Numbers

Lim and Leek (2012) presented a formalization of information along object contours, which they argued was an alternative to the approach taken in our article (Feldman & Singh, 2005). Here, we summarize the 2 approaches, showing that--notwithstanding Lim and Leek's (2012) critical rhetoric--their approach is substantially identical to ours, except for the technical details of the formalism. Following the logic of our article point by point, Lim and Leek (a) defined probabilistic expectations about the geometry of smooth contours (which they based on differential contour geometry, while we used a discrete approximation--the only essential difference in their approach), (b) assumed that information along the contour was proportional to the negative logarithm of probability, following standard information theory, and then (c) extended this formulation to closed contours. We analyze what they described as errors in our approach, all of which rest on mathematical misunderstandings or ...

Abstract: In nonprofit settings, numbers are ubiquitous. Therefore, when Spanish community service-learning (CSL) students work in nonprofits, they, too, must manage and manipulate numbers accurately-in Spanish. This can be surprisingly difficult for second language learners of Spanish. This chapter details the author's experiences with upper-level Spanish CSL students enrolled in a language for specific purposes (LSP) course about social entrepreneurship who volunteer in local nonprofits. In nonprofits serving Latino immigrants, the seemingly simple-numbers-is embedded within the complexities of the immigrant experience in the United States today. LSP instructors should explicitly address numeracy to prepare students for professional tasks that require accuracy and to better understand the issues behind the numbers.
Resumen: Los números son ubicuos en las organizaciones sin ánimo de lucro. Por eso, los estudiantes en los cursos de aprendizaje-servicio comunitario (ApSC) que prestan servicio en una asociación sin fines lucrativos necesitan usar los números correctamente-y en español. Para los aprendices de español como segunda lengua, esto puede ser muy difícil. Este artículo describe las experiencias de la autora con los estudiantes en un curso avanzado de español para fines específicos en que se estudia el emprendimiento social y los estudiantes prestan servicio en organizaciones sin fines de lucro. Hay que preparar a los estudiantes a usar los números y a entender el contexto sumamente complejo de los inmigrantes en los EE. UU. en que surgen esos números. Palabras clave: español para fines específicos, aprendizaje-servicio comunitario, emprendimiento social, organizaciones sin ánimo de lucro, números

Forty-five children with mathematics learning disabilities, with and without comorbid reading disabilities, were compared to 45 normally achieving peers in tasks assessing basic numerical skills. Children with mathematics disabilities were only impaired when comparing Arabic digits (i.e., symbolic number magnitude) but not when comparing collections (i.e., non-symbolic number magnitude). Moreover, they automatically processed number magnitude when comparing the physical size of Arabic digits in an Stroop paradigm adapted for processing speed differences. Finally, no evidence was found for differential patterns of performance between MD and MD/RD children in these tasks. These findings suggest that children with mathematics learning disabilities have difficulty in accessing number magnitude from symbols rather than in processing numerosity per se.

IT IS often claimed that young children do not understand the principle of the invariance of quantity. This conclusion is based on the results of the well-known conservation experiments by Piaget and Szeminska (1952) which apparently show that children below 7 or 8 yr ...

Humans show a remarkable tendency to describe and think of numbers as being placed on a mental number line (MNL), with smaller numbers located on the left and larger ones on the right. Faster responses to small numbers are indeed performed on the left side of space, while responses to large numbers are facilitated on the right side of space (spatial-numerical association of response codes, SNARC effect). This phenomenon is considered the experimental demonstration of the MNL and has been extensively replicated throughout a variety of paradigms. Nevertheless, the majority of previous literature has mainly investigated this effect by means of response times and accuracy, whereas studies considering more subtle and automatic measures such as kinematic parameters are rare (e.g., in a reaching-to-grasp movement, the grip aperture is enlarged in responding to larger numbers than in responding to small numbers). In this brief review we suggest that numerical magnitude can also affect the what and how of action execution (i.e., temporal and spatial components of movement). This evidence could have large implications in the strongly debated issue concerning the effect of experience and culture on the orientation of MNL. In the 19th century Galton first noted that humans visualize and think of numbers as represented on a mental number line (MNL), usually oriented from left-to-right. Along the MNL smaller numbers are located on the left side and larger ones on the right side (Galton, 1880; Dehaene, 2011). The first, and often replicated, experimental demonstration of the MNL is the fact that adult humans are faster at processing small numbers when responses are executed on the left side of space, and at processing large numbers when responses are executed on the right side of space (spatial-numerical association of response codes, SNARC effect; Dehaene et al., 1993). Since this first evidence, large body of studies have investigated the cognitive representation of numbers using chronometric methods, but the impact of number processing on motor control has been scarcely explored. According to a recent influential hypothesis, cognitive representations of perceptual and semantic information cannot be fully understood without considering their impact on actions (Gallese and Lakoff, 2005). In this vein, here we present a critical review to highlight how the existing knowledge on MNL could be fostered by studies that critically analyze the link between motor actions and numbers.

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In 2013, Ecuadorian President Rafael Correa announced the end of the Yasuní-ITT initiative. The initiative had proposed to combat climate change by not exploiting oil reserves in one section of the Yasuní National Park. Anticipating outcry, Correa promised that operations would affect less than one thousandth of the park, or “menos del uno por mil.” This article examines the role of numerical calculations in the governance of subterranean resources. Numbers do a particular kind of labor to rationalize the shift contained in the Yasuní-ITT initiative that rhetoric alone does not. Metrics such as el uno por mil constitute and translate between diverse realms of value. Yet, contrary to the assumption that numbers are derived from strictly technical, expert processes, I show how such metrics are fundamental to translations between incalculable matters of nature, the future, and the “good” when deployed in contests over the effects of oil on life.

L’heure, la qualité d’un restaurant, la température, le taux de chômage, le QI, la durée d’un entrainement, la réussite d’un lycée, la richesse, une côte de popularité... Il semble impossible d’échapper aux chiffres ! Mais à quoi servent-ils exactement ? D’où viennent-ils ? Et pourquoi met-on le monde en chiffres ?
Les chiffres régissent une bonne partie de nos vies : ils servent à coordonner nos actions, à établir des règles de vie commune et à trouver des conventions au sein des collectifs. Ils contribuent aux prises de décision et à l’exercice du pouvoir. Ils participent à nos quêtes de justice et d’harmonie, et à la construction de la confiance. Et ils prétendent aussi refléter la réalité de façon objective.
La puissance des chiffres provient-elle de leur capacité à énoncer des certitudes, de notre soumission volontaire à des artifices utiles, de leur aptitude à fabriquer un monde et à nous l’imposer, ou des leviers qu’ils nous offrent pour s’entendre et agir ?
À travers une analyse sociologique et historique de la quantification, Olivier Martin nous montre toute l’étendue de l’empire des chiffres dans nos sociétés.

Olivier Martin, sociologue et statisticien, est professeur à l’Université de Paris et dirige le Centre de recherche sur les liens sociaux (CERLIS - CNRS).

This article reports on the activity of two pairs of sixth grade students who participated in an 8-month teaching experiment that investigated the students’ construction of fraction composition schemes. A fraction composition scheme consists of the operations and concepts used to determine, for example, the size of 1/3 of 1/5 of a whole in relation to the whole. Students’ whole number multiplicative concepts were found to be critical constructive resources for students’ fraction composition schemes. Specifically, the interiorization of two levels of units, a particular multiplicative concept, was found to be necessary for the construction of a unit fraction composition scheme, while the interiorization of three levels of units was necessary for the construction of a general fraction composition scheme. These findings contribute to previous research on students’ construction of fraction multiplication that has emphasized partitioning and conceptualizing quantitative units. Implications of the findings for teaching are considered.

Several researchers have noted how children’s whole number schemes can interfere with their efforts to learn fractions. An Australian study found that children who were successful with the solution of rational number tasks exhibited greater whole number knowledge and more flexible solution strategies. Behr and Post (1988) indicated that children needed to be competent in the four operations of whole numbers, along with an understanding of measurement, for them to understand rational numbers. This paper describes a “hands on” approach developed by researchers that focuses on the use of paper folding, fraction walls and number lines to develop an understanding of fractions using a measurement model.

People these days know the Universe as a Whole, because not knowing the edge between This and That. Its secret is the secret of a forgotten body, the seventh in the series of multifaceted as Life, Seven. We know six of it now. But the Ancestors knew all seven. // Люди ныне не знают Вселенной как Целого, не зная грани меж Этим и Тем. Тайна  ее есть тайна забытого тела, седьмого в строю многогранных как Жизнь, Семь. Мы знаем шесть ныне. А Пращуры знали все семь.

Literacy educators have been actively theorising the demands of literacy in New Times yet mathematics educators have taken little of this debate up. If, as literacy educators suggest, literacy demands are different in these New Times, what are the implications for numeracy or mathematics educators? This paper explores perceptions of young and older people who are engaged in work practices. It was found that there were statistically significant differences in a number of areas. Numeracy was found to be an important variable in discerning differences between older and younger people, and that technology was also seen to differentiate the two cohorts. Within numeracy, older people were more like to see number as important, whereas younger people were more likely to identify statistics, applied areas of mathematics and the use of technology to support numeracy as being important. These finding shave implications for theorising and practice in mathematics education.

Decimal Numbers:-Base 10 uses ten digits = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Binary Numbers:-Base 2 uses 2 digits = 0, 1 Octal Numbers:-Base 8 uses 8 digits = 0, 1, 2, 3, 4, 5, 6, 7 Hexadecimal Numbers:-Base 16 uses 16 digits = 0, 1, 2, 3, 4, ……., 14, 15-{ A=10 }, { B=11 }, { C=12 }, { D=13}, { E=14 }, { F=15 } > These conversion shows how to convert any base to decimal… • Converting Octal to Decimal…. • Example : 1234568 = (1x8 5) + (2x8 4) + (3x8 3) + (4x8 2) + (5x8 1) + (6x8 0) = 4279810 • Converting Hexadecimal to decimal…. • Example : ABC123 16 = (Ax16 5) + (Bx16 4) + (Cx16 3) + (1x16 2) + (2x16 1) + (3x16 0) = (10x16 5) + (11x16 4) + (12x16 3) + (1x16 2) + (2x16 1) + (3x16 0) = 17388410 • Converting Binary to decimal…. • Example : 110101 2 = (1x2 5) + (1x2 4) + (1x2 2) + (1x2 0) = 5310 *Tiny numbers that are written under each number system shows what number system is that ,for example: 2 means Binary, 8 means Octal, 10 means Decimal, 16 means Hexadecimal..

This article seeks to examine how a theological reflection on the priestly emolument in Numbers 18:8-32 would enhance a better interpretation of stewardship amongst believing communities in Africa. Dependency syndrome amongst most African churches, especially those established by Europeans has robbed them of the prestige of adopting a self-supporting/propagating programme. The thesis of this paper maintains that a good synchronization of the tradition-historical exegetical method proposed by Gnuse will facilitate a good interpretation of the priestly emoluments in Numbers 18 and their subsequent application to the church in Africa today. Comparable texts from the Ancient Near East that may have influenced Numbers 18 were surveyed; the possible oral pre-history of Numbers 18 was scrutinized; the connection of Numbers 18 to other priestly traditions was examined; and the use or interpretation of the pericope by the wider biblical tradition concluded the study. The practice of tithes i...

«Everything is Number», says Pythagoras. This is the truth: the essence of the Number is the being of beings, their I: if it is numered, then it exists. Therefore, ignorance of the Number and neglect of it are destructive for us. An example of this is the number Eleven, the Entrance to Heaven. Its guardian, Apollo-Phoebus execute those who betray on it.
// «Всё есть Число», — говорит Пифагор. Это истинно так: суть Числа — бытие сущих, Я их: что числимо — есть. Поэтому незнание Числа и небрежение им губительны для нас. Пример тому — число Одиннадцать, Вход в Небеса. Страж его, Аполлон-Феб казнит за измену ему.

Filosofie čísla [Philosophy of Number], Filosofia, Praha 2008, 672 s.

The book deals with basic principles of arithmetic and calculus from the perspective of modern logic. The central line of the text examines the concept of real number or, more precisely, the concept of continuum in its development, beginning with Eudoxus, Descartes and Leibniz, through Bolzano, Cantor and Dedekind, to Frege, Brouwer, Hilbert and Wittgenstein. Every significant movement in the philosophy of mathematics (Platonism, formalism, intuitionism, logicism, constructivism, structuralism etc.) is covered, not abstractly, but against the background of particular results or phenomena of modern logic and mathematics. Among those mentioned are Cantor’s diagonal argument, Dedekind’s recursion theorem, Bolzano’s intermediate value theorem, Russell’s paradox along with other logical paradoxes, Zermelo’s well-ordering theorem, Skolem’s paradox, Hilbert’s program, and Gödel’s theorems. The book also contains the author’s own original results relating to the untenability of a structuralistic (re)interpretation of Frege’s logicism (in the neo-logicism of Wright and Hale) and a complex defense of semantic holism including its most radical inferentialist version. In mathematics, this is done against the background of the exegesis of Hilbert’s works.

All the fields of Mathematics-‘Algebra’, ‘Trigonometry’, ‘Geometry’, ‘Calculus’ and ‘Statistics’ are based on the Patterns, Shapes and Numbers and thus we can conclude that Mathematics is based on Pattern, Shapes and Numbers. Defining mathematics is always been keen concern of mathematicians as well as any introduction math class. One way of definition is defining it by “what it does in the era?” and that is the definition of mathematics for the era. So, in this era of analytical science where everyday people are dealing with lots and lots of data analysis in each and every field, the Pattern, Shapes and Numbers have become the limelight of Mathematics-Research and now mathematics has grown from just solving sums to an experimentation and observation, finding relation to the real world and thus it involves science which brings us to conclusion, “Mathematics is the Science of Patterns, Shapes and Numbers.” Thus, Mathematics can be defined as the science of “Pattern, Shapes and Numbers”.

This module deals with fractions. This includes how to order and compare fractions and how to perform operations on fractions and apply these basic concepts to problem-solving. This module also includes common errors committed by students in dealing with fractions. The module is divided into three lessons, namely: Lesson 1 – Rational Numbers with subtopics, Changing Fractions to Decimals and Changing Decimals to Fractions; Lesson 2 – Rational Numbers on the Number Line, and Lesson 3 – Operations with Fractions with subtopics Addition and Subtraction and Multiplication and Division.

This article outlines a history of numerical knowledge. It focuses on the  forms of use that were developed for dealing with numbers. I begin with the act of counting and the notation of numbers (B); move from the role of numerals in medieval writing practices (C.) to the practices of measuring (D.) and calculating (E.); and close with comments on medieval theory building (F.), on speculative interpretations of numbers (G.), and with a short conclusion (H.).

In doing so, the article focuses on the phenomenality of number—i.e., number as a spoken counting word (B.); as a graphic figure carved in wood or written on parchment (B.); as a formal pattern that organizes books and memory (C.); as a verbal expression for the documentation of quantities (D.); as a manual or symbolic instrument of calculation (E.); as a formally structured multitude determined by arithmetic properties (F.), which as symbolic carriers organize interpretation processes as well as the production of texts and works of art (G.). Thus, the approach allows for an exploration of how these varying phenomenons of number incorporate different kinds of semantic saturation that derive from the various fields of its use. As a result, this focus also contributes to dissolving traditional disciplinary gaps, especially the opposition between the history of science, which traditionally deals with the history of numerical knowledge, and historical branches of the humanities, which handle semantic and narrative phenomena.

Shapes defined by the golden ratio have long been considered aesthetically pleasing in western cultures, reflecting nature's balance between symmetry and asymmetry. The ratio is still used frequently in art and design. The golden ratio is also known as the golden mean, golden section, golden number or divine proportion.It is usually denoted by the Greek letter  (phi).

Numeration systems vary widely across traditional societies in the world. From reported societies in the Amazon with no numbers at all, to widespread spread numeration systems which count only to three, to the elaborate numerology of Ancient India which conceived of numbers larger than the atoms in the universe and the  ‘long count’ of the Maya, systems very wildly. This paper argues that part of the answer may lie in the phenomenon of savant calculators who somehow infiltrate their private fascinations into a cultural nexus.