scholarly journals Engaging Young Children with Mathematical Activities Involving Different Representations: Triangles, Patterns, and Counting Objects

2018 ◽  
Vol 8 (2) ◽  
pp. 9 ◽  
Author(s):  
Dina Tirosh ◽  
Pessia Tsamir ◽  
Ruthi Barkai ◽  
Esther Levenson
Keyword(s):  
Young Children ◽  
Mathematical Concept ◽  
External Representations ◽  
Multiple External Representations ◽  
Stable Order ◽  
Critical Attribute ◽  
One To One ◽  
The One ◽  
Repeating Patterns ◽  
Mathematical Activities

This paper synthesises research from three separate studies, analysing how different representations of a mathematical concept may affect young children’s engagement with mathematical activities. Children between five and seven years old engaged in counting objects, identifying triangles and completing repeating patterns. The implementation of three counting principles were investigated: the one-to-one principle, the stable-order principle and the cardinal principal. Children’s reasoning when identifying triangles was analysed in terms of visual, critical and non-critical attribute reasoning. With regard to repeating patterns, we analyse children’s references to the minimal unit of repeat of the pattern. Results are discussed in terms of three functions of multiple external representations: to complement, to constrain and to construct. 

Influence of Rim Run-Out on the Nonuniformity of Tire-Wheel Assemblies

1994 ◽  
Vol 22 (2) ◽  
pp. 99-120 ◽  
Author(s):  
T. B. Rhyne ◽  
R. Gall ◽  
L. Y. Chang
Keyword(s):  
Finite Element ◽  
Radial Force ◽  
Membrane Model ◽  
Model Experiments ◽  
Force Variation ◽  
One To One ◽  
The One

Abstract An analytical membrane model is used to study how wheel imperfections are converted into radial force variation of the tire-wheel assembly. This model indicates that the radial run-out of the rim generates run-out of the tire-wheel assembly at slightly less than the one to one ratio that was expected. Lateral run-out of the rim is found to generate radial run-out of the tire-wheel assembly at a ratio that is dependent on the tire design and the wheel width. Finite element studies of a production tire validate and quantify the results of the membrane model. Experiments using a specially constructed precision wheel demonstrate the behavior predicted by the models. Finally, a population of production tires and wheels show that the lateral run-out of the rims contribute a significant portion to the assembly radial force variation. These findings might be used to improve match-mounting results by taking lateral rim run-out into account.

Tree Rewriting Systems, Combinatory Weak Reduction Systems and Type Free Languages1

1982 ◽  
Vol 5 (3-4) ◽  
pp. 279-299
Author(s):  
Alberto Pettorossi
Keyword(s):  
Combinatory Logic ◽  
Rewriting Systems ◽  
Tree Transducers ◽  
Tree Languages ◽  
One To One ◽  
The One ◽  
Weak Reduction

In this paper we consider combinators as tree transducers: this approach is based on the one-to-one correspondence between terms of Combinatory Logic and trees, and on the fact that combinators may be considered as transformers of terms. Since combinators are terms themselves, we will deal with trees as objects to be transformed and tree transformers as well. Methods for defining and studying tree rewriting systems inside Combinatory Weak Reduction Systems and Weak Combinatory Logic are also analyzed and particular attention is devoted to the problem of finiteness and infinity of the generated tree languages (here defined). This implies the study of the termination of the rewriting process (i.e. reduction) for combinators.

In search of the perfect orthography

2005 ◽  
Vol 7 (2) ◽  
pp. 139-163 ◽  
Author(s):  
Richard L. Venezky
Keyword(s):  
Writing System ◽  
Writing Systems ◽  
International Phonetic Alphabet ◽  
Experienced Reader ◽  
Cultural Considerations ◽  
Advanced Stages ◽  
One To One ◽  
The One ◽  
Psychological Processing ◽  
The Ideal

Philologists, linguists, and educators have insisted for several centuries that the ideal orthography has a one-to-one correspondence between grapheme and phoneme. Others, however, have suggested deviations for such functions as distinguishing homophones, displaying popular alternative spellings, and retaining morpheme identity. If, indeed, the one-to-one ideal were accepted, the International Phonetic Alphabet should become the orthographic standard for all enlightened nations, yet the failure of even a single country to adopt it for practical writing suggests that other factors besides phonology are considered important for a writing system. Whatever the ideal orthography might be, the practical writing systems adopted upon this earth reflect linguistic, psychological, and cultural considerations. Knowingly or unknowingly, countries have adopted orthographies that favour either the early stages of learning to read or the advanced stages, that is, the experienced reader. The more a system tends towards a one-to-one relationship between graphemes and phonemes, the more it assists the new reader and the non-speaker of the language while the more it marks etymology and morphology, the more it favours the experienced reader. The study of psychological processing in reading demonstrates that human capacities for processing print are so powerful that complex patterns and irregularities pose only a small challenge. Orthographic regularity is extracted from lexical input and used to recognise words during reading. To understand how such a system develops, researchers should draw on the general mechanisms of perceptual learning.

Development of a Single-Code/Default Coding Strategy in Pigeons

2000 ◽  
Vol 11 (3) ◽  
pp. 261-264 ◽  
Author(s):  
Tricia S. Clement ◽  
Thomas R. Zentall
Keyword(s):  
Conditional Discrimination ◽  
The Other ◽  
Matching Accuracy ◽  
Efficient Coding ◽  
Coding Strategy ◽  
One To One ◽  
Retention Intervals ◽  
The Many ◽  
The One ◽  
Better Than

We tested the hypothesis that pigeons could use a cognitively efficient coding strategy by training them on a conditional discrimination (delayed symbolic matching) in which one alternative was correct following the presentation of one sample (one-to-one), whereas the other alternative was correct following the presentation of any one of four other samples (many-to-one). When retention intervals of different durations were inserted between the offset of the sample and the onset of the choice stimuli, divergent retention functions were found. With increasing retention interval, matching accuracy on trials involving any of the many-to-one samples was increasingly better than matching accuracy on trials involving the one-to-one sample. Furthermore, following this test, pigeons treated a novel sample as if it had been one of the many-to-one samples. The data suggest that rather than learning each of the five sample-comparison associations independently, the pigeons developed a cognitively efficient single-code/default coding strategy.

Intervention in Psychiatric Nursing; Process in the One-to-One Relationship

1970 ◽  
Vol 70 (11) ◽  
pp. 2450
Author(s):  
Ilse S. Wolff ◽  
Joyce Travelbee
Keyword(s):  
Psychiatric Nursing ◽  
Nursing Process ◽  
One To One ◽  
The One

Balancing the One-To-One Equation: Equity and Access in Three Laptop Programs

2014 ◽  
Vol 47 (1) ◽  
pp. 46-62 ◽  
Author(s):  
Mark Warschauer ◽  
Binbin Zheng ◽  
Melissa Niiya ◽  
Shelia Cotten ◽  
George Farkas
Keyword(s):  
Laptop Programs ◽  
Equity And Access ◽  
One To One ◽  
The One

scholarly journals O Problema do Poder Efetivo na Câmara dos Deputados

2021 ◽  
Author(s):  
Renan Barbosa de Morais ◽  
Mário César San Felice ◽  
Pedro Henrique Del Bianco Hokama ◽  
Gabriel Ávila Casalecchi
Keyword(s):  
Game Theory ◽  
Empirical Research ◽  
Power Index ◽  
Political Representation ◽  
Political Process ◽  
Mathematical Concept ◽  
The Political ◽  
Effective Power ◽  
The One ◽  
Index Problem

Proportionality in political representation is an essential theme forrepresentative democracy. In Brazil, this debate appears in the contextof non-proportionality between a federative unit’s populationsize and its number of representatives in the Chamber of Deputies.In other words, the number of deputies in a state is not proportionalto its number of inhabitants, which violates the "one man, one vote"principle.Discussions around this disproportionality have motivated scholarsto develop empirical research that aims to identify the causesand consequences of the phenomenon and to analyze the impactthat the rule introduces in the political process. This article seeksto contribute to this debate by measuring the effective power ofeach Brazilian federation’s entity and proposing alternatives ofdistribution for the Brazilian Chamber of Deputies.To this end, we use a mathematical concept from game theory,called Power Index, which allows quantifying the existing representationaldiscrepancies. After evaluating several distributions, wesolved the Inverse Power Index Problem (IPIP) to obtain a distributionof chairs that reduces such disparities. To solve the IPIP, whichis computationally hard, we use an evolutionary heuristic. As anobjective function to minimize the discrepancy, we use the linearShapley rule, in which the power index of each state is proportionalto its population.

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