In times when we taught face-to-face, some of these challenges would be overcome through the use of concrete materials, at least with younger students. Unfortunately, it is common for the use of concrete materials to decline as students grow older. Fortunately, this pattern, and the prejudiced beliefs on which it is founded, are today being questioned.

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?

Praise and Feedback occupy significant spaces in the lives of our learners. It should not be surprising then that the language we use to communicate praise and feedback can enhance or hinder our efforts.

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?

What changes when we refer to ourselves or our students as members of the community of thinkers and learners that they are apprenticed to? What changes when we are mindful in our use of a language of identity?

Why might it be that our students struggle with independence? Maybe it comes from the language moves we make. As with the language of thinking, being deliberate with our choices can help us to create a classroom culture where students demonstrate independence and initiative.

A good place to start in our efforts to shift the impact that our language choices have is with a focus on the language of thinking. If we believe that all learning is a consequence of thinking, it is natural to select language moves that encourage this from our learners.

The landing of the Perseverance rover on Mars is an excellent catalyst for a discussion with students about the nature of Mathematics. It is a chance to inspire curiosity and wonderment and to do so through a mathematical lens.

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?

n practical terms, any change effort that does not consider the culture into which it is introduced is unlikely to succeed. The worst-case scenario is that the change effort is resisted to such a degree that it is never truly implemented. In many cases, however, the change effort fails to produce the sort of results initially imagined despite the efforts of all involved to adopt the change. Although the new behaviours are adopted, something goes wrong, and it isn't always that the new idea itself is to be blamed. - Maybe it's culture?

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.

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?

often think in metaphors. They help me to clarify and communicate my thinking. A metaphor can make a complex idea accessible and comprehensible. They invite understanding and are a useful catalyst for conversation. A metaphor can be made even more powerful when it is combined with a practical demonstration. One metaphor I like to share with colleagues revolves around the impact that we might have as teachers. - A guest post by Stellina Sim

As schools prepare for the upcoming Christmas break here is a list of books that are bound to get you thinking.

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.

To ensure reflective practice is more than an activity added to our schedule, we need to take a reflective stance. Too often, reflection becomes the thing we do at the end of a task or the end of the day. We look back and contemplate what was, and with that in mind, we look forward to what we might do differently next time. It is in this way a very reactionary process. By all means, this form of reflection has its place, and it can be a powerful strategy to deploy as we seek to learn from experience. If we value reflective practice, we will be sure to set aside time for this form of reflection on a routine basis. By engaging in reflection habitually, we ensure that it is a routine part of our day. But adopting a reflective stance can make this more powerful.

Explore the website of any school, and you will undoubtedly find a page dedicated to their Mission and Vision. Here you will find carefully crafted statements of purpose couched in the vocabulary of educational excellence and reflecting the pinnacle of human possibility. A blend of educational philosophy and marketing speak designed to promote student achievement and enrolments. The question is, to what degree does the lived experience of the typical student align with the stated purposes? Does the product do what it says on the tin?

"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?

Two resources that might appeal to educators pondering the future.