Two-digit number processing: holistic,decomposed or hybrid? A computational modelling approach

Currently, there are three competing theoretical accounts concerning the nature of two-digit number magnitude representation: a holistic, a strictly decomposed, and a hybrid model. Observation of the unit-decade compatibility effect (Nuerk et al. in Cognition 82:B25–B33, 2001) challenged the view of two-digit number magnitude to be represented as one integrated entity. However, at the moment there is no study distinguishing between the decomposed and the hybrid model. The present study addressed this issue using a computational modelling approach. Three network models complying with the constraints of all three theoretical models were programmed and trained on two-digit number comparison. Models were compared as to how well they accounted for empirical effects in the most parsimonious way. Generally, this evaluation indicated that the empirical data were simulated best by the strictly decomposed model. Implications of these results for our understanding of the nature of human number magnitude representation are discussed.     

Reciprocal relations between cognitive neuroscience and formal cognitive models: opposites attract?

Cognitive neuroscientists study how the brain implements particular cognitive processes such as perception, learning, and decision-making. Traditional approaches in which experiments are designed to target a specific cognitive process have been supplemented by two recent innovations. First, formal cognitive models can decompose observed behavioral data into multiple latent cognitive processes, allowing brain measurements to be associated with a particular cognitive process more precisely and more confidently. Second, cognitive neuroscience can provide additional data to inform the development of formal cognitive models, providing greater constraint than behavioral data alone. We argue that these fields are mutually dependent; not only can models guide neuroscientific endeavors, but understanding neural mechanisms can provide key insights into formal models of cognition.     

Binding targets’ responses to distractors’ locations: Distractor response bindings in a location-priming task

Responses to target stimuli can be encoded together with distracting objects accompanying these targets into a single stimulus-response episode or a single event file. Repeating any object of such an episode can trigger the response encoded in this episode. Hence, repeating a distractor may retrieve the response given to the target that was accompanied by this distractor. In the present experiments, we analyzed whether the binding of target responses to the distractor can be generalized even to the location of a distractor. In two experiments, we used a location-based prime-probe task and found that repeating the location of a distractor triggered the response to the target that had previously been accompanied by a distractor in the repeated location, even if the identity of the distractor changed from the prime to the probe.     

When knowledge matters—differential effects of available knowledge in standard and basic anchoring tasks

The present research examines whether anchoring effects—the assimilation of a numeric estimate towards a previously considered standard—depend on judges' available knowledge in the target domain. Based on previous research, I distinguish two types of anchoring effects. Standard anchoring is obtained if judges are explicitly asked to compare the anchor to the target. Basic anchoring results if the accessibility of the anchor is increased prior to judgments about the target. I expected that only basic but not standard anchoring is reduced by providing judges with judgment‐relevant knowledge. Using a standard versus basic anchoring paradigm, 112 participants were confronted with a high versus low anchor before estimating the average price of a German midsize car. Prior to this task, participants were provided with information about prices of cars (relevant knowledge) versus kitchens (irrelevant knowledge). Results demonstrate that this knowledge only influenced the magnitude of basic but not standard anchoring effects. This finding demonstrates that knowledge has differential effects in different types of anchoring. Copyright © 2007 John Wiley & Sons, Ltd.     

Seeing oneself in one’s choices: Construal level and self-pertinence of electoral and consumer decisions

Building on previous research examining the implications for self-regulation and decision making of construing action at varying levels of abstraction, the authors proposed that construing action in terms of its abstract purposes facilitates orienting one’s decisions toward the standards, characteristics, and goals that define one’s desired self-concept. Consistent with this proposal, desiring for oneself a political candidate’s personal qualities predicted evaluating favorably (in Study 1) and voting for (in Study 2) that candidate to a greater extent among participants focused on the distal future (and presumably construing action at a relatively high-level of abstraction) than the proximal future (and presumably construing action at a relatively low-level of abstraction). Moreover, individuals chronically construing action in high-level terms responded more favorably to advertisements appealing to their desired self-concept (in Study 3) than to product quality. These findings’ implications for decision making are discussed.     

Sex differences in the association of math achievement with visual-spatial and verbal working memory: Does the type of math test matter?

Previous research on sex differences in mathematical achievement shows mixed findings, which have been argued to depend on types of math tests used and the type of solution strategies (i.e., verbal versus visual-spatial) these tests evoke. The current study evaluated sex differences in (a) performance (development) on two types of math tests in primary schools and (b) the predictive value of verbal and visual-spatial working memory on math achievement. Children (N = 3175) from grades 2 through five participated. Visual-spatial and verbal working memory were assessed using online computerized tasks. Math performance was assessed five times during two school years using a speeded arithmetic test (math fluency) and a word problem test (math problem solving). Results from Multilevel Multigroup Latent Growth Modeling, showed that sex differences in level and growth of math performance were mixed and very small. Sex differences in the predictive value of verbal and visual-spatial working memory for math performance suggested that boys seemed to rely more on verbal strategies than girls. Explanations focus on cognitive and emotional factors and how these may interact to possibly amplify sex differences as children grow older.     

Methodological and empirical issues when dissociating cue-related from task-related processes in the explicit task-cuing procedure

In the explicit cuing version of the task-switching paradigm, each individual task is indicated by a unique task cue. Consequently, a task switch is accompanied by a cue switch. Recently, it has been proposed that priming of cue encoding contributes to the empirically observed switch costs. This proposal was experimentally supported by using a 2:1 mapping of cues to tasks, so that a cue switch does not necessarily imply a task switch. The results indeed suggested a substantial contribution of “cue-switch costs” to task-switch costs. Here we argue that the 2:1 mapping potentially leads to an underestimation of “pure” task-switch costs. To support this argument, we report the results of a new study in which we used “transition cues” that indicate the identity of the current task based on the identity of the preceding task. This new type of cue allows a full factorial manipulation of cue switches and task switches because it includes the condition in which a cue repetition can also indicate a task switch (i.e., when the “switch” cue is repeated). We discuss the methodological implications and argue that the present approach has merits relative to the previously used 2:1 mapping of cues to tasks.     

On the language specificity of basic number processing: transcoding in a language with inversion and its relation to working memory capacity

Transcoding Arabic numbers from and into verbal number words is one of the most basic number processing tasks commonly used to index the verbal representation of numbers. The inversion property, which is an important feature of some number word systems (e.g., German einundzwanzig [one and twenty]), might represent a major difficulty in transcoding and a challenge to current transcoding models. The mastery of inversion, and of transcoding in general, might be related to nonnumerical factors such as working memory resources given that different elements and their sequence need to be memorized and manipulated. In this study, transcoding skills and different working memory components in Austrian (German-speaking) 7-year-olds were assessed. We observed that inversion poses a major problem in transcoding for German-speaking children. In addition, different components of working memory skills were differentially correlated with particular transcoding error types. We discuss how current transcoding models could account for these results and how they might need to be adapted to accommodate inversion properties and their relation to different working memory components.