Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2

proof Related Abstracts

2 Developing Proof Demonstration Skills in Teaching Mathematics in the Secondary School

Authors: M. Rodionov, Z. Dedovets

Abstract:

The article describes the theoretical concept of teaching secondary school students proof demonstration skills in mathematics. It describes in detail different levels of mastery of the concept of proof-which correspond to Piaget’s idea of there being three distinct and progressively more complex stages in the development of human reflection. Lessons for each level contain a specific combination of the visual-figurative components and deductive reasoning. It is vital at the transition point between levels to carefully and rigorously recalibrate teaching to reflect the development of more complex reflective understanding. This can apply even within the same age range, since students will develop at different speeds and to different potential. The authors argue that this requires an aware and adaptive approach to lessons to reflect this complexity and variation. The authors also contend that effective teaching which enables students to properly understand the implementation of proof arguments must develop specific competences. These are: understanding of the importance of completeness and generality in making a valid argument; being task focused; having an internalised locus of control and being flexible in approach and evaluation. These criteria must be correlated with the systematic application of corresponding methodologies which are best likely to achieve success. The particular pedagogical decisions which are made to deliver this objective are illustrated by concrete examples from the existing secondary school mathematics courses. The proposed theoretical concept formed the basis of the development of methodological materials which have been tested in 47 secondary schools.

Keywords: Education, proof, secondary school, teaching of mathematics, deductive reasoning

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1 Moral Rights: Judicial Evidence Insufficiency in the Determination of the Truth and Reasoning in Brazilian Morally Charged Cases

Authors: Rainner Roweder

Abstract:

Theme: The present paper aims to analyze the specificity of the judicial evidence linked to the subjects of dignity and personality rights, otherwise known as moral rights, in the determination of the truth and formation of the judicial reasoning in cases concerning these areas. This research is about the way courts in Brazilian domestic law search for truth and handles evidence in cases involving moral rights that are abundant and important in Brazil. The main object of the paper is to analyze the effectiveness of the evidence in the formation of judicial conviction in matters related to morally controverted rights, based on the Brazilian, and as a comparison, the Latin American legal systems. In short, the rights of dignity and personality are moral. However, the evidential legal system expects a rational demonstration of moral rights that generate judicial conviction or persuasion. Moral, in turn, tends to be difficult or impossible to demonstrate in court, generating the problem considered in this paper, that is, the study of the moral demonstration problem as proof in court. In this sense, the more linked to moral, the more difficult to be demonstrated in court that right is, expanding the field of judicial discretion, generating legal uncertainty. More specifically, the new personality rights, such as gender, and their possibility of alteration, further amplify the problem being essentially an intimate manner, which does not exist in the objective, rational evidential system, as normally occurs in other categories, such as contracts. Therefore, evidencing this legal category in court, with the level of security required by the law, is a herculean task. It becomes virtually impossible to use the same evidentiary system when judging the rights researched here; therefore, it generates the need for a new design of the evidential task regarding the rights of the personality, a central effort of the present paper. Methodology: Concerning the methodology, the Method used in the Investigation phase was Inductive, with the use of the comparative law method; in the data treatment phase, the Inductive Method was also used. Doctrine, Legislative, and jurisprudential comparison was the technique research used. Results: In addition to the peculiar characteristics of personality rights that are not found in other rights, part of them are essentially linked to morale and are not objectively verifiable by design, and it is necessary to use specific argumentative theories for their secure confirmation, such as interdisciplinary support. The traditional pragmatic theory of proof, for having an obvious objective character, when applied in the rights linked to the morale, aggravates decisionism and generates legal insecurity, being necessary its reconstruction for morally charged cases, with the possible use of the “predictive theory” ( and predictive facts) through algorithms in data collection and treatment.

Keywords: proof, Brazil, moral rights, pragmatic proof theory, insufficiency

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