Extending the reach of mousetracking in numerical cognition: a comment on Fischer and Hartmann (2014)

In a recent article, Fischer and Hartmann (2014) present a brief methodological review of the use of computer mousetracking in analyzing the processes involved in numerical cognition. Most certainly this review is a welcome addition to the mathematical cognition literature, especially in light of recent studies that have used the technique to study numerical decision processes. After presenting a general overview of the computer mousetracking method, Fischer and Hartmann make several recommendations (e.g., reporting exact mouse settings, constraining wrist movement, etc.) that will surely help to facilitate comparison and interpretation across a variety of studies as we continue to advance our knowledge of the dynamics of numerical processing. The purpose of the present commentary is not to be critical; rather, we hope that this commentary will be seen as complementary to (as well as complimentary of) the recommendations of Fischer and Hartmann (2014). We feel that their review is timely and informative. However, we also feel that some of the issues raised by Fischer and Hartmann warrant further discussion. At its core, computer mousetracking is used to construct a temporally rich set of data during decision-making that allows one to conduct a more fine-grained analysis than end-state performance measures alone (such as RT and/or error rates). Most of the recent studies that use this technique to study numerical processes specifically look for the dynamic signature of increased trajectory curvature in certain comparison conditions (e.g., Santens et al., 2011; Faulkenberry, 2014). This signature has been used as evidence for parallel consideration of response options. For example, Santens et al. (2011) measured trajectories in a numerical comparison task in which participants were asked to compare a presented number to the fixed standard 5. As the distance from the stimulus number to 5 decreased, trajectories became more differentially curved, revealing a dynamic interpretation of the numerical distance effect (Moyer and Landauer, 1967). Santens et al. interpreted their results to be in line with a competitionbased model of numerical representations. Faulkenberry (2014) extended this result to a numerical odd/even task and showed (via distributional analyses of the response trajectories) that such differential curvatures result from a graded competition between parallel and partially-active representations, and not from averaging across widely different trajectory types. It is important to note that neither of these results could easily have been obtained via traditional cognitive processing measures. It is on this note that we feel the review of Fischer and Hartmann (2014) unintentionally limits the utility of computer mousetracking to only providing evidence of continuous competition in numerical processing. On the contrary, several recent studies have used the technique to analyze the selective influence of various stimulus factors over the time course of a response. For example, Freeman and Ambady (2011) showed that trajectory deviations happen earlier for inconsistencies in pigmentation cues vs. shape cues in face recognition. Similarly, (Freeman et al., 2013) demonstrated earlier deviations for Chinese participants vs. American participants when processing faces with inconsistent contextual cues. While there are not yet any published studies in the domain of numerical cognition that look specifically at when trajectory deviations happen, Faulkenberry and Montgomery (2012) showed that in fraction processing, trajectory deviations which stem from components happen earlier than deviations which stem from holistic magnitude processing. The basic logic of these studies is that with an underlying mapping between response trajectories and perceptual/cognitive processes, any observed difference in the onset of motor deviations necessarily reflects a difference in the time course of the underlying perceptual and/or cognitive processes. As such, these types of manipulations hold promise for number researchers to tease apart the predictions from competing models of numerical processing. There is one claim from which we hold a divergent opinion compared to Fischer and Hartmann (2014). Specifically, Fischer and Hartmann propose that competitive