Tracking and quantifying objects and non‐cohesive substances

vanMarle, Kristy; Wynn, Karen

doi:10.1111/j.1467-7687.2010.00998.x

Cited by 54 publications

(44 citation statements)

References 57 publications

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“…(i.e., 2 − 1 =?). Infants within these paradigms are remarkably good at doing simple addition, subtraction, and comparisons (Gallistel and Gelman 1992;Gilmore et al 2007;McCrink and Wynn 2004;Van Marle and Wynn 2011;Wynn 1998aWynn , 1998bXu and Spelke 2000). Infants can also perform matching to samples (Xu and Garcia 2008).…”

Section: What About Infants and Children?mentioning

confidence: 99%

Intuitive Conceptions of Probability and the Development of Basic Math Skills

Brase

Martinie

Castillo-Garsow

2014

Advances in Mathematics Education

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The idea of probabilities has been described as a "Janus-faced" concept, which can be thought of either in terms of frequencies or in terms of subjective confidence. This dualism contributes to debates about the nature of human rationality, and therefore the pedagogical assumptions and goals of education. For this reason, the present chapter explores the evidence regarding how quantitative information is intuitively understood in the human mind over the course of elementary school education. Are particular interpretations of probability equally weighted or does one interpretation predominate as mathematical concepts are being acquired? We find multiple, converging lines of evidence that indicate a frequency interpretation of probabilistic information is developmentally primary and privileged. This has implications for mathematics education, even before the introduction of actual probabilities, in areas such as learning fractions and decimals. Educational practices should work to bootstrap from these privileged representations (rather than fight them) and built towards a more inclusive and comprehensive model of probability knowledge. We conclude that a fundamental issue is not just whether students think about probabilities as a frequentist or as a subjectivist, but rather how they recognize when to be one versus the other.

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Section: What About Infants and Children?mentioning

confidence: 99%

Intuitive Conceptions of Probability and the Development of Basic Math Skills

Brase

Martinie

Castillo-Garsow

2014

Advances in Mathematics Education

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“…However, the perceptual properties of the referent over the morphosyntactic properties of the noun modulate its interpretation as an object or a substance; a linguistic label of mass or of count assigned to the referent is not necessary to define it as an object or a substance (Soja, 1992). Moreover, some studies have found that the ability to discriminate objects from substances, at least for what concerns their tracking and quantification, is prelinguistic and present by at least 10 months of age (i.e., before most children are producing their first words; Hespos, Ferry, & Rips, 2009;vanMarle & Wynn, 2011; for a review, see Hespos & vanMarle, 2012). However, some specific cognitive biases in early word learning seem to favor objects over substances.…”

Section: Morphological Number Conservation Operations Countabilitymentioning

confidence: 99%

Mass is more: The conceiving of (un)countability and its encoding into language in 5-year-old-children

et al. 2016

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Is the mass-count distinction merely a linguistic issue, or is it coded in representations other than language? We hypothesized that a difference between mass and count properties should be observed even in absence of linguistic distinctions driven by the morphosyntactic context. We tested 5-6-year-old children's ability to judge sentences with mass nouns (sand), count nouns (ring), and neutral nouns (i.e., those that appear in mass and count contexts with similar frequency; cake). Children refused neutral nouns embedded in uncountable morphosyntactic contexts, showing a preference for a count interpretation. This suggests that linguistic features alone are not sufficient to define the mass-count distinction. Additional analyses showed that children's performance with mass-but not count-morphosyntax correlated with their performance in tasks concerning logical and conservation operations. Altogether, these results suggest that the processing of mass features is not more demanding than count features from a linguistic point of view; rather, mass features entail additional abstraction abilities.Keywords Count/mass distinction . Language acquisition . Morphological number . Conservation operations . CountabilityTraditional grammar descriptions (after Cheng, 1973) trace a division between mass and count nouns. Specifically, mass nouns refer to substances (e.g., sand), a n d c o u n t n o u n s r e f e r t o o b j ec t s ( e . g . , r i n g ) . Morphosyntactic properties are crucial to distinguish between these two categories of nouns: Mass nouns do not take the plural (e.g., sands) and in the singular form cannot be modified by some determiners (e.g., a sand, each sand). Count nouns do have a plural form (e.g., rings) and in the singular form can be modified by those determiners (e.g., a ring, each ring).Even though the properties that distinguish mass from count nouns have been debated for a long time, both by philosophers (e.g., Pelletier, 1975Pelletier, , 2012Quine, 1960) and linguists (e.g., Allan, 1980;Bale & Barner, 2009;Gillon, 1992;Jackendoff, 1991), influential linguistic approaches (e.g., Borer, 2005;Chierchia, 1998Chierchia, , 2010De Belder, 2011) agree that m ass nouns (or mass morphosyntax) are formally simpler than count nouns (or count morphosyntax). The argument is that the computation of these latter requires more operations at the morphosyntactic level or at the semantic level. In fact, mass nouns can appear only in the singular (e.g., sand) while count nouns display a full inflection for number morphology (e.g., ring vs. rings). Even in the philosophical perspective advanced by Quine (1960), the mass interpretation would be the basic one from which the count interpretation derives.However, as already observed in many theoretical works (e.g., Allan, 1980;Pelletier, 2012;Rothstein, 2010), the simplicity of mass nouns as compared to count nouns in linguistics does not seem as straightforward in terms of cognition. The assumption that mass nouns (or mass morphosyntax) are formally simpler t...

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“…Using procedures similar to Feigenson et al (2002), a study found that 10- to 12-month-olds were equally successful at choosing the larger amount of discrete food items with a set that was below (1 vs. 2) and above (5 vs. 10) the capacity limit predicted by object-based individuation models (Van Marle and Wynn, 2011). This result suggests that an approximate representation system is at work when responding to quantitative order.…”

Section: Ordinal Basis Of Relative Quantity Judgmentmentioning

confidence: 99%

“…The parallel that exists between cardination and ordination means that repeated assessments about whether two quantities are different or the same in size are governed by the same representation systems as repeated assessments about whether one numerical set is larger or smaller than another set. Unfortunately, only one infant study has broached the topic of large set RQJs (Van Marle and Wynn, 2011) so it remains to be seen whether the same pattern holds for our youngest counterparts.…”

Section: Ordinal Basis Of Relative Quantity Judgmentmentioning

confidence: 99%

1â€‰<â€‰2 and 2â€‰<â€‰3: Non-Linguistic Appreciations of Numerical Order

Anderson¹,

Cordes²

2013

Front. Psychology

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Ordinal understanding is involved in understanding social hierarchies, series of actions, and everyday events. Moreover, an appreciation of numerical order is critical to understanding number at a highly abstract, conceptual level. In this paper, we review findings concerning the development and expression of ordinal numerical knowledge in preverbal human infants in light of literature about the same cognitive abilities in non-human animals. We attempt to reconcile seemingly contradictory evidence, provide new directions for prospective research, and evaluate the shared basis of ordinal knowledge among non-verbal organisms. Our review of the research leads us to conclude that both infants and non-human animals are adapted to respond to monotonic progressions in numerical order, consonant with mathematical definitions of numerical order. Further, we suggest that patterns in the way that infants and non-human animals process numerical order can be accounted for by changes across development, the conditions under which representations are generated, or both.

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Tracking and quantifying objects and non‐cohesive substances

Cited by 54 publications

References 57 publications

Intuitive Conceptions of Probability and the Development of Basic Math Skills

Intuitive Conceptions of Probability and the Development of Basic Math Skills

Mass is more: The conceiving of (un)countability and its encoding into language in 5-year-old-children

1â€‰<â€‰2 and 2â€‰<â€‰3: Non-Linguistic Appreciations of Numerical Order

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