Miscategorized subset-knowers: Five- and six-knowers can compare only the numbers they know.

Initial acquisition of the first symbolic numbers is measured with the Give a Number (GaN) task. According to the classic method, it is assumed that children who know only 1, 2, 3, or 4 in the GaN task, (termed separately one-, two-, three-, and four-knowers, or collectively subset-knowers) have only a limited conceptual understanding of numbers. On the other hand, it is assumed that children who know larger numbers understand the fundamental properties of numbers (termed cardinality-principle-knowers), even if they do not know all the numbers as measured with the GaN task, that are in their counting list (e.

The complexity of measuring reliability in learning tasks: An illustration using the Alternating Serial Reaction Time Task.

Despite the fact that reliability estimation is crucial for robust inference, it is underutilized in neuroscience and cognitive psychology. Appreciating reliability can help researchers increase statistical power, effect sizes, and reproducibility, decrease the impact of measurement error, and inform methodological choices. However, accurately calculating reliability for many experimental learning tasks is challenging.

Stimulus frequency alone can account for the size effect in number comparison.

In a number comparison task, the size effect (i.e, smaller values are easier to compare than larger values) is usually attributed to a psychophysics-based representation. However, alternative models assume that the size effect is a frequency effect: Smaller numbers are easier to process because they are observed more frequently.

Symbolic number comparison and number priming do not rely on the same mechanism.

In elementary symbolic number processing, the comparison distance effect (in a comparison task, the task is more difficult with smaller numerical distance between the values) and the priming distance effect (in a number processing task, actual number is easier to process with a numerically close previous number) are two essential phenomena. While a dominant model, the approximate number system model, assumes that the two effects rely on the same mechanism, some other models, such as the discrete semantic system model, assume that the two effects are rooted in different generators. In a correlational study, here we investigate the relation of the two effects.

Development of Preschoolers' Understanding of Zero.

While knowledge on the development of understanding positive integers is rapidly growing, the development of understanding zero remains not well-understood. Here, we test several components of preschoolers' understanding of zero: Whether they can use empty sets in numerical tasks (as measured with comparison, addition, and subtraction tasks); whether they can use empty sets soon after they understand the cardinality principle (cardinality-principle knowledge is measured with the give-N task); whether they know what the word "zero" refers to (tested in all tasks in this study); and whether they categorize zero as a number (as measured with the smallest-number and is-it-a-number tasks). The results show that preschoolers can handle empty sets in numerical tasks as soon as they can handle positive numbers and as soon as, or even earlier than, they understand the cardinality principle.

Ratio effect slope can sometimes be an appropriate metric of the approximate number system sensitivity.

The approximate number system (ANS) is believed to be an essential component of numerical understanding. The sensitivity of the ANS has been found to be correlating with various mathematical abilities. Recently, Chesney (2018, Attention, Perception, & Psychophysics, 80[5], 1057-1063) demonstrated that if the ANS sensitivity is measured with the ratio effect slope, the slope may measure the sensitivity imprecisely.

Two components of the Indo-Arabic numerical size effect.

In the symbolic number comparison task, the size effect (better performance for small than for large numbers) is usually interpreted as the result of the more general ratio effect, in line with Weber's law. In alternative models, the size effect might be a result of stimulus frequency: smaller numbers are more frequent, and more frequent stimuli are easier to process. It has been demonstrated earlier, that in artificial new number digits, the size effect reflects the frequencies of those digits.

The Indo-Arabic distance effect originates in the response statistics of the task.

In the number comparison task distance effect (better performance with larger distance between the two numbers) and size effect (better performance with smaller numbers) are used extensively to find the representation underlying numerical cognition. According to the dominant analog number system (ANS) explanation, both effects depend on the extent of the overlap between the noisy representations of the two values. An alternative discrete semantic system (DSS) account supposes that the distance effect is rooted in the association between the numbers and the "small-large" properties with better performance for numbers with relatively high differences in their strength of association, and that the size effect depends on the everyday frequency of the numbers with smaller numbers being more frequent and thus easier to process.

Interference Between Number Magnitude and Parity.

Interference between number magnitude and other properties can be explained by either an analogue magnitude system interfering with a continuous representation of the other properties or by discrete, categorical representations in which the corresponding number and property categories interfere. In this study, we investigated whether parity, a discrete property which supposedly cannot be stored on an analogue representation, could interfere with number magnitude. We found that in a parity decision task the magnitude interfered with the parity, highlighting the role of discrete representations in numerical interference.

Symbolic Number Comparison Is Not Processed by the Analog Number System: Different Symbolic and Non-symbolic Numerical Distance and Size Effects.

We test whether symbolic number comparison is handled by an analog noisy system.Analog system model has systematic biases in describing symbolic number comparison.This suggests that symbolic and non-symbolic numbers are processed by different systems.

Symbolic Numerical Distance Effect Does Not Reflect the Difference between Numbers.

In a comparison task, the larger the distance between the two numbers to be compared, the better the performance-a phenomenon termed as the numerical distance effect. According to the dominant explanation, the distance effect is rooted in a noisy representation, and performance is proportional to the size of the overlap between the noisy representations of the two values. According to alternative explanations, the distance effect may be rooted in the association between the numbers and the small-large categories, and performance is better when the numbers show relatively high differences in their strength of association with the small-large properties.

The Source of the Symbolic Numerical Distance and Size Effects.

Human number understanding is thought to rely on the analog number system (ANS), working according to Weber's law. We propose an alternative account, suggesting that symbolic mathematical knowledge is based on a discrete semantic system (DSS), a representation that stores values in a semantic network, similar to the mental lexicon or to a conceptual network. Here, focusing on the phenomena of numerical distance and size effects in comparison tasks, first we discuss how a DSS model could explain these numerical effects.

Numerical distance and size effects dissociate in Indo-Arabic number comparison.

Numerical distance and size effects (easier number comparisons with large distance or small size) are mostly supposed to reflect a single effect, the ratio effect, which is a consequence of activation of the analog number system (ANS), working according to Weber's law. In an alternative model, symbolic numbers can be processed by a discrete semantic system (DSS), in which the distance and size effects could originate in two independent factors: the distance effect depending on the semantic distance of the units, and the size effect depending on the frequency of the symbols. Whereas in the classic view both symbolic and nonsymbolic numbers are processed by the ANS, in the alternative view only nonsymbolic numbers are processed by the ANS, but symbolic numbers are handled by the DSS.

The interplay of holistic shape, local feature and color information in object categorization.

Although it is widely accepted that colors facilitate object and scene recognition under various circumstances, several studies found no effects of color removal in tasks requiring categorization of briefly presented animals in natural scenes. In this study, three experiments were performed to test the assumption that the discrepancy between empirical data is related to variations of the available meaningful global information such as object shapes and contextual cues. Sixty-one individuals categorized chromatic and achromatic versions of intact and scrambled images containing either cars or birds.

Subitizing is sensitive to the arrangement of objects.

Subitizing is a fast and accurate enumeration process of small sets of usually less than four objects. Several models were proposed in the literature. Critically, only pattern recognition theory suggests that subitizing performance is sensitive to the arrangement of the array.

The Role of Number Notation: Sign-Value Notation Number Processing is Easier than Place-Value.

Number notations can influence the way numbers are handled in computations; however, the role of notation itself in mental processing has not been examined directly. From a mathematical point of view, it is believed that place-value number notation systems, such as the Indo-Arabic numbers, are superior to sign-value systems, such as the Roman numbers. However, sign-value notation might have sufficient efficiency; for example, sign-value notations were common in flourishing cultures, such as in ancient Egypt.

Inhibition and interference in the think/no-think task.

Five experiments using the think/no-think (TNT) procedure investigated the effect of the no-think and substitute instructions on cued recall. In Experiment 1, when unrelated A-B paired associates were studied and cued for recall with A items, recall rates were reliably enhanced in the think condition and reliably impaired below baseline in the no-think condition. In Experiments 2 and 5, final recall was cued with B items, leading to reliably higher recall rates, as compared with baseline, in both the think and no-think conditions.

Numerical abilities in Williams syndrome: dissociating the analogue magnitude system and verbal retrieval.

Two numerical systems--the analogue magnitude system and verbal retrieval--were investigated in Williams syndrome (WS) with three numerical tasks: simple addition, simple multiplication, and number comparison. A new matching technique was introduced in selecting the proper control groups. The WS group was relatively fast in the addition and multiplication tasks, but was slow in number comparison.

Obstetric and sociodemographic risk of vulnerability to postnatal depression.

Objective: To assess the associated obstetric and sociodemographic risk of vulnerability to postnatal depression in a population-based study.

Methods: All women presenting for postpartum care (n=1656) were surveyed at pregnancy care units of southern-eastern Hungary between January 2004 and May 2006 with an anonymously completed Leverton questionnaire (LQ). The demographic characteristics, obstetric data and related variables were determined as potential correlates of vulnerability to postnatal depression.