Brief Summary of the Research Article: Children’s intuitive sense of number develops independently of their perception of area, density, length, and time (Odic, 2018)
This study investigated whether the developmental improvements in the precision of the Approximate Number System (ANS) are driven by maturation in the perception of non-numeric dimensions (area, density, line length, and time) or by improvements in domain-general abilities, such as inhibitory control. Researchers tested 185 children (ages 2–12) and adults on five discrimination tasks.
The main findings challenged the theory of a unified, generalized magnitude system:
- Distinct Developmental Trajectories: The five dimensions showed distinct developmental timelines. ANS precision reached adult-like levels by adolescence, but time and density did not fully develop until early adulthood. Area and length developed at the same time as or sooner than the ANS.
- Independence of ANS Development: Developmental improvements in ANS accuracy and Weber fractions continued to correlate with age even when controlling for performance in area, density, length, and time. This provided evidence that ANS precision develops independently of these four non-numeric dimensions.
- Inhibitory Control: The difference in accuracy between Congruent and Incongruent ANS trials (used to index inhibitory control) did not correlate with age and could not explain the development of ANS precision.
These results support the hypothesis that domain-specific improvements drive the development of ANS precision.
Important
- Attention to time and arousal – These are the two modulators in the pacemaker-accumulator model of precise time perception. Higher levels of either factor (attention or arousal) increase the number of pulses accumulated, leading to longer perceived duration.
- Cognitive Diversity – The policy-relevant upshot of research on genetic enhancement argues that we should preserve cognitive diversity.
- Evidence for the Approximate Number System (ANS) – Empirical evidence includes animal research, infant research, and the ability of people to quickly distinguish between groups of numbers based on size or quantity without counting.
- ANS and Symbolic Math Relationship – There is a meaningful, complex, and probably bidirectional relationship between the ANS and symbolic math skills.
- Impulsive Behavior and Time Perception – Impulsive individuals tend to overestimate how much time has passed (e.g., in an estimation task) but underproduce a temporal interval when asked to tap out a specific duration.
- Mueller-Lyer Illusion and Perceptual Representation – This illusion is often used to demonstrate that higher-level knowledge (knowing the lines are equal) does not penetrate or change the perceptual representation, illustrating informational encapsulation.
- Common Magnitude Code Evidence – Although processing number and length yields overlapping activity in the parietal cortex, researchers found no significant cross-dimensional distance effect, challenging the prediction of a common magnitude code.
Core Concepts
- Common Magnitude System (CMS): The hypothesis, originating with Walsh’s Theory of Magnitude (ATOM), that time, space, and number are all represented by a single, shared system.
- Weber’s Law: A psychophysical principle stating that the difference threshold required to distinguish between two stimuli is proportional to the intensity of the standard stimulus; this ratio is constant across magnitudes like time, space, and number.
- Incongruency Paradigms: Experimental designs where participants must process simultaneous quantities (e.g., numerosity and area). Slower, less accurate responses on incongruent trials (where quantities conflict) suggest demands are placed on a shared system.
- Magnitude Code: The brain’s representation of stimuli ordered according to their magnitude. The CMS predicts a common code, implying that distance effects (where close magnitudes activate closer brain areas) should generalize across dimensions.
- Interferences Across Representations: A prediction of the CMS is that simultaneous processing of temporal, spatial, and numerical quantities should interfere, especially when those quantities are incongruent.
- Asymmetry in Interference Effects: Challenges the CMS, as numerical and spatial information often biases temporal judgments, but temporal information does not reliably alter numerical or spatial judgments.
- Developmental Divergence Model: An alternative to the CMS, proposing that while infants may start with a single magnitude system, the system separates into several independent systems as development and brain maturation occur.
- Comorbid Quantity Deficits: Simultaneous spatial, numerical, and temporal deficits are typically observed in developmental disorders early in life (e.g., ADHD), but later damage to specific brain areas often results in dissociations (e.g., cerebellar damage affecting only temporal estimation).
- Modularity/Informational Encapsulation: A concept relevant to the debate on spatial perception, where modular cognitive systems (like vision) operate without penetration from higher-level knowledge, making the visual experience of illusions persist despite knowledge of physical reality.
- Response Biases (Emotional Stimuli): Emotional faces (e.g., happy or angry) interfere with quantity processing in an asymmetric manner: they cause temporal overestimation but numerical underestimation relative to neutral faces.
Theories and Frameworks
- Theory of Magnitude (ATOM): Proposed by Vincent Walsh (2003), this sensorimotor theory posits that time, space, and number are represented by a common magnitude system, primarily in the parietal cortex, because successful action requires integrating these quantities.
- Amodal Accumulator Mechanism (Meck & Church, 1983): Based on rat studies, this theory suggests a shared analog magnitude system for time and number, demonstrated by equivalent discrimination sensitivity (similar Weber fractions) and cross-modal transfer of learned discriminations.
- Developmental Divergence Model (Newcombe, 2014): Explains similarities in magnitude processing in infancy as a potential starting point (a single system), which then diverges into separable systems as development proceeds.
- Evaluation Criteria for Theories: Criteria used to assess theories include Empirical Adequacy, Consistency (internal and external), Simplicity (Parsimony), Scope, Fruitfulness, Predictive Power, and Explanatory Power.
Notable Individuals
- Vincent Walsh: Proposed the Theory of Magnitude (ATOM), originating the debate on the common magnitude system in 2003.
- Meck and Church: Demonstrated that rats could generalize rules learned in one domain (time or number) to the other, supporting a shared analog magnitude system.
- Darko Odic: Conducted the influential study showing that the developmental trajectory of the ANS is distinct and independent from area, density, length, and time perception.
- Borghesani, V., de Hevia, M. D., et al.: Used fMRI to show that despite overlapping activation in the parietal cortex for number and length processing, there was no significant cross-dimensional distance effect, suggesting resource sharing but not a common code.