Representation Of Negative Numbers Research Articles

Spatial Representation of Negative Numbers Induces Spatial Shifts of Attention

The SNARC Effect (Dehaene, Bossini, Giraux, 1993; Dehaene, Dupoux, Mehler,1990) and Spatial Shifts of Attention (Fischer, Castel, Dodd, Pratt, 2003; Casarotti, Michielin, Zorzi, Umilta, 2007) indicate that there are tight connections between number processing and representation and space. These discoveries, however, are only regarded with positive numbers presently, there are few effective experimental studies or evidence on the mechanism of the processing and representation of negative numbers with 0, or on the connections between negative numbers and space. For a lack of effective experimental methodology (Fischer, Rottmann, 2005; Nuerk, Iversen, Willmes, 2005; Fischer, 2003), it is less than possible to set up research to investigate the secrets behind the processing and representation of negative numbers with 0. As a result, there’s no persuasive answer to the questions about whether there are connections between negative numbers and space; or whether the low level processing of negative numbers with 0 can induce Spatial Shifts of Attention. The present study, including 3 effective experiments by using stimuli detection task with number cues, was to investigate the connections between negative numbers with 0 and space, and the mechanism of the processing and representation of negative numbers and 0, through observing if the low level processing of negative numbers can induce spatial shifts of attention, and whether it depends upon their magnitude or absolute value. Experiment 1 was a within-subject design of 2 (target side: left and right) × 2 (magnitude of cueing number: small and large) × 6 (variable delays: 50 ms, 100 ms, 200 ms, 300 ms, 400ms and 500 ms). Results from Experiment 1, in which only negative numbers were included, showed that left (right) targets were detected significantly faster than right (left) ones when numbers with small (large) absolute value were preceded, revealing spatial shifts of attention depending upon absolute value of negative numbers. Experiment 2 was a 2 (target side: left, right) × 5 (number magnitude: quite small, small, medium, large, quite large) × 6 (variable delays: 50 ms, 100 ms, 200 ms, 300 ms, 400 ms, or 500 ms) within-subject design, in which both positive and negative numbers, and zero were mixed as cues, showed that left (right) targets were detected significantly faster than right (left) ones when numbers with small (large) magnitude were preceded, revealing spatial shifts of attention depending upon their magnitude, therefore, there is a mental number line extending to the left side of zero, and representing numbers depending upon number magnitude. Experiment 3 was a 2 (target side: left, right) × 3 (number magnitude: small, large, 0) × 6 (variable delays: 50ms, 100ms, 200ms, 300ms, 400ms, or 500ms) within-subject design, in which only negative numbers with 0 were designed as effective cues, although still cued by the whole mix of all negative, 0 and positive numbers as numbers preceding the targets, subjects were only requested to respond to targets preceded by effective cues (negative numbers and 0), while not respond to targets preceded by non-effective cues (positive numbers). Consistently, spatial shifts of attention depending upon number magnitude were successfully induced by processing effective cueing numbers (-8, -9, -1, -2,0). By ensuring that the minus signs were processed with the numbers holistically, it can be put that there can be a low-level processing of negative number magnitude to some extent of automation. As a whole, the present study suggested that low level processing of negative numbers as cues can induce spatial shifts of attention, whether it depends upon their magnitude or absolute value, however, seems to depend upon the task requirement and the inter-influence from other involved numbers in the task; there are connections between negative numbers, 0 and space; there can be a low-level processing of negative number magnitude to some extent of automation; the forming and representing of mental number line is dynamic and flexible to fit the task requirements, mental number line, therefore, can extend to the left side of zero, while representing number magnitude.

Components representation of negative numbers: Evidence from auditory stimuli detection and number classification tasks

Past research suggested that negative numbers could be represented in terms of their components in the visual modality. The present study examined the processing of negative numbers in the auditory modality and whether it is affected by context. Experiment 1 employed a stimuli detection task where only negative numbers were presented binaurally. Experiment 2 employed the same task, but both positive and negative numbers were mixed as cues. A reverse attentional spatial-numerical association of response codes (SNARC) effect for negative numbers was obtained in these two experiments. Experiment 3 employed a number classification task where only negative numbers were presented binaurally. Experiment 4 employed the same task, but both positive and negative numbers were mixed. A reverse SNARC effect for negative numbers was obtained in these two experiments. These findings suggest that negative numbers in the auditory modality are generated from the set of positive numbers, thus supporting a components representation.

Extending the Mental Number Line—How Do Negative Numbers Contribute?

Previous studies suggest that there is an association between positive numbers and space; however, there is less agreement for negative numbers. The main purpose of the present study was to investigate the nature of the processing and representation of negative numbers, and the association between negative numbers and space. Results of the two experiments show that low-level processing (perception) of negative numbers can induce spatial shifts of attention. Whether this is caused by their numerical value or absolute value depends on the numerical context and task requirements, indicating that there are both components and holistic processing, and representation for negative numbers. The representation is automatically associated with leftward space; the coding and representation of the mental number line is adaptable to the specific numerical context and task requirements. The mental number line, therefore, can extend to the left side of zero, thus supporting the context-dependent view.

The Representation of Negative Numbers: Exploring the Effects of Mode of Processing and Notation

The representation of negative numbers was explored during intentional processing (i.e., when participants performed a numerical comparison task) and during automatic processing (i.e., when participants performed a physical comparison task). Performance in both cases suggested that negative numbers were not represented as a whole but rather their polarity and numerical magnitudes were represented separately. To explore whether this was due to the fact that polarity and magnitude are marked by two spatially separated symbols, participants were trained to mark polarity by colour. In this case there was still evidence for a separate representation of polarity and magnitude. However, when a different set of stimuli was used to refer to positive and negative numbers, and polarity was not marked separately, participants were able to represent polarity and magnitude together when numerical processing was performed intentionally but not when it was conducted automatically. These results suggest that notation is only partly responsible for the components representation of negative numbers and that the concept of negative numbers can be grasped only through that of positive numbers.

Negative Numbers Are Generated in the Mind

The goal of the present study was to disentangle two possible representations of negative numbers--the holistic representation, where absolute magnitude is integrated with polarity; and the components representation, where absolute magnitude is stored separately from polarity. Participants' performance was examined in two tasks involving numbers from--100 to 100. In the numerical comparison task, participants had to decide which number of a pair was numerically larger/smaller. In the number line task, participants were presented with a spatial number line on which they had to place a number. The results of both tasks support the components representation of negative numbers. The findings suggest that processing of negative numbers does not involve retrieval of their meaning from memory, but rather the integration of the polarity sign with the digits' magnitudes.