Abstract

Previous research has reported on students' uses of mathematics textbooks at pre-university and undergraduate levels. Also, some research has been done on textbooks as standalone objects, looking at their format and didactic and mathematical discourses. However, very few researchers have investigated instructors' uses of textbooks. In this thesis we do so at the graduate level; in particular, we investigate one instructor's account of his use of a textbook and two mathematics professors' views of which textbook they would use and how if they were to teach a Measure Theory course. We chose measure theory because of its important role as a foundation for much of what is modern analysis, a branch of mathematics with many applications such as electronics, signal processing and even probability and statistics. We chose the graduate level because textbooks we assume them to have an important role in the teaching and learning of graduate mathematics courses; this is based on our own classroom experiences as little research has been done so far in this direction. In the first part of our research, we draw on Eco's notion of model reader and characterized the target instructor audience of four measure theory textbooks. We also analyzed the mathematical knowledge that these textbooks contain in light of a review of the history of the development of measure theory. Finally, we analyzed the textbooks as teaching instruments from the perspective of Sierpinska's notion of apodictic vs. liberal textbooks. In the second part of our research, we interviewed three university professors in order to understand their beliefs about textbooks, mathematics and learning. In particular, we sketched different types of instructors' profiles and have been able to match them with textbooks whose use in their teaching activity would likely be most effective.