Eye fixation behaviour in the number bisection task: Evidence for temporal specificity

Together with magnitude representations, knowledge about multiplicativity and parity contributes to numerical problem solving. In the present study, we used eye tracking to document how and when multiplicativity and parity are recruited in the number bisection task. Fourteen healthy adults evaluated whether the central number of a triplet (e.g., 21_24_27) corresponds to the arithmetic integer mean of the interval defined by the two outer numbers. We observed multiplicativity to specifically affect gaze duration on numbers, indicating that the information of multiplicative relatedness is activated at early processing stages. In contrast, parity only affected total reading time, suggesting involvement in later processing stages. We conclude that different representational features of numbers are available and integrated at different processing stages within the same task and outline a processing model for these temporal dynamics of numerical cognition.     

Sequential or parallel decomposed processing of two-digit numbers? Evidence from eye-tracking

While reaction time data have shown that decomposed processing of two-digit numbers occurs, there is little evidence about how decomposed processing functions. Poltrock and Schwartz (1984) argued that multi-digit numbers are compared in a sequential digit-by-digit fashion starting at the leftmost digit pair. In contrast, Nuerk and Willmes (2005) favoured parallel processing of the digits constituting a number. These models (i.e., sequential decomposition, parallel decomposition) make different predictions regarding the fixation pattern in a two-digit number magnitude comparison task and can therefore be differentiated by eye fixation data. We tested these models by evaluating participants' eye fixation behaviour while selecting the larger of two numbers. The stimulus set consisted of within-decade comparisons (e.g., 53_57) and between-decade comparisons (e.g., 42_57). The between-decade comparisons were further divided into compatible and incompatible trials (cf. Nuerk, Weger, & Willmes, 2001) and trials with different decade and unit distances. The observed fixation pattern implies that the comparison of two-digit numbers is not executed by sequentially comparing decade and unit digits as proposed by Poltrock and Schwartz (1984) but rather in a decomposed but parallel fashion. Moreover, the present fixation data provide first evidence that digit processing in multi-digit numbers is not a pure bottom-up effect, but is also influenced by top-down factors. Finally, implications for multi-digit number processing beyond the range of two-digit numbers are discussed.     

Is there parallel and independent hemispheric processing of intonational and phonetic components of dichotic speech stimuli?

The possibility of hemisphere interaction in the processing of spoken language was studied in two dichotic listening experiments. The stimulus material consisted of six CV syllable triplets each spoken with each one of six intonation contours. In Experiment I, 15 aphasic patients, 8 patients with unilateral right hemisphere lesions, and 10 normal controls were asked to identify the four components of a dichotic item from a multiple-choice (MC) set comprising all possible CV triplets and intonation contours. In Experiment II, 30 normal subjects were required to identify either the right or left ear stimulus alone from an MC set comprising the right and left ear stimulus together with the two wrong combinations of right ear CV triplet with left ear intonation and vice versa. It is concluded from the results that the left hemisphere is capable of processing both phonetic and intonational information and that there is neither the necessity nor the tendency for right hemisphere participation in the perception of spoken language.     

Energetic effects of stimulus intensity on prolonged simple reaction-time performance

The efficiency of cognition is modulated by energetic factors like effort, fatigue or circadian variation, which affect even the most basic cognitive operations. For instance, speeded detection in simple reaction-time (SRT) tasks usually slows down over time. The literature suggests that either mindlessness due to routinization or mental fatigue due to attentional resource depletion might underlie this decrement. We tested these assumptions in three 25-min visual SRT tasks using easy-to-detect high-intensity and hard-to-detect low-intensity stimuli presented in both blocked and mixed fashion. Mindlessness theory predicts that less monotonous stimulation (i.e. the mixed presentation) would mitigate the time-related decrement for high- and low-intensity stimuli alike, whereas resource-depletion theory predicts opposite effects of mixed presentation on high- versus low-intensity stimuli. Indeed, stimulus intensity and presentation mode cross-interacted significantly, indicating that the performance decline was steeper for high-intensity stimuli but less steep for low-intensity stimuli during mixed compared to blocked presentation, respectively. These results strongly suggest that the time-related efficiency decrement during prolonged SRT performance is related to accumulating mental fatigue. A conjecture is put forward that explains both resource depletion and mindlessness from the perspective of self-regulation. Our study underscores the need to incorporate energetic factors into models of cognition to facilitate their translation into real-world applications.     

The role of crossmodal competition and dimensional overlap in crossmodal attention switching

Crossmodal selective attention was investigated in a cued task switching paradigm using bimodal visual and auditory stimulation. A cue indicated the imperative modality. Three levels of spatial S–R associations were established following perceptual (location), structural (numerical), and conceptual (verbal) set-level compatibility. In Experiment 1, participants switched attention between the auditory and visual modality either with a spatial-location or spatial-numerical stimulus set. In the spatial-location set, participants performed a localization judgment on left vs. right presented stimuli, whereas the spatial-numerical set required a magnitude judgment about a visually or auditorily presented number word. Single-modality blocks with unimodal stimuli were included as a control condition. In Experiment 2, the spatial-numerical stimulus set was replaced by a spatial-verbal stimulus set using direction words (e.g., “left”). RT data showed modality switch costs, which were asymmetric across modalities in the spatial-numerical and spatial-verbal stimulus set (i.e., larger for auditory than for visual stimuli), and congruency effects, which were asymmetric primarily in the spatial-location stimulus set (i.e., larger for auditory than for visual stimuli). This pattern of effects suggests task-dependent visual dominance.     

Modality-specific preparatory influences on the flexibility of cognitive control in task switching

In the current study, we addressed modality-specificity of the flexibility of cognitive control. We compared performance in single-task and mixed-tasks blocks between blocked auditory and visual stimuli assessing alternation costs (single vs. mixed). Mixed blocks comprised task switches only. The tasks consisted of numerical parity, magnitude, and distance judgments about numbers between one and nine without five. A cue indicated the relevant task. The cue–stimulus interval was varied (short vs. long interval) to examine preparation effects. The results indicated higher response times (RTs) and error rates (ERs) in mixed- vs. single-tasks blocks. The alternation costs in ERs were larger for auditory compared to visual stimulus presentation. Moreover, the reduction of RT alternation costs based on increased preparation time was more pronounced for the auditory modality compared to the visual modality. These results suggest a modality-specific influence on processes involved in maintaining and updating task sets in working memory.     

On the perceptual generality of the unit-decade compatibility effect

Number magnitude is assumed to be holistically represented along a single mental number line. Recently, we have observed a unit-decade-compatibility effect which is inconsistent with that assumption (Nuerk, Weger, & Willmes, 2001). In two-digit Arabic number comparison, we have demonstrated that compatible comparisons in which separate decade and unit comparisons lead to the same decision (32_47, 3 < 4 and 2 < 7) were faster than incompatible trials (37_52, 3 < 5, but 7 > 2). Because overall distance was matched, a holistic model could not account for the compatibility effect. However, one could argue that the compatibility effect was due to the specific vertical perceptual arrangement of the two-digit numbers in Nuerk et al.'s (2001) experiment where the decade digits and unit digits were presented column-wise above each other. To examine this objection, we studied the perceptual generality of the compatibility effect with diagonal presentation. We replicated the compatibility effect with diagonal presentation. It is concluded that the compatibility effect is not due to encoding characteristics imposed by the perceptual setting of the original experiment. In particular, the assumption of an overall analog magnitude representation for two-digit numbers is not consistent with these data.     

Magnitude representation in sequential comparison of two-digit numbers is not holistic either

There is accumulating evidence suggesting that two-digit number magnitude is represented in a decomposed fashion into tens and units rather than holistically as one integrated entity. However, recently, it has been claimed that this property does not hold for the case when two to-be-compared numbers are presented sequentially. In the present study, we pursued this issue in two experiments by evaluating perceptual as well as strategic aspects arising for sequential stimulus presentation in a magnitude comparison task. We observed reliable unit-decade compatibility effects indicating decomposed processing of tens and units in a magnitude comparison task with sequential presentation of the to-be-compared numbers. In particular, we found that both confounding low-level perceptual features and stimulus set characteristics determining cue validity of the units influenced the compatibility effect. Taken together, our results clearly indicate that decomposed representations of tens and units seem to be a general characteristic of multi-digit number magnitude processing, rather than an exception occurring under very specific conditions only. Implications of these results for the understanding of number magnitude representations are discussed.