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In secondary education many programs have been developed in order to improve education, training and skills of students with learning difficulties or those who may need special education services. However no much effort has been focused on addressing needs of students with high learning abilities. Sometimes these students get bored in class and waste time as teachers do not have enough time for them. Therefore, it is important to detect talented students, nurture their growth and provide them with opportunities to take advantage of their learning potential in order to achieve maximum personal and social development. It will benefit not only the student but the society as a whole, helping to eradicate mediocrity which too often is present in all areas of society.

For this purpose, it is necessary to know these students’ characteristics and how to work with them in class in order to meet their specific needs.
Authors of this project have been analyzed some theories and practical tools to develop in class with the aim of knowing pedagogical and methodological basis of intellectual giftedness and so may establish basic, structural and methodological elements that should be incorporated to mathematical activities designed for these students.

Therefore, in this contribution we show our project, which general objective is to help intellectual gifted students to bring out their best and reach their cultural, scientific and technological potential in the area of Mathematics. Topics such as Geometry, Graph Theory or Statistics are considered in this project and different activities, which are described in the present contribution, have been designed in order to reach our purposes. In the present academic year 2014/2015, they are being implemented with students enrolled in the first and second year of “Compulsory Secondary Education” (ESO) in two high schools located in Albacete (Spain). Teachers from Secondary Schools located in the province of Albacete and professors from the University of Castilla-La Mancha are involved in this initiative. Another goal of this work team is to encourage more teachers, professors and institutions to take part in this project.