Skimming: a response to Weber and Mejia-Ramos

We recently reported a study in which undergraduate students and research mathematicians were asked to read and validate purported proofs (Inglis & Alcock, 2012). In our eye-movement data, we found no evidence of the initial skimming strategy hypothesized by Weber (2008). Weber and Mejía-Ramos (2013) argued that this was due to a flawed analysis of eye-movement data and that a more fine-grained analysis led to the opposite conclusion. Here we demonstrate that this is not the case, and show that their analysis is based on an invalid assumption. Weber and Mejía-Ramos (2013) suggested that our analysis was flawed because, after calculating what proportion of reading time a mathematician took to reach the last line of a proof (which they called an Initial Reading [IR] ratio), we took means across different tasks. Considering means, they argued, obscures reading strategy variation. Clearly, this is true in principle, and at the end of this response, we discuss what exactly is obscured in our data. First, however, we respond to Weber and Mejía-Ramos’s more specific criticisms.