scholarly journals Fostering Representational Flexibility in the Mathematical Working Space of Rational Numbers

2016 ◽  
Vol 30 (54) ◽  
pp. 287-307 ◽  
Author(s):  
Athanasios Gagatsis ◽  
Eleni Deliyianni ◽  
Iliada Elia ◽  
Areti Panaoura ◽  
Paraskevi Michael-Chrysanthou
Keyword(s):  
Rational Numbers ◽  
Developmental Pattern ◽  
Cognitive Level ◽  
Working Space ◽  
Decimal Number ◽  
Mathematical Working Space ◽  
Semiotic Representations ◽  
Hierarchical Levels ◽  
Representational Flexibility ◽  
Over Time

Abstract The study focuses on the cognitive level of Mathematical Working Space (MWS) and the component of the epistemological level related to semiotic representations in two mathematical domains of rational numbers: fraction and decimal number addition. Within this scope, it aims to explore how representational flexibility develops over time. A similar developmental pattern of four distinct hierarchical levels of student representational flexibility in both domains is identified. The findings indicate that the genesis of the semiotic axis in fraction and decimal addition is not automatic, but a long process of developmental steps that could be referred to as MWS1, MWS2, MWS3, MWS4 (final). There is not a clear and stable correspondence between developmental levels of representational flexibility and school grades. Didactical implications in order to foster representational flexibility in the MWS of fraction and decimal addition are discussed.

The Role of Internal Communication in Commitment Management

2012 ◽  
pp. 162-172
Author(s):  
José Antonio Carazo
Keyword(s):  
Human Capital ◽  
Internal Communication ◽  
Competitive Advantages ◽  
Overhead Cost ◽  
Hierarchical Levels ◽  
Sustainable Competitive Advantages ◽  
Special Relevance ◽  
Over Time ◽  
Means Of Production

The economic situation in the last few years has forced companies to adjust their workforces and reduce hierarchical levels. They have also had to undertake overhead cost and expense adjustment programmes, including salary freeze and the reduction of training budgets, amongst others; all of it within an environment where human capital has acquired special relevance. It has been shown that individuals represent enterprises’ main asset, the element that can generate sustainable competitive advantages over time. Power has changed hands; it no longer lies in the traditional means of production, but in knowledge. And knowledge resides in people. Knowledge and people are the new engines of economy. The management of individuals, which is nothing but the management of their intangibles and the need to attract and retain talent, becomes especially important in this context. Commitment management is one of the most effective policies to achieve this aim. Managers must implement policies to commit employees to not only retain them, but also encourage them to do their best. The best tool to achieve this necessary commitment is internal communication. This chapter aims to offer a conceptual reflection on commitment management and analyses the state of internal communication in Spanish companies. The purpose is to establish a link between the emphasis placed by companies on achieving their employees’ commitment and internal communication as a tool that can help to reach that goal.

scholarly journals Order and Equivalence of Rational Numbers: A Cognitive Analysis

1985 ◽  
Vol 16 (1) ◽  
pp. 18-36 ◽  
Author(s):  
Thomas R. Post ◽  
Ipke Wachsmuth ◽  
Richard Lesh ◽  
Merlyn J. Behr
Keyword(s):  
Fourth Grade ◽  
Rational Numbers ◽  
Teaching Experiment ◽  
Cognitive Analysis ◽  
Experiment Data ◽  
Successful Performance ◽  
Fourth Grade Students ◽  
Over Time

Fourth-grade students' understanding of the order and equivalence of rational numbers was investigated in an 18-week teaching experiment. Data from observations of, and interviews with, two children were employed to identify patterns over time in the strategies used in performing tasks. Three related characteristics of thinking are hypothesized to be related to the successful performance of tasks on order and equivalence: (a) thought flexibility in coordinating between-mode translations, (b) thought flexibility for within-mode transformations, and (c) reasoning that becomes increasingly independent of specific concrete embodiments.

scholarly journals Semiotic Representations In The Learning Of Rational Numbers By 2nd Grade Portuguese Students

2021 ◽  
Vol 13 (5) ◽  
pp. 611-624
Author(s):  
Floriano Viseu ◽  
Ana Luísa Pires ◽  
Luís Menezes ◽  
Ana Maria Costa
Keyword(s):  
Rational Numbers ◽  
Semiotic Representations

Is diachronic thought a specific reasoning ability? 1The authors are grateful to Fawzia Campana, Florence Dokic, Stéphanie Jaccard, Rachel Luternauer, Isabelle Maeder, Delphine Rinaldi and Lise Rubin for their important help during the collection and analysis of the data. They also wish to thank the children who participated in the experiment and their teachers for their cooperation.

1999 ◽  
Vol 58 (3) ◽  
pp. 191-200 ◽  
Author(s):  
Francisco Pons ◽  
Jacques Montangero
Keyword(s):  
Cognitive Abilities ◽  
Probabilistic Reasoning ◽  
Spatial Reasoning ◽  
Reasoning Ability ◽  
Cognitive Level ◽  
Change Over Time ◽  
Significant Development ◽  
Dynamic Synthesis ◽  
Effect Of Age ◽  
Over Time

Several experiments have shown that cognitive abilities involved in the representation and understanding of change over time (what we term “diachronic thought”) develop strikingly in various domains between the ages of 8 and 12 years. Do these abilities simply reflect the child's general cognitive level or are they specific reasoning competencies related to change over time? The present research deals with this question and studies the relationships between three tasks assessing diachronic thought (Qualitative transformation, Temporal dissociation and Dynamic synthesis) and two tasks assessing the children's operatory level (Probabilistic reasoning and Spatial reasoning). Each set of tasks was presented during a separate session to 45 children aged 8, 10 and 12 years. As expected, a significant development in the subjects' answers to diachronic and operatory tasks was observed. Moreover, the results revealed that there was a significant correlation between two diachronic tasks and the operatory tasks as long as the effect of age was not controlled, but that only the correlation between tasks in the same set (either diachronic or operatory) remained significant when the age effect was controlled. We interpret these results as showing that diachronic thought, as assessed with our three tasks, can be considered as a specific reasoning ability.

Problem solving and the use of digital technologies within the Mathematical Working Space framework

ZDM ◽  
2016 ◽  
Vol 48 (6) ◽  
pp. 827-842 ◽  
Author(s):  
Manuel Santos-Trigo ◽  
Luis Moreno-Armella ◽  
Matías Camacho-Machín
Keyword(s):  
Problem Solving ◽  
Digital Technologies ◽  
Working Space ◽  
Mathematical Working Space
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