An Axiomatic Approach To Teaching and Learning
I wrote this book because I needed my own thoughts on mathematics teaching and learning to be “in the world”. And now I have these 30,000 words, stating that which I believe. I say this not because I think you should read it – you can read it if you like, or not. I mention the book because I decided to examine what I believe about mathematics teaching and learning, right down to the core, through a personal set of axioms about teaching and learning.
I do a lot of “fanboying” about Dr. Eugenia Cheng, and her books. Her new book, on logic, is terrific. I recommend it to readers, for your holidays. It teaches us how to construct better arguments. We are not all capable of pure logic, and emotion always plays into human arguments. It is best to just admit that. She deftly examines a number of social justice issues to show where false equivalences occur. Her section on privilege dazzles. It is remarkable to me that she is using her obscure field, category theory, to make these points. Category theory is the “math of math”, and is really about arrows pointing between categories. Sounds simple, but it is really not so – she is elaborating really complex relationships between “things”, and in the case of pure category theory, relationships between sets, mathematical objects, and even different branches of mathematics.
A point Dr. Cheng makes is that axioms, even in mathematics, come from somewhere. We have to start with something – some assumptions, some starting point. A lot of arguments about teaching and learning come down to not going all the way back to the beginning, to examining our unshakeable core beliefs.
You probably proceed from different axioms than your classroom neighbour. But what are they? Take a few minutes to write down a few. Many are deeply woven into the fabric of who you are. Some could change, given new information, for example, research about teaching and learning.
As Parker Posey said, “we teach who we are”. So who are you between those 4 walls?
The answer is axiomatic – you might just not know it yet.
Written by Matthew Oldridge (@MatthewOldridge)