Reading mathematics: a textbook approach

Mathematics textbooks have always been a staple of mathematics classrooms around the world. Furthermore, despite the digital age and the ever-increasing amount of online resources, mathematical textbooks have endured. In recent years, research into mathematics textbooks has increased to reflect this; however, research into how students use their mathematics textbooks remains limited.

In this thesis, I investigate how students use their mathematics textbooks, situating this with the practical aspect of textbook research, i.e., how are textbooks designed to be read? My PhD studentship involved a collaboration with Oxford University Press so practical considerations for my research are woven throughout the thesis, including the use of real-world materials. As such, my findings contribute to conversations in the publishing world as well as the research literature.

I split the thesis into two parts. In the first part, I interviewed students and textbook authors to understand how students use their textbooks and how the publishing company expects them to. Illuminating this relationship enabled me to review the efficacy of students’ textbook use and whether they used their textbooks as intended. I found that some textbook features might not encourage beneficial learning strategies and that more students used the exposition than expected. As such, I focused on the exposition in the second part of this thesis.

Indeed, I started the second part by investigating the characteristics of expositions using comparative judgement. Not only did I find that comparative judgement appears to be an appropriate measure of exposition quality, but I found several characteristics of mathematical texts which appear to affect its quality. I followed these findings up with two final empirical studies, using eyetracking technology and comparative judgement again. I found that presenting text or pictures in the margin affects how students read them, and that exposition quality could be improved by highlighting key text. My findings identify various avenues of future work. In particular, the importance of finding a relatively straightforward and low-cost approach to support publishers and help improve mathematical textbook expositions using research-based evidence.