Understanding students I think is, in some ways, the chief art of a teacher, and it’s very challenging because it’s a personal thing, the relationship with the kids, and what matters to them and what motivates them. It’s difficult because it’s not quite a science and every kid is unique and different when they walk in the door. So I think that firstly, making sure that I have substantive conversations with them, making sure I see them in contexts outside of the classroom. All of these things contribute to understanding, alright, what’s important to this student, what is it that will be the part of their life that I can connect to mathematics and help them to realise, oh this is worth doing, you know? It’s very frequent for me to work with students who have no interest in proving that triangles are congruent to one another and understanding the sufficiency conditions for different categories of quadrilaterals, but if I can say well you know what, those of you who are heading into a trade, this trigonometry is going to be so important to you, or those of you who are trying to design something in textiles because you’re really interested in that design aspect of things, I can say these will be the bits of financial mathematics, or you know, proportion and ratios and measurement that are going to be important to you doing your job effectively and being a great craftsman or craftswoman. All those kinds of things happen as a result of knowing our students, and knowing them outside the context of the classroom. So I think those things are really important.
 
I also reckon that the assessment that I do with students in formal structures, their big exams, their big ticket assessment tasks twice a year, and also the regular little tasks are so vitally important. So I think that I gain a lot out of making sure students are regularly being exposed to, okay, this is what it means to articulate my understanding and express it. Yes, I get it, I know how to answer the question, but can I explain it to others? So putting students in that position of being almost a peer teacher helps me as I watch them actually teach through something, that gives me a real sense of ‘do you actually understand this or not?’ I often tell kids there’s understanding to answer the question, to get to the right number at the end, and then there’s real understanding of what this is about and why it actually works, and that kind of understanding is not often revealed, or you know, unmasked as being you know, fake, until you put a student in the position of, hey, can you get up, show me this on the white board, or get into pairs, get into groups of four, explain that question, you can prepare, take as much time as you like to wrap your head around the question, but then I want you to stand there, be ready to take questions, be ready to be scrutinised in terms of your understanding. I feel like those are the most effective mechanisms for assessments that I can use in my classroom from day to day.