Editor’s Section Commentary

I begin this Part C of the book with an account of the kind of mathematics education that I received in my early years. The teaching methods focused on the reproduction of preformatted answers to textbook questions. Teachers never appeared to be interested in asking whether I, as my peers, were really engaging and identifying a problematic in the way I had done during my nocturnal efforts in mental calculations and the algebraic understanding that I developed. However, cultural-historical activity theory suggests that it is out of a concern with real problematic issue that students orient toward a motive, in the pursuit of which they will do what is required to enlarge their room to maneuver, that is, they engage in learning loops that expand their possibilities of acting. The object/motive does not and perhaps should not have to be mathematics itself, to which students will inherently turn when they can see in it something that will allow them to better work toward their chosen object/motive.