Sampling from the Mental Number Line 1 Sampling from the Mental

Sampling from the mental number line: how are approximate number system representations formed? Sampling from the mental number line: how are approximate number system representations formed? Cognition, 129 (1), pp. 63-69. Abstract Nonsymbolic comparison tasks are commonly used to index the acuity of an individual's approximate number system (ANS), a cognitive mechanism believed to be involved in the development of number skills. Here we asked whether the time that an individual spends observing numerical stimuli influences the precision of the resultant ANS representations. Contrary to standard computational models of the ANS, we found that the longer the stimulus was displayed, the more precise was the resultant representation. We propose an adaptation of the standard model, and suggest that this finding has significant methodological implications for numerical cognition research. Fluency with mathematics is essential for day-today life. To successfully interact in a modern society it is frequently necessary to interpret, compare and calculate with numerical quantities. Along with a capacity to understand numerical ideas when represented symbolically, humans also have an Approximate Number System (ANS) which can be used to perform arithmetic operations on non-symbolic quantities such as arrays of dots or tones. The ANS is present in very young infants and some non-human animals (for a review see Dehaene, 1997), and recently some theorists have begun to speculate that it serves as the cognitive basis for symbolic mathematics (e. The ANS is widely believed to follow Weber's law: the standard model proposes that when we encounter non-symbolic stimuli, a box of n oranges say, the distribution of possible ANS representations follows a normal distribution with mean n and standard deviation wn. Here w is the Weber fraction, a parameter which represents the acuity of an individual's ANS have shown that individuals' ANS acuities are correlated with achievement in symbolic credence to the suggestion that the ANS is implicated in the development of symbolic mathematics competence. Although the capabilities of the ANS are now fairly well understood, the process by which the ANS forms representations from visual numerical stimuli is less clear. Several researchers have proposed that a mental 'accumulator' is central to this process (e.g. Dehaene Gallistel and Gelman drew an analogy between filling up a beaker with cups of liquid, and filling up the accumulator with " accumulator units ". They suggested that when an array of objects is observed, the scene is first normalized to remove numerically-irrelevant between-object …