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Walk into any McDonald's, anywhere in the world, and you know where you are and what to expect. For the homesick traveller, the consistency of McDonald's' design aesthetic is comforting. You know how this is going to work, you understand what to do, and you know what you are likely to get. McDonald's requires minimal cognitive load on the customer's behalf.

How do move from an emphasis on rote learning of procedures in mathematics towards a focus on mathematical reasoning?

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?

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?

If we believe that all learning is a consequence of thinking, then we should consider what types of thinking our learners are likely to benefit from at each phase of their inquiry. This is where the Understanding Map, developed by Ritchhart, Church & Morrison offers useful guidance. By contemplating the demands of each phase of our chosen inquiry model, we can plan for how we might scaffold thinking moves which will enhance our learners' learning.

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.

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. 

It is difficult to understate the importance of reflective practice for learning. Dewey states that "We do not learn from experience. . . we learn from reflecting on experience", and it is worth taking time to consider the implications of this. How might we maximise the benefits of reflective practise amidst the many competing pressures we confront?

When we approach this task with key questions in mind, we focus our thinking on how we might plan learning experiences and opportunities that will have the impact we desire.

Not all learning is created equal. Sometimes the learning that we achieve and the success generated through our engagement with a learning opportunity is spectacular. At its very best, our learning unlocks fresh understandings for ourselves and sometimes even for others. What conditions allow for such spectacular learning, and how might we bring these conditions into our classrooms?

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.

Number Talks are a wonderful way to see where our students are with their mathematical thinking. As a part of a daily routine, a Number Talk promotes number sense and mathematical reasoning. In this post, I revisit what a Number Talk can reveal about our students' understanding of mathematics, and how they might be used to promote a fresh perspective. In addition, I examine a success criteria for Number Talks that is more expansive and recognises their true power.

These two powerful questions framed a recent webinar presented by Professor David Perkins of Harvard Graduate School of Education's Project Zero. Answering these questions and helping teachers find meaningful and contextually relevant answers to these questions has been a focus of Perkins' work, especially in recent times. His book "Future Wise: Educating Our Children for a Changing World" introduced us to the notion of lifeworthy learning or that which is "likely to matter in the lives our learners are likely to live". This is a powerful notion and one that has the potential to change not only what we teach but also how we go about teaching what we do.

Perhaps the disruption of a global pandemic will prompt a rethinking of how education might be framed to best serve the needs of those who rely on it most? Perhaps now is the time to rethink the curriculum?

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.

"Nothing in this world can take the place of persistence. Talent will not; nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not; the world is full of educated derelicts. Persistence and determination alone are omnipotent. The slogan Press On! has solved and always will solve the problems of the human race." ― Calvin Coolidge Growing up, I had a copy of this quote on my wall. It is one of those things that stuck with me over the years. For a long time I might not have truly appreciated its wisdom. Now as a teacher in times of volatility, uncertainty, complexity and ambiguity, its significance seems to have grown. When we can instantaneous consumers of the all of the worlds information, as we access anything and everything at the speed of light, how do we learn the value of persistence?

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