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For well over one-hundred years, several key factors have been well established in the study of number comparison, including mental number line, numerical distance effect, and effect of sensory representation on number processing. The purpose of this article is to put some of these studies together to discuss design parameters and research questions addressed in the mental number comparison studies. Most of the studies discuss sensory representation and abstract number representation as well as degree of their interaction. In order to give the different views on a particular research question, the author classified studies under the related research questions. For example, Stroop and size congruity effect studies are addressed under this title chronologically. It was very clear that the design parameters and research question might change the interpretation of a task. It may be time to shift attention from the question of the interaction degree of sensory representation and abstract representation to a larger scope. The larger scope would be to understand the differences and similarities between different groups using a universal approach.

Number comparison studies have been an interesting topic for the cognitive neuroscientists who examine the sensory representation and magnitude representation of numbers. This review article starts with the mental number line term first defined by Galton [

After the SNARC effect topic, three number processing models are discussed as those models have been frequently revisited to understand the effects of sensory representation on mental number comparison. The first one is the abstract-modular number processing model [

The brief description of background studies is followed by the main topic, number comparison studies. The literature review on number comparison began with a search on PUBMED database with the key word of “number comparison” for the period of 1970 to January 2012. In order to keep the focus in adult number comparison studies, we excluded studies on disorders like acalculia, synthesia, cultural differences, and language studies along with brain imaging studies. Of the 112 articles, 24 articles that met the criteria are included in the review.

Some of these 24 articles were putting forward the earlier findings revisiting the empirical and theoretical studies published earlier. All those that did not appear in the PUBMED database were included in the review to provide comprehensive coverage.

With respect to theoretical and empirical results, the design parameters and the research questions are varied in the aspect of sensory representations and abstract representations of numbers. Most of the works included in this review focused on distance effect and different variations of sensory representations. The overall arguments of these studies are the degree of interaction between sensory perception, decision and motor response in the temporal and spatial domains.

One of the first number processing studies was conducted over 100 years ago by Galton [

Almost a century later, Restle [

In their seminal paper, Moyer and Landauer [

The distance effect on number comparison has been extensively studied in order to analyze comparison efficiency. In most cases, the distance effect is the dependent variable facilitated or unaffected by sensory representations. The scientists studying number comparison mainly agreed on the distance effect phenomena (e.g., [

At this point, it is clear that there is a mental number line and their relative distances from each other process numbers. But, what about spatial representation of numbers? Is there a mental spatial code for the numbers? Dehaene et al. [

McCloskey et al. [

Another alternative model discussed frequently is the triple-code model by Dehaene [

Campbell [

Later, Dehaene and Akhavein [

Accordingly, Noel and Seron [

The size congruity effect (sometimes called Stroop effect) refers to the fact that physical size comparison of numerals is affected by the magnitude of the respective numeral or vice versa. Size congruity effect tasks are the most common tasks to study the automaticity in numerical processing [

In their study, Besner and Coltheart [

Henik and Tzelgov [

Fitousi and Algom [

In the context of two-digit numbers, Foltz et al. [

Borgmann et al. [

Kadosh and Henik [

As it is discussed above, size congruity (or Stroop effect) has been visited frequently in Arabic and verbal number comparison studies. However, the number comparison studies on patterns, dots, and cumulative area covered by numerical values are not well studied in adults.

Recently, Burr and Ross [

In the context of number comparison, Nys and Content [

A more recent study by Schwarz and Ischebeck [

In recent article, Naccache and Dehaene [

Stoianov et al. [

Later, a semantic alignment study was developed to examine the influence of semantic priming on number comparison [

More recently, Sigman and Dehaene [

In the same context, Oriet et al. [

Santens et al. [

Goldfarb et al. [

Ratinckx and Fias [

The number bisection task is an expanded number comparison task to examine the difficulty of the task. It is basically the calculation of a numerical middle value between two presented numbers, usually called outer numbers (i.e., 5 is the numerical middle value between 3 and 7). Nuerk et al. [

The studies on two-digit number comparison can be classified in three main models; (i) holistic model, in which internal representation of numbers overrides units and digits are processed as a whole (e.g., [

Hinrichs et al. [

In the same context, Dehaene et al. [

On the other hand, Nuerk et al. [

A year later, Zhang and Wang [_{54} > RT_{53} as the ones- places are taken into account). The function of the sequential model looks like a step logarithmic function increasing with decreasing distance [

In the parallel model, the ones-place interacts with the comparison of two-digit numbers [

In the holistic model, the sensory representations of the numbers do not play any role on the processing model. The mental number is abstract and perceived as a whole numerical value. The function of this model is a logarithmic model of ones-places and tens-places. In other words, the stimulus will be processed as a whole and compared with a processed whole numerical value of the reference number [

Accordingly, Ganor-Stern et al. [

Moeller et al. [

It is suggested that the numbers such as 4 + 2 and 2 + 4 are mentally represented first as the minimum and maximum addends of the addition operation and the addition is completed later [

In general, the results revealed that number naming and number comparison are independent factors affecting number comparison (i.e., additive effect) excluding strategy used to identify 0 [

In a very recent study, Charras et al. [

The studies discussed in this review and also the others on number comparison directly or indirectly address the effects of sensory representation on number processing. The model of the interaction changes from one study to another depending on the research question and study design. For example, some scientists agree that sensory representation of numbers affects numerical magnitude representation [

With two-digit numbers, another dichotomous processing question is asked: whether digits are processed holistically or parallel. The holistic approach suggests that mental number perception overrides units [

In these contexts, there needs to be an effort to put all these findings in a common domain to develop a meta-task. A universal task model would allow scientists to understand the underlying behavior and brain mechanisms of number processing in a common domain.

Ultimately, such a meta-approach might provide some insights on mathematics or aging related disorders, for example, Dyscalculia [

The author thanks Sherman N. Hinson, Sr. for his valuable commends on editing and revision of the article.