What assumptions do you hold about mathematics? As people who teach mathematics, have you spent time thinking, talking, and challenging what mathematics might be? There are three readings for you in the next section of our course that deal with the nature of mathematics.
First Reading:
What is the impact that traditional definitions have on us as learners? Please read "The Theory of Embodied Mathematics" from the book Where Mathematics Comes From by Lakoff and Nunez.
Using Lakoff and Nunez's notion of the mythology that surrounds math, (what they refer to as 'the romance of mathematics') it is important to look at traditional notions of mathematics and bump it up against a reconceptualized view.
Figuring out our own positioning towards mathematics is critical to becoming a reflective teacher of mathematics. What part of the romance do you believe? How does what you think about mathematics affect how you teach it?
Second Reading:
Reuben Hersh is an American mathematician who has written extensively about mathematics. He takes up his ideas from What is Mathematics, Really? in the following interview that I would like you to read: What Kind of Thing Is a Number? A Talk with Reuben Hersh Be sure to click on THE TALK at the bottom of the page to read the entire interview. He delves into his view of mathematics, the teaching of mathematics, and how our stance towards mathematics impacts how and what we teach.
Third Reading:
Your third reading is by Brent Davis, Professor and Research Chair for Mathematics Education, currently at the University of Calgary. His article Davis, B. (1995). Why teach mathematics? Mathematics education and enactivist theory. For the Learning of Mathematics, 15(2), 2-8 can be downloaded but cannot be linked directly. Please go to this link that contains a list of articles to be downloaded as PDFs: You will find the article second from the bottom of the page. Click on 1995 07 FLM.pdf to download the article.
Your next critical reflection shall focus on the nature of mathematics and why we should teach it. What, for you, are the big ideas? How, if at all, have your beliefs about mathematics shifted? What is it that you will need to know, to read, to figure out, to study to gain a better understanding of the nature of mathematics as something that might be a living discipline, a human activity?
