期刊名称：Bolema: Mathematics Education Bulletin = Bolema: Boletim de Educação Matemática
印刷版ISSN：1980-4415
出版年度：2008
卷号：21
期号：31
页码：79-102
语种：Portuguese
出版社：UNESP - Campus de Rio Claro - Instituto de Geociências e Ciências Exatas
摘要：We address the different “personalities” of the rational number and the concept of proportionality, analyzing the possibilities for using the Mathematics Teaching and Learning through Problem-solving Method. This method is based on the principle that knowledge can be constructed through the use of problems that generate new concepts and new contents. The different meanings of rational number – rational point, quotient, fraction, ratio, and operator – are constructs that depend on mathematical theories in which they are imbedded and the situations that evoke them in problem-solving. Some data will be presented from continuing education courses for teachers, aiming to contribute to understanding regarding the different “personalities” of the rational number. In general, these “personalities” are not easily identified by teachers and students, which is the reason for the many difficulties encountered during problem-solving involving rational numbers. One of these “personalities”, the ratio, provides the basis for the concept of proportionality, which is relevant because it is a unifying idea in mathematics. Key-words: Rational Numbers and Proportionality. Problem Solving. Teacher Education.
其他摘要：We address the different “personalities” of the rational number and the concept of proportionality, analyzing the possibilities for using the Mathematics Teaching and Learning through Problem-solving Method. This method is based on the principle that knowledge can be constructed through the use of problems that generate new concepts and new contents. The different meanings of rational number – rational point, quotient, fraction, ratio, and operator – are constructs that depend on mathematical theories in which they are imbedded and the situations that evoke them in problem-solving. Some data will be presented from continuing education courses for teachers, aiming to contribute to understanding regarding the different “personalities” of the rational number. In general, these “personalities” are not easily identified by teachers and students, which is the reason for the many difficulties encountered during problem-solving involving rational numbers. One of these “personalities”, the ratio, provides the basis for the concept of proportionality, which is relevant because it is a unifying idea in mathematics. Key-words: Rational Numbers and Proportionality. Problem Solving. Teacher Education.
