths person and approach mathematics with fear and anxiety. 

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?

Particular patterns of pedagogy have been of most interest to me across the years, particularly those that shift the focus from what the teacher does to what the student does. With this shift comes an emphasis on understanding how students learn and with this knowledge in mind developing learning experiences that will allow them to develop their skills for learning.

For schools in Australia and many parts of the world, we are heading towards the end of another school term and year. That means report writing season. For the next few weeks, teachers across the country will be huddled in front of computer screens, writing reflections on the progress their learners have made. Mark books will be opened, assessments consulted, work samples will be reviewed. All so that in the first week of the long Summer vacation students can sit and read their report and make plans for how they will enhance their learning in the coming year.

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.

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. 

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.

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. 

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.

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 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. 

In the post-truth era, does the capacity to utilise knowledge prepare one adequately to do battle against falsehood? When those selling untruths know the falsehood of their stories, does the bright light of truth shine through? Perhaps not.

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. 

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

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. 

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?

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. 

The Future of Education is a topic often discussed, and at the recent gathering of educators in Florence, it was the title and theme for the conference. Now in its ninth year, The Future of Education is an international conference that attracts educators from around the world and across all domains touched by education. The conference is an inspiring two days of discussion and sharing, with the city of Florence, the centre of the Renaissance, providing a constant reminder of what might be possible when creativity and critical thinking combine. Here are my key takeaways from this event.

This week I am in Florence having spent two days at "The Future of Education" conference. Visiting this city, which has played such a significant role in western history, is inspiring. It encourages one to not only look back at what was, but also to look ahead at what might be, especially when the t