The development of area discrimination and its implications for number representation in infancy

Brannon, Elizabeth M.; Lutz, Donna J.; Cordes, Sara

doi:10.1111/j.1467-7687.2006.00530.x

Cited by 176 publications

(177 citation statements)

References 27 publications

(38 reference statements)

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“…As described earlier, numerical discriminations are modulated by the ratio between the values, as per Weber's law. In human infants, the ratio effects for judgments of size, time, and number are refined at a similar rate of development (11,51,52). Infants' discriminations of size, time, and number improve by approximately 30% between 6 and 9 mo of age.…”

Section: For Review)mentioning

confidence: 99%

Math, monkeys, and the developing brain

Cantlon

2012

Proc. Natl. Acad. Sci. U.S.A.

103

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Thirty thousand years ago, humans kept track of numerical quantities by carving slashes on fragments of bone. It took approximately 25,000 y for the first iconic written numerals to emerge among human cultures (e.g., Sumerian cuneiform). Now, children acquire the meanings of verbal counting words, Arabic numerals, written number words, and the procedures of basic arithmetic operations, such as addition and subtraction, in just 6 y (between ages 2 and 8). What cognitive abilities enabled our ancestors to record tallies in the first place? Additionally, what cognitive abilities allow children to rapidly acquire the formal mathematics knowledge that took our ancestors many millennia to invent? Current research aims to discover the origins and organization of numerical information in humans using clues from child development, the organization of the human brain, and animal cognition.analog magnitude | functional MRI | mathematics education | numerical cognition | numerosity T his review traces the origins of numerical processing from "primitive" quantitative abilities to math intelligence quotient (IQ). "Primitive" quantitative abilities are those that many animals use to estimate the value of an object or event, for instance its distance, length, duration, number, amplitude, saturation, or luminance (among others). The constraints on how human and animal minds process these different quantities are similar (1). For example, all of these quantities show cognitive processing limitations that can be predicted by Weber's law. Weber's law states that quantity discrimination is determined by the objective ratio between their values. This ratio-based psychological and neural signature of quantity processing indicates that many quantities are represented in an analog format, akin to the way in which a machine represents intensities in currents or voltages (1). I discuss the types of constraints that influence quantity discrimination, using "number" as the initial example, and then consider the psychological and neural relationship between "number" and other quantitative dimensions. Similar constraints on processing across different quantities have been interpreted as evidence that they have a common evolutionary and/or developmental origin and a common foundation in the mind and brain (2-11). The resolution of these issues is important for understanding the inherent organization of our most basic conceptual faculties. The issue is also important for understanding how our formal mathematical abilities originated.Primitive quantitative abilities play a role in how modern humans learn culture-specific, formal mathematical concepts (1). Preverbal children and nonhuman animals possess a primitive ability to appreciate quantities, such as the approximate number of objects in a set, without counting them verbally. Instead of counting, children and animals can mentally represent quantities approximately, in an analog format. Studies from our group and others have shown that human adults, children, and nonhuman primates share cogni...

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Section: For Review)mentioning

confidence: 99%

Math, monkeys, and the developing brain

Cantlon

2012

Proc. Natl. Acad. Sci. U.S.A.

103

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“…In particular, it was shown that infants (5.5-7.5 months) could distinguish between dowels of different height when another object, serving as a standard, was present; they could not make such distinctions when no standard was available (Duffy, Huttenlocher, Levine, & Duffy, 2005;Huttenlocher, Duffy, & Levine, 2002;see also, Feigenson, Carey, & Spelke, 2002). There is evidence that only when the sizes being compared involve fairly large differences are infants (and older children) capable of making spatial discriminations in the absence of a standard (e.g., Brannon, Lutz, & Cordes, 2006;Huttenlocher et al, 2002).…”

Section: Object Sizementioning

confidence: 99%

The Representation of Geometric Cues in Infancy

Lourenco¹,

Huttenlocher²

2008

Infancy

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There is evidence that, from an early age, humans are sensitive to spatial information such as simple landmarks and the size of objects. This study concerns the ability to represent a particular kind of spatial information, namely, the geometry of an enclosed layout-an ability present in older children, adults, and nonhuman animals (e.g., Cheng, 1986;Hermer & Spelke, 1996). Using a looking-time procedure, 4.5-to 6.5-montholds were tested on whether they could distinguish among the corners of an isosceles triangle. On each trial, the target corner was marked by a red dot. The stimulus (triangle with dot) appeared from different orientations across trials, ensuring that only cues related to the triangle itself could be used to differentiate the corners. When orientations were highly variable, infants discriminated the unique corner (i.e., the corner with the smaller angle and two equal-length sides) from a nonunique corner; they could not discriminate between the two nonunique corners. With less variable orientations, however, infants did discriminate between the nonunique corners of the isosceles triangle. Implications for how infants represent geometric cues are discussed.

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“…Looking time studies revealed that 5-month-old infants are sensitive to changes in metric distances (Newcombe, Huttenlocher, & Learmonth, 1999;Newcombe, Sluzenski & Huttenlocher, 2005), and toddlers encode distance metrically in a hide-and-seek game (Huttenlocher, Newcombe, & Sandberg, 1994). Furthermore, magnitude coding is used early in life, as evidenced by infants' discrimination of space, time, number, and speed (Brannon, Lutz, & Cordes, 2006;Brannon, Suanda, & Libertus, 2007;Möhring, Libertus, & Bertin, 2012;Xu & Spelke, 2000), and recent studies yielded evidence for cross-dimensional transfer, suggesting that magnitude information regarding various dimensions is coded in one representational system (de Hevia & Spelke, 2010;Lourenco & Longo, 2010). It is likely that metric understanding is based on this fundamental comparative system, termed the general magnitude system (Walsh, 2003).…”

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confidence: 99%

Zooming in on spatial scaling: Preschool children and adults use mental transformations to scale spaces.

Möhring¹,

Newcombe²,

Frick³

2014

Developmental Psychology

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Spatial scaling is an important prerequisite for many spatial tasks and involves an understanding of how distances in different-sized spaces correspond. Previous studies have found evidence for such an understanding in preschoolers; however, the mental processes involved remain unclear. The present study investigated whether children and adults use mental transformations to scale distances in space. Adults and 4-and 5-year-old children (N = 60) were asked to use maps to locate target objects in a larger referent space on a touchscreen. The size of the referent space was held constant, but the sizes of the maps were varied systematically, resulting in seven scaling factors. A linear increase in response times and errors with increasing scaling factor suggested that participants of every age group mentally transformed the size of the map to compare it to the referent, providing evidence for an analog imagery strategy in children's and adults' spatial scaling. Spatial scaling is fundamental to many spatial tasks that require an understanding of how distances in different-sized spaces are related. The ability to map distances from one space to another is involved in many daily activities, such as interpreting navigation aids or imagining the height of a building by looking at its blueprint. Around the age of 3 years, children are able to establish symbolic correspondence between a model and its referent (DeLoache, 1987), but successful mapping between spatial representations also requires an understanding of geometric correspondence (Downs, 1985;Newcombe & Huttenlocher, 2000).A crucial precondition for establishing geometric correspondence is the ability to encode distances in a metric manner. There is evidence that metric coding is present early in life. Looking time studies revealed that 5-month-old infants are sensitive to changes in metric distances (Newcombe, Huttenlocher, & Learmonth, 1999;Newcombe, Sluzenski & Huttenlocher, 2005), and toddlers encode distance metrically in a hide-and-seek game (Huttenlocher, Newcombe, & Sandberg, 1994). Furthermore, magnitude coding is used early in life, as evidenced by infants' discrimination of space, time, number, and speed (Brannon, Lutz, & Cordes, 2006;Brannon, Suanda, & Libertus, 2007;Möhring, Libertus, & Bertin, 2012;Xu & Spelke, 2000), and recent studies yielded evidence for cross-dimensional transfer, suggesting that magnitude information regarding various dimensions is coded in one representational system (de Hevia & Spelke, 2010;Lourenco & Longo, 2010). It is likely that metric understanding is based on this fundamental comparative system, termed the general magnitude system (Walsh, 2003).A second crucial step in establishing geometric correspondence is to map distances from one space to another, which -for different sized spaces -requires spatial scaling. Running Head: ZOOMING IN ON SPATIAL SCALING 4Previous research has shown that if task demands are low and locations vary on one dimension only, 3-year-olds are able to locate objects in a referent space,...

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The development of area discrimination and its implications for number representation in infancy

Cited by 176 publications

References 27 publications

Math, monkeys, and the developing brain

Math, monkeys, and the developing brain

The Representation of Geometric Cues in Infancy

Zooming in on spatial scaling: Preschool children and adults use mental transformations to scale spaces.

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