Current mathematics curricula have as one of their fundamental objectives the development of number sense. This is understood as a set of skills. Some of them have an algebraic nature such as acquiring an abstract understanding of relations between numbers, developing awareness of properties and of the structure of the decimal number system and using it in a strategic manner. In this framework, the term relational thinking directs attention towards a way of working with arithmetic expressions that promotes relations between their terms and the use of properties. A teaching experiment has allowed to characterize the way in which third grade students use this type of thinking for solving number equalities by distinguishing four profiles of use. These profiles inform about how students employ relations and arithmetic properties to solve the equalities. They also ease the description of the evolution of the use of relational thinking along the sessions in the classroom. Uses of relational thinking of different sophistication are distinguished depending on whether a general known rule is applied, or relations and properties are used in a flexible way. Results contribute to understanding the process of developing the algebraic component of number sense.

中文翻译：

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三年级学生对关系思维的运用

当前的数学课程具有发展数字感作为其基本目标之一。这被理解为一套技能。其中一些具有代数性质，例如获得对数字之间关系的抽象理解，发展对十进制数字系统的性质和结构的认识，并以策略性方式使用它。在此框架中，术语“关系思考”将注意力集中在一种使用算术表达式的方式上，以促进其术语与属性使用之间的关系。通过一项教学实验，可以区分四年级学生如何通过区分使用的四种方式来使用这种类型的思维来解决数字均等问题。这些资料介绍了学生如何利用关系和算术属性来解决平等问题。他们还简化了课堂上使用关系思维的演变的描述。根据是应用通用规则，还是以灵活的方式使用关系和属性，来区分不同技巧的关系思维的用法。结果有助于理解数感的代数成分的发展过程。