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Books on the topic 'Non-arithmetic'

Author: Grafiati

Published: 4 June 2021

Last updated: 17 February 2022

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1

Charles, Sayward, and Garavaso Pieranna, eds. Arithmetic and ontology: A non-realist philosophy of arithmetic. Amsterdam: Rodopi, 2006.

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2

Hilbert, David. Anschauliche Geometrie. 2nd ed. Berlin: Springer, 2011.

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3

Moduli spaces and arithmetic dynamics. Providence, R.I: American Mathematical Society, 2012.

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4

Arakelov geometry. Providence, Rhode Island: American Mathematical Society, 2014.

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5

Tschinkel, Yuri, Carlo Gasbarri, Steven Lu, and Mike Roth. Rational points, rational curves, and entire holomorphic curves on projective varieties: CRM short thematic program, June 3-28, 2013, Centre de Recherches Mathematiques, Universite de Montreal, Quebec, Canada. Providence, Rhode Island: American Mathematical Society, 2015.

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6

1978-, Ghioca Dragos, and Tucker Thomas J. 1969-, eds. The dynamical Mordell-Lang conjecture. Providence, Rhode Island: American Mathematical Society, 2016.

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7

Germany) International Conference on p-adic Functional Analysis (13th 2014 Paderborn. Advances in non-Archimedean analysis: 13th International Conference on p-adic Functional Analysis, August 12-16, 2014, University of Paderborn, Paderborn, Germany. Edited by Glöckner Helge 1969 editor, Escassut Alain editor, and Shamseddine Khodr 1966 editor. Providence, Rhode Island: American Mathematical Society, 2016.

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8

Barbados) Bellairs Workshop in Number Theory (2011 Holetown. Tropical and non-Archimedean geometry: Bellairs Workshop in Number Theory, May 6-13, 2011, Bellairs Research Institute, Holetown, Barbados. Edited by Amini, Omid, 1980- editor of compilation, Baker, Matthew, 1973- editor of compilation, and Faber, Xander, editor of compilation. Providence, Rhode Island: American Mathematical Society, 2013.

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9

Applegate, Katherine. The visitor. New York: Scholastic Inc., 2011.

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10

Agrillo, Christian. Numerical and Arithmetic Abilities in Non-primate Species. Edited by Roi Cohen Kadosh and Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.002.

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In the last decade, several studies have suggested that dozens of animal species are capable of processing numerical information. Animals as diverse as mammals, birds, amphibians, fish, and even some invertebrates have been successfully investigated through extensive training and the observation of spontaneous behaviour, providing evidence that numerical abilities are not limited to primates. The study of non-primate species represents a useful tool to broaden our comprehension of the uniqueness of our cognitive abilities, particularly with regard to the evolutionary roots of the mathematical mind. In this chapter, I will summarize the current state of our understanding of non-primate numerical abilities in the comparative literature, focusing on three main topics: the relationship between discrete (numerical) and continuous quantity, the debate surrounding the existence of a precise subitizing-like process, and the ontogeny of numerical abilities.

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11

Gilmore, Camilla. Approximate Arithmetic Abilities in Childhood. Edited by Roi Cohen Kadosh and Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.006.

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This article reviews recent research exploring children’s abilities to perform approximate arithmetic with non-symbolic and symbolic quantities, and considers what role this ability might play in mathematics achievement. It has been suggested that children can use their approximate number system (ANS) to solve approximate arithmetic problems before they have been taught exact arithmetic in school. Recent studies provide evidence that preschool children can add, subtract, multiply, and divide non-symbolic quantities represented as dot arrays. Children can also use their ANS to perform simple approximate arithmetic with non-symbolic quantities presented in different modalities (e.g. sequences of tones) or even with symbolic representations of number. This article reviews these studies, and consider whether children’s performance can be explained through the use of alternative non-arithmetical strategies. Finally, it discusses the potential role of this ability in the learning of formal symbolic mathematics.

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12

(Editor), Philip Hugly, and Charles Sayward (Editor), eds. Arithmetic and Ontology: A Non-Realist Philosophy of Arithmetic. Edited by Pieranna Garavaso (Poznan Studies 90) (Poznan Studies in Philosophy of the Sciences and the Humanities). Editions Rodopi BV., 2006.

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13

Covarrubias Díaz, Felipe. Evaluación de la Contribución de las Capacidades Numéricas Básicas y de la Memoria de Trabajo al Rendimiento Aritmético en Niños de Edad Escolar. Universidad Autónoma de Chile, 2019. http://dx.doi.org/10.32457/20.500.12728/88642019mnc12.

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Introduction: There are several causes and explanations of the cognitive mechanisms that underlie the deficits of mathematical learning difficulties. Several studies have evaluated the relations among general domain cognitive abilities (like intellectual coefficient and working memory (WM)) or cognitive abilities of specific domain; However, there are a few studies that evaluate simultaneously the contribution of cognitive variables of both domains to the arithmetic efficiency. Aim: The present study aims to simultaneously evaluate the unique contribution of the basic numerical capacities (BNC-subitizing, counting and symbolic and non-symbolic comparison) and the different components of WM (verbal and visual-spatial) to the explanation of the variance in academic achievement in basic arithmetic, in third-year students of Basic General Education with and without difficulties in basic arithmetic Methodology: A sample of 93 children was evaluated through computerized tests of BNC and working memory tasks: A group of 25 children with arithmetic learning difficulties (ALD) and 68 children without difficulties in arithmetic (NAD). Results: We found that the symbolic comparison and visuo-spatial WM contribute significantly to efficiency in basic arithmetic. Discussion: The results support the hypothesis of a deficit in the access to the symbolic numerical representations as the origin of the difficulties in the performance in arithmetic and show that certain skills of general domain (WM) contribute significantly to the development of mental numerical representations. Conclusions: It is interesting to evaluate the predictive capacity of these variables, delving into pedagogical issues related to assessment and intervention in mathematics.

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14

Button, Tim, and Sean Walsh. Internal categoricity and the sets. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198790396.003.0011.

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As the previous chapter discussed the internalist perspective on the categoricity of arithmetic, this chapter presents the internalist perspective on sets. In particular, we show both how to internalise Scott-Potter set theory its quasi-categoricity theorem, and how to internalise Zermelo’s Quasi-Categoricity Theorem. As in the case of arithmetic, this gives a non-semantic way to draw the boundary between algebraic and univocal theories. A particularly compelling case of the quasi-univocity of set theory revolves around the continuum hypothesis. Furthermore, by additionally postulating that the size of the pure sets is the same as the size of the universe, these famous quasi-categoricity results can actually be turned into internal categoricity results simpliciter, so that one has full univocity instead of mere quasi-univocity. In the appendices we prove these results, and we discuss how they relate to important work by McGee and Martin.

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15

Koons, Robert C. The General Argument from Intuition. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780190842215.003.0015.

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Argument Q, the seventeenth argument in Plantinga’s battery, concerns the problem of explaining how we can take seriously our capacity for intuition in such areas as logic, arithmetic, morality, and philosophy. This argument involves a comparison between theistic and non-theistic accounts of these cognitive capacities of human beings. The argument can take three forms: an inference to the best explanation, an appeal to something like the causal theory of knowledge, and an argument turning on the potential threat of undercutting epistemic defeaters concerning the reliability of intuition. All three support the conclusion that we can have intuitive knowledge only if the reliability of that intuition is adequately grounded, as it can be by God’s creation of us.

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16

Rational Points and Arithmetic of Fundamental Groups Lecture Notes in Mathematics. Springer, 2012.

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17

Button, Tim, and Sean Walsh. Categoricity and the natural numbers. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198790396.003.0007.

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This chapter focuses on modelists who want to pin down the isomorphism type of the natural numbers. This aim immediately runs into two technical barriers: the Compactness Theorem and the Löwenheim-Skolem Theorem (the latter is proven in the appendix to this chapter). These results show that no first-order theory with an infinite model can be categorical; all such theories have non-standard models. Other logics, such as second-order logic with its full semantics, are not so expressively limited. Indeed, Dedekind's Categoricity Theorem tells us that all full models of the Peano axioms are isomorphic. However, it is a subtle philosophical question, whether one is entitled to invoke the full semantics for second-order logic — there are at least four distinct attitudes which one can adopt to these categoricity result — but moderate modelists are unable to invoke the full semantics, or indeed any other logic with a categorical theory of arithmetic.

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18

Graham, Patricia Albjerg. Schooling America. Oxford University Press, 2005. http://dx.doi.org/10.1093/oso/9780195172225.001.0001.

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In this informative volume, Patricia Graham, one of America's most esteemed historians of education, offers a vibrant history of American education in the last century. Drawing on a wide array of sources, from government reports to colorful anecdotes, Graham skillfully illustrates Americans' changing demands for our schools, and how schools have responded by providing what critics want, though never as completely or as quickly as they would like. In 1900, as waves of immigrants arrived, the American public wanted schools to assimilate students into American life, combining the basics of English and arithmetic with emphasis on patriotism, hard work, fair play, and honesty. In the 1920s, the focus shifted from schools serving a national need to serving individual needs; education was to help children adjust to life. By 1954 the emphasis moved to access, particularly for African-American children to desegregated classrooms, but also access to special programs for the gifted, the poor, the disabled, and non-English speakers. Now Americans want achievement for all, defined as higher test scores. While presenting this intricate history, Graham introduces us to the passionate educators, scholars, and journalists who drove particular agendas, as well as her own family, starting with her immigrant father's first day of school and ending with her own experiences as a teacher. Invaluable background in the ongoing debate on education in the United States, this book offers an insightful look at what the public has sought from its educational institutions, what educators have delivered, and what remains to be done.

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19

D, Matthews Dawn, ed. Learning disabilities sourcebook: Basic consumer health information about learning disabilities, including dyslexia, developmental speech and language disabilities, non-verbal learning disorders, developmental arithmetic disorder, developmental writing disorder, and other conditions that impede learning such as attention deficit/hyperactivity disorder, brain injury, hearing impairment, Klinefelter syndrome, dyspraxia, and Tourette syndrome, along with facts about educational issues and assistive technology, coping strategies, a glossary of related terms, and resources for further help and information. 2nd ed. Detroit, MI: Omnigraphics, 2003.

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