No Innate Number Line in the Human Brain

Núñez, Rafael

doi:10.1177/0022022111406097

Cited by 76 publications

(58 citation statements)

References 58 publications

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“…Such a conclusion is consistent with recent findings showing that number-to-space mappings are not as fundamental as previously thought, and that linear number line mappings require cultural practices to be established [31]. Moreover, these observations also seem to match the available records of the history of mathematics, which show no documentation of depictions of number lines proper prior to the 17 th Century [4], [32]. The number line seems to explicitly appear for the first time with the work of John Napier [33] and John Wallis [34] as a response to demands imposed by the conceptualization of more sophisticated mathematical objects, such as logarithms (Napier) and negative squares and their imaginary roots (Wallis).…”

Section: Discussionsupporting

confidence: 89%

Number Concepts without Number Lines in an Indigenous Group of Papua New Guinea

2012

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BackgroundThe generic concept of number line, which maps numbers to unidimensional space, is a fundamental concept in mathematics, but its cognitive origins are uncertain. Two defining criteria of the number line are that (i) there is a mapping of each individual number (or numerosity) under consideration onto a specific location on the line, and (ii) that the mapping defines a unidimensional space representing numbers with a metric — a distance function. It has been proposed that the number line is based on a spontaneous universal human intuition, rooted directly in brain evolution, that maps number magnitude to linear space with a metric. To date, no culture lacking this intuition has been documented.Methodology/Principal FindingsBy means of a number line task, we investigated the universality proposal with the Yupno of Papua New Guinea. Unschooled adults did exhibit a number-to-space mapping (criterion i) but, strikingly, despite having precise cardinal number concepts, they located numbers only on the endpoints, thus failing to use the extent of the line. The produced mapping was bi-categorical and metric-free, in violation of criterion ii. In contrast, Yupnos with scholastic experience used the extent of the segment according to known standards, but they did so not as evenly as western controls, exhibiting a bias towards the endpoints.Conclusions/SignificanceResults suggest that cardinal number concepts can exist independently from number line representations. They also suggest that the number line mapping, although ubiquitous in the modern world, is not universally spontaneous, but rather seems to be learned through — and continually reinforced by — specific cultural practices.

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Section: Discussionsupporting

confidence: 89%

Number Concepts without Number Lines in an Indigenous Group of Papua New Guinea

2012

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“…Even the few number words in their lexicon are not comparable to Western number words because they represent approximate numbers . Importantly, in the study of Dehaene et al (2008), 22% of the uneducated Amazonian adults failed to map numbers 1–3 in the right order and 37% of the participants exhibited bimodal mapping, using only the end points of the line (Núñez, 2011). …”

Section: Theoretical Issuesmentioning

confidence: 99%

Magnitude processing in non-symbolic stimuli

Leibovich¹,

Henik²

2013

Front. Psychol.

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Dot arrays are often used to study basic numerical skills across cultures, species and development. Researchers investigate the ability of subjects to discriminate between dot arrays, as a function of the ratio or distance between their numerosities. Such studies have contributed significantly to the number sense theory (i.e., that humans are born with the ability to process numerosities, and share this ability with various species)—possibly the most influential theory in numerical cognition literature today. However, a dot array contains, in addition to numerosity, continuous properties such as the total surface area of the dots, their density, etc. These properties are highly correlated with numerosity and therefore might influence participants' performance. Different ways in which different studies choose to deal with this confound sometimes lead to contradicting results, and in our opinion, do not completely eliminate the confound. In this work, we review these studies and suggest several possible reasons for the contradictions in the literature. We also suggest that studying continuous properties, instead of just trying to control them, may contribute to unraveling the building blocks of numerical abilities.

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“…Preverbal human infants can discriminate among numbers (Strauss and Curtis, 1981; Wynn, 1992; Cordes and Brannon, 2009), though the basis on which they do so is controversial (Ansari and Karmiloff-Smith, 2002; Sophian, 2007; Izard et al, 2009; Núñez, 2011). While early perceptual abilities may provide a foundation on which to map some number terms, subsequent developments are—for typically developing (TD) children—inevitably interwoven with linguistic experiences and language development (Spelke and Tsivkin, 2001).…”

Section: Introductionmentioning

confidence: 99%

Severity of specific language impairment predicts delayed development in number skills

Durkin¹,

Mok²,

Conti‐Ramsden³

2013

Front. Psychol.

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The extent to which mathematical development is dependent upon language is controversial. This longitudinal study investigates the role of language ability in children's development of number skills. Participants were 229 children with specific language impairment (SLI) who were assessed initially at age 7 and again 1 year later. All participants completed measures of psycholinguistic development (expressive and receptive), performance IQ, and the Basic Number Skills subtest of the British Ability Scales. Number skills data for this sample were compared with normative population data. Consistent with predictions that language impairment would impact on numerical development, average standard scores were more than 1 SD below the population mean at both ages. Although the children showed improvements in raw scores at the second wave of the study, the discrepancy between their scores and the population data nonetheless increased over time. Regression analyses showed that, after controlling for the effect of PIQ, language skills explained an additional 19 and 17% of the variance in number skills for ages 7 and 8, respectively. Furthermore, logistic regression analyses revealed that less improvement in the child's language ability over the course of the year was associated with a greater odds of a drop in performance in basic number skills from 7 to 8 years. The results are discussed in relation to the interaction of linguistic and cognitive factors in numerical development and the implications for mathematical education.

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No Innate Number Line in the Human Brain

Cited by 76 publications

References 58 publications

Number Concepts without Number Lines in an Indigenous Group of Papua New Guinea

Number Concepts without Number Lines in an Indigenous Group of Papua New Guinea

Magnitude processing in non-symbolic stimuli

Severity of specific language impairment predicts delayed development in number skills

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