There has long been dispute in mathematics between the drill and practice orientation that focuses primarily on memorizing mathematics as meaningless rote algorithms and the approach based on understanding and making creative use of mathematics. This 25-chapter book, based on a 7-year study at the University of Illinois, seeks to explain and…

In this paper, we draw on a 16-month study funded by the Learning and Teaching Support Network in the UK and entitled "Mathematicians as Educational Co-Researchers." The study's aims were two-fold. Primarily we intended to explore mathematicians' reflections on issues identified in the literature as highly topical in the area of teaching…

This is volume 4 of the series of translations of books from the Soviet literature on research in the psychology of mathematics instruction and on teaching methods influenced by the research. The introduction to this English language translation highlights the fact that significant advances have been made in the understanding of both the…