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

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. 

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. 

COVID19 has taken the rule book on change, torn it into small pieces and thrown most of it out the window. What might this mean for education?

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.

As thousands take to the streets as part of a global 'March for Science' it is worth considering the significant role that education has to play. What are the messages we need to send our students about science and what role have schools played in creating the current climate? Now seems like the time to pause and reflect on the place of science in our community and our schools.

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.

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.

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.

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?

I am wanting to take a slightly different approach to this weeks post. The past week has seen the latest round of PISA results and the media has had a field day. Headlines have routinely attacked students, educators and education systems in equal measure. The Canberra Times reported that "Australian school scores plummet on world stage", the Sydney Morning Herald led with "Alarm bells': Australian students record worst result in global tests" and The Weekend Australian went with "PISA global educational rankings: Schools fail on maths, science". 

This week I joined with teachers, students, researchers and policy writers at Melbourne University to discuss student voice. This conference was hosted by Social Education Victoria and made possible by the conference partners, The University of Melbourne, Education and Training Victoria, Foundation for Young Australians and Connect. Over three days, participants engaged in rigorous dialogue about the significance of student voice and what is required to ensure its benefits are maximised for all.

The bushfire crisis that is currently impacting Australia is beyond devastating. The scale of these fires defies the imagination. For so long now we have lived with skies laden with smoke as a constant and inescapable reminder that this is not an ordinary summer. This is weather and drought at its most extreme. Our only salvation will be rain but this is not the season for that and the long term forecasts are not promising. Our young people, in particular, will be affected and will need special care in the weeks and months to come. What might this mean for schools and for student agency?

With summer in the southern hemisphere, long days combined with school holidays for school teachers create the perfect opportunity to relax with a good book. Here are five great reads that might spark some curiosity and keep the brain working over the break.

This page makes it easy to find information and resources that are relevant to particular concepts, approaches and strategies. Each Collection is curated to serve a particular need and shares a set of resources pooled from The Learner's Way. In time this set of Collection will grow. In addition to articles from The Learner's Way you will be able to find resources designed to help you get started with the key concepts presented. The aim is to produce a set of resources which are readily accessible and of immediate benefit to classroom teachers and school leaders.

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.

If you are interested in building a classroom culture where thinking is noticed, named and celebrated, there are three books which make essential reading. They provide clear evidence for why teachers should focus their efforts on encouraging and normalising thinking and offer research-backed strategies to support this. The books are the result of ongoing research by Harvard's Project Zero and their lead author Ron Ritchhart.

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.