Abstract: This article contains a theoretical research study that interprets the learning and understanding of the mathematical objects from an ontological position with respect to its nature. The nature of mathematical objects is associated with their functional origin, and the aspects of representation and meaning that configured the mathematical object are constituted from this functionality. The representation allows the expression and use of the object. The meaning attends to the interpretation of the object. The set of interpretations that may be associated with an object by the functionality that it represents configures its meaning. The learning of a mathematical object serves the representational aspect that sets him, and to the development of a meaning staff on it, from the experiences of the individual with the object. Finally, understanding of the mathematical objects is recognition of organizational or interpretative functionality of the context that represents the object, and the development of the ability to use this functionality.
Keywords: mathematical objects, learning, understanding, representation, meaning.