Alumnos con estilo de aprendizaje pragmático

Eye-movements have been increasingly used as a measure of overt attention while cognitively processing complex tasks (Rayner, 2009) because the rapidity of eye-movements matches the rapidity of cognitive processing (Just & Carpenter, 1976). As stated by Just and Carpenter’s (1980) eye-mind assumption, a word is being processed as long as the eye remains fixated on it. Accordingly, time spent fixating on that word directly indicates the duration spent processing it. The eye-mind assumption postulates that the locus of the eye gaze is strictly tied to what is being cognitively processed (Just & Carpenter, 1976). When a student is engaged in

a complex task such as reading or problem solving, then his/her attention and eye gaze are inseparable (Rayner, 2009).

Although eye-tracking methodology has been implemented mainly in research on reading and text comprehension (see Rayner, 1998; Rayner, 2009 for reviews), its use is becoming more popular in various domains including: mathematics problem solving (Beitlich, Obersteiner, & Reiss, 2015; Hegarty et al., 1992; Hegarty, Mayer, & Monk, 1995) and proof comprehension and validation (e.g., Hodds et al., 2014; Inglis & Alcock, 2012), science problem solving (e.g., Tsai et al., 2012), multimedia learning (e.g., Canham & Hegarty, 2010; Meyer et al., 2010), and more recently to infer mindful cognitive processing by students processing received PF (Bolzer et al., 2015). The proof validation and proof comprehension studies suggested that undergraduate students focus on surface features when validating proofs (Inglis & Alcock, 2012) and that short self-explanation training could lead students to process the proofs more deeply when reading for comprehension (Hodds et al., 2014). However, to date no study to our knowledge employed an eye-tracking methodology to examine PF providers’ cognitive processing while providing PF on peer solutions to complex tasks like geometry proofs, and to explore whether specific types of PF are associated with gazing at specific components of geometry proofs (i.e., text or figure). There is a need to explore preservice mathematics teachers cognitive processing while providing PF on peer solutions to geometry proofs, to provide better support for them during PF activities and to develop better PF training for preservice mathematics teachers. Various eye-tracking measures can be used to infer cognitive processing, and they are described next.

3.1.5.1. Eye-tracking measures and terminology

The two main measures of eye-movement are fixations and saccades. Fixations are defined as time periods (200-300 milliseconds) during which the eye remains relatively still while information is being processed from the visual field (Rayner, 1998; Rayner, 2009).

Saccades are the rapid eye-movements, with high velocity (up to 500° per second), during which no processing takes place as the position of the eye-center (i.e., fovea) is shifted to a new location within the visual field (Rayner, 1998; Hyönä, 2010). The unit of analysis used to relate eye-movement measures to cognitive processing differs depending on the theory behind the analysis (Just & Carpenter, 1976). The unit of analysis could be a single word or a larger block that is called an Area Of Interest (AOI) (Holmqvist, Nyström, Andersson, Dewhurst, Jarodzka, & De Weijer, 2011).

Different types of measures can be computed from the two main eye-movement measurements including, number of fixations, mean fixation duration, mean number of fixations, gaze duration, and total fixation time (Rayner, Chace, Slattery, & Ashby, 2006). Some of these terms (e.g., gaze duration vs. fixation duration) are used interchangeably due to their conceptual similarities (Holmqvist et al., 2011). Two famous measures are fixation duration, which is defined as the time duration during which an eye remains still, and dwell time (also known as gaze or glance duration) being defined as the time duration spent on an AOI from entry to exit of an AOI (Holmqvist et al., 2011). The term dwell time is also often confused with total dwell time which is the sum of all dwell times on a specific AOI accumulated over a trail (Holmqvist et al., 2011).

There is no agreement on the best measure to use for analyzing eye-tracking data in general because that depends on the research question and the size of AOI being used. Whereas fixation duration is very informative about the processing of a single-word, it might not be an optimal measure for larger AOIs that include words processed differently (Rayner, 1998). Furthermore, although total dwell time is a useful measure because it shows where students allocate their attention throughout the learning task, it does not provide information about moment-to-moment processing (Hyönä, 2010). When the unit of analysis is larger than a single word, total dwell time is usually used as a measure of eye-movement (Rayner et al., 2006). Due

to the individual variation in most eye-tracking measures (Holmqvist et al., 2011), some studies use proportional measures in their investigations to account for this variation (e.g., Bednarik & Tukiainen, 2008; Hu, Wang, Fu, Quinn, & Lee, 2014; Yi, Liu, Li, Fan, Haung, & Gao, 2012).

3.1.5.2. Factors influencing eye-movements

Eye-movements differ depending on the nature of the encountered task, with complex tasks requiring more or longer fixations (e.g., silent vs. loud reading, or simple vs. complex problem solving; Rayner, 1998). This also applies to different parts of the same problem. For instance, the earlier context in a text influences how long readers look at later parts of the text (Rayner, 1998). Mathematics problem solving studies (e.g., Hegarty et al., 1992) also showed that inconsistent arithmetic problems resulted in longer fixations. Another factor that can influence how students distribute their attention on different components of the learning task is domain knowledge. Some mathematics and science problem solving studies showed that successful problem solvers focus more on the task-relevant information than the task-irrelevant information compared to unsuccessful problem solvers (e.g., Hegarty et al., 1995; Tsai et al., 2012), and that acquiring domain knowledge through instruction makes students focus more on task-relevant information and less on task-irrelevant information (Canham & Hegarty, 2010). Consequently, students’ domain knowledge should be taken into account when eye- movements are being used as a measure of cognitive processing.

Despite the immediacy of eye-tracking measures, which makes them very essential to measure different cognitive processes (Just & Carpenter, 1976), this methodology has its limitations. Interpreting eye-tracking data requires a large degree of inference that must be backed up with clear and specific theoretical assumptions (Just & Carpenter, 1976) because this type of data does not provide any information about the success or failure of processing (Hyönä, 2010). For example, a student might spend a long time reading a proof without being able to understand it fully. This issue creates a need for complementary measures such as

performance, or cued-retrospective reporting (Hyönä, 2010; Van Gog, Paas, & Van Merriёnboer, 2005).