I have recently finished reading Jo Boaler's Mathematical Mindsets.
While some of the things in the book I disagree with (Einstein was not illiterate before the age of nine - he was accepted into the prestigious Luitpold-Gymnasium when he was 9), there are many that seem to be in agreement with other works.
This book doesn't just bring about ideas of how should students approach mathematics, but what is mathematics for these days? Why teach mathematics? While we can be sure that traditional teaching of speed and accuracy was important in the past, we now have computers that can calculate faster and more accurately than any human ever could. Instead, we need mathematics to learn what to tell the computers. To think abstractly, creatively, communicatively.
I've been attempting this ideas in my classes since the beginning of the year, but this book has given me some really great ideas for bringing in multiple areas of math.
One thing I have struggled with is that mentors have told us students need to think deeper about mathematics. To be honest, I didn't actually know what this meant. Did it mean that if they have mastered factorisation of polynomials, then they move onto the quadratic formula? It turns out the answer is no. This book gives really great ideas to get the deeper thinking.
Unfortunately, many of the students I teach (especially those in the extension class) are very resistant to deep thinking. They are in the extension class because they have been told they are smart. They became 'smart' by practicing workbook problems and getting high grades. Not by thinking about different processes or communicating their thoughts. I have always seen this as a terrible mindset. It fixes the student in their ways and does not produce any form of growth.
Interestingly, one of the students has said that she doesn't need mathematics because she is going to be an actor, so she just wants to get through to gain the marks. After showing the class the skills required in the real world, they all match to being an actor but she is insistent on keeping her fixed mindset instead of using the skills I am attempting to teach her that will actually be used in her chosen career. I don't get it.. Maybe next year will work out better..