(mini rant) I love how Australians call math "maths". I feel this is the real language we should use because there is more than one strand in math.
I had PD today at St. Anthony's (patron Saint of lost things I think). I just looked there are about two dozen Saint Anthonys!
We had a video session where we respond to video clips of lessons. Most of the video clips I watched dealt with Multiplication and Division. Quite a few different styles of arrays were used to demonstrate how we can build numbers through Multiplication and Division.
I appreciated the different ways that the students in each example understood the concepts of Multiplication and Division. It is great to see a classroom where students aren't set into a fixed way of thinking. They are free to create personal understanding which is so much more valuable than the steps I learned. As long as their ways of thinking work in different ways they are free use it. Of course it is important to challenge students to try new ways so they can expand their understandings.