This paper explores different ways in which mathematics students read a section of a prescribed mathematics textbook. In this case, the students are mathematics teachers learning new mathematics in a self-study calculus course. Two students were video-taped, while they studied a prescribed portion of the textbook. The reading styles of these two empirical readers are analysed according to how they exploit opportunities for learning from the textbook, how they inject productive knowledge such as prior knowledge, from outside the textbook, into their reading and how they make connections between different objects in the textbook. Their reading styles are compared to that of a hypothetical 'implied' reader. This implied reader engages with the text in a fruitful manner. The analyses are used as a platform from which to highlight productive and less productive ways for reading to learn mathematics.