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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.

What makes a team truly great? What are the qualities which allow some teams to perform at a high level while others seem trapped? One approach to this question is to consider a team as though they were a meal. Thinking metaphorically, we ask what are the ingredients that make a great team and how might we combine them to produce the best results?

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".