•Acquisition of the cardinality is crucial to the development of early numerical skills•The richness of number inputs children receive influences the acquisition of cardinality•A finger-based ...enriched intervention accelerated the understanding of cardinality in 3-year-olds•The intervention can be easily implemented into real-life learning settings
The acquisition of cardinal numbers represents a crucial milestone in the development of early numerical skills and more advanced math abilities. However, relatively few studies have investigated how children's grasping of the cardinality principle can be supported. It has been suggested that the richness of number inputs children receive influences the acquisition of cardinal numbers. The present study was designed to investigate whether canonical finger patterns representing numbers may contribute to this acquisition. Fifty-one 3-year-olds were randomly assigned to 1 of 2 training conditions: (a) a condition that involved counting and labeling, which has shown efficacy to support the acquisition of cardinality, and (b) a condition in which counting and labeling were enriched with finger patterns. Crucially, we aimed at providing evidence of both training programs in a real-life learning environment where teachers incorporated the training as a group-based activity into their regular schedule of daily activities. Children assigned to the finger-based condition outperformed those who received the counting-and-label training. Findings suggest that finger patterns may have a role in children's cardinality understanding. Furthermore, our study shows that instructional approaches for improving cardinality understanding can be easily and successfully implemented into real-life learning settings.
Mucho de lo que sabemos sobre la sociedad de los tobas del Chaco boliviano se encuentra en publicaciones de misioneros franciscanos que interactuaron con ellos en el siglo XIX. Exploradores y ...etnógrafos europeos publicaron breves descripciones etnográficas y anotaron palabras sueltas en lengua toba que resultan insuficientes para analizar su lengua. La falta de datos lingüísticos impide corroborar nuestra presunción acerca de vínculos culturales y sociales que históricamente habrían vinculado a los tobas bolivianos con los llamados tobas occidentales de Argentina. En este trabajo, sistematizamos los datos lingüísticos de un vocabulario toba inédito atribuido al franciscano Hermán Cattunar (c. 1911), atendiendo al contexto histórico de su producción. Presentamos la estructura del vocabulario y describimos, desde una perspectiva funcionalista, los pronombres libres, los índices pronominales verbales (Haspelmath 2013; Cysouw 2003), las estrategias de negación (Miestamo 2000, 2006), y los números cardinales registrados por Cattunar. Nuestro análisis contribuye al estudio de posibles procesos de gramaticalización entre lenguas guaycurúes, no detectables al estudiar cada lengua sincrónicamente, y proporciona materiales para investigar la hipótesis de contacto entre los tobas bolivianos y otros tobas de la región.
Much of what we know about the society of Toba peoples in the Bolivian Chaco comes from publications of Franciscan missionaries who interacted with them in the 19th century. European explorers and ethnographers published short ethnographic descriptions and wrote down some words in Toba language, but those are insufficient for analyzing their language. Lack of linguistic data prevents us from corroborating our presumption about cultural and social ties that historically would have linked the Bolivian Tobas with the so-called western Tobas of Argentina. In this work, we systematize linguistic data in an unpublished Toba vocabulary attributed to the Franciscan Hermán Cattunar (c. 1911), considering the context in which it was produced. We present the structure of the vocabulary and describe, from a functionalist perspective, the free pronouns, the verbal pronominal indexes (Haspelmath 2013; Cysouw 2003), the negation strategies (Miestamo 2000, 2006), and the cardinal numbers as recorded by Cattunar. Our analysis contributes to understand possible grammaticalization processes in Guaycuruan languages, undetectable when each language is analyzed synchronically. It also provides materials to investigate the hypothesis of contact between the Bolivian Tobas and other Tobas in the region.
Lineability and Spaceability: A New Approach Fávaro, V. V.; Pellegrino, D.; Tomaz, D.
Boletim da Sociedade Brasileira de Matemática,
03/2020, Letnik:
51, Številka:
1
Journal Article
Recenzirano
The area of research called “Lineability” looks for linear structures inside exotic subsets of vector spaces. In the last decade lineability/spaceability has been investigated in rather general ...settings; for instance, Set Theory, Probability Theory, Functional Analysis, Measure Theory, etc. It is a common feeling that positive results on lineability/spaceability are quite natural (i.e., in general “large” subspaces can be found inside exotic subsets of vector spaces, in quite different settings) and more restrictive approaches have been attempted. In this paper we introduce and explore a new approach in this direction.
In this contribution we propose new methodology to compare interval-valued fuzzy cardinal numbers (IVFCN). The new methods are based on interval subsethood measures which take into account widths of ...the intervals. An application of introduced methodology is presented on an example of decision algorithm for medical diagnosis support.
This paper presents the first empirical investigation that compares Euler and linear diagrams when they are used to represent set cardinality. A common approach is to use area-proportional Euler ...diagrams but linear diagrams can exploit length-proportional straight-lines for the same purpose. Another common approach is to use numerical annotations. We first conducted two empirical studies, one on Euler diagrams and the other on linear diagrams. These suggest that area-proportional Euler diagrams with numerical annotations and length-proportional linear diagrams without numerical annotations support significantly better task performance. We then conducted a third study to investigate which of these two notations should be used in practice. This suggests that area-proportional Euler diagrams with numerical annotations most effectively supports task performance and so should be used to visualize set cardinalities. However, these studies focused on data that can be visualized reasonably accurately using circles and the results should be taken as valid within that context. Future work needs to determine whether the results generalize both to when circles cannot be used and for other ways of encoding cardinality information.
A graph G is called an ℓ-apex tree if there exist a vertex subset A ⊂ V ( G ) with cardinality ℓ such that G − A is a tree and there is no other subset of smaller cardinality with this property. In ...the paper, we investigate extremal values of several monotonic distance-based topological indices for this class of graphs, namely generalized Wiener index, and consequently for the Wiener index and the Harary index, and also for some newer indices as connective eccentricity index, generalized degree distance, and others. For the one extreme value we obtain that the extremal graph is a join of a tree and a clique. Regarding the other extreme value, which turns out to be a harder problem, we obtain results for ℓ = 1 and pose some open questions for higher ℓ. Symmetry has always played an important role in Graph Theory, in recent years, this role has increased significantly in several branches of this field, including topological indices of graphs.
One anaphora (e.g., this is a good one) has been used as a key diagnostic in syntactic analyses of the English noun phrase, and “one‐replacement” has also figured prominently in debates about the ...learnability of language. However, much of this work has been based on faulty premises, as a few perceptive researchers, including Ray Jackendoff, have made clear. Abandoning the view of anaphoric one (a‐one) as a form of syntactic replacement allows us to take a fresh look at various uses of the word one. In the present work, we investigate its use as a cardinal number (1‐one) in order to better understand its anaphoric use. Like all cardinal numbers, 1‐one can only quantify an individuated entity and provides an indefinite reading by default. Owing to unique combinatoric properties, cardinal numbers defy consistent classification as determiners, quantifiers, adjectives, or nouns. Once the semantics and distribution of cardinal numbers, including 1‐one, are appreciated, many properties of a‐one follow with minimal stipulation. We claim that 1‐one and a‐one are distinct but very closely related lexemes. When 1‐one appears without a noun (e.g., Take one), it is nearly indistinguishable from a‐one (e.g., take one)—the only differences being interpretive (1‐one foregrounds its cardinality while a‐one does not) and prosodic (presence versus absence of primary accent). While we ultimately argue that a family of constructions is required to describe the full range of syntactic contexts in which one appears, the proposed network accounts for properties of a‐one by allowing it to inherit most of its syntactic and interpretive constraints from its historical predecessor, 1‐one.
Galileo’s paradox and numerosities Błaszczyk, Piotr
Zagadnienia Filozoficzne w Nauce (Online),
01/2021, Letnik:
70, Številka:
70
Journal Article
Recenzirano
Odprti dostop
Galileo's paradox of infinity involves comparing the set of natural numbers, N, and the set of squares, {n2 : n ∈ N}. Galileo (1638) sets up a one-to-one correspondence between these sets; on this ...basis, the number of the elements of N is considered to be equal to the number of the elements of {n2 : n ∈ N}. It also characterizes the set of squares as smaller than the set of natural numbers, since ``there are many more numbers than squares". As a result, it concludes that infinities cannot be compared in terms of greater--lesser and the law of trichotomy does not apply to them.Cantor's cardinal numbers provide a measure for sets.Cantor (1897) gives a definition of the relation greater–lesser between cardinal numbers and establishes the law of trichotomy for these numbers. Yet, when Cantor's theory is applied to subsets of N, it gives that any set can be either finite or of the power ℵ0. Thus, although the set of squares is the subset of N, they are of the same cardinality.Benci, Di Nasso (2019) introduces specific numbers to measure sets called numerosities. With numerosities, the following claim is true: numerosity of A < numerosity of B, whenever A ⊈ B.In this paper, we present a simplified version of the theory of numerosities that applies to subsets of N. This theory complies with Galileo's presupposition that when A ⊈ B, then the number of elements in A is smaller than the number of elements in B. Specifically, we show that as the numerosity of N is the number α, the numerosity of the set of squares is the integer part of the number √α, that is ⌊√α⌋, and the inequality ⌊√α⌋ < α holds.
In this paper we have obtained the similarity measures between single valued neutrosophic rough sets by analyzing th concept of its distance between them and studied its properties. Further we have ...studied its similarity based on its membership degree and studied its properties. We have also defined the cardinality of two single valued neutrosophic rough sets. A numerical example i medical diagnosis is given for the proposed similarity measure of the single valued neutrosophic rough sets which helps us to prove th usefulness and flexibility of the proposed method. Keywords: Single valued neutrosophic rough sets, similarity measure, cardinality.
packing number of some graph products Mojdeh, Doost Ali; Peterin, Iztok; Samadi, Babak ...
Discrete Mathematics and Theoretical Computer Science,
08/2020, Letnik:
22, Številka:
4
Journal Article
Recenzirano
Odprti dostop
The packing number of a graph G is the maximum number of closed neighborhoods of vertices in G with pairwise empty intersections. Similarly, the open packing number of G is the maximum number of open ...neighborhoods in G with pairwise empty intersections. We consider the packing and open packing numbers on graph products. In particular we give a complete solution with respect to some properties of factors in the case of lexicographic and rooted products. For Cartesian, strong and direct products, we present several lower and upper bounds on these parameters.
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