This study’s main objectifs were to identify children with high capacities for reasoning and learning from a constructivist point of view, to describe their psychopedagogical characteristics and to elaborate an educational strategy to attend their needs. Two tests, André Rey’s Six Minutes Written Vocabulary and Mathematical Reasoning were applied to fourth grade students of 5 schools belonging to different administrative categories. From a methodological perspective this study is a combination of cuantitative analysis (deciles) and qualitative design (analysis of interviews of children and teachers). Deciles were calculated for each of the groups and for the whole population. The results of the children in these tests were the basis for the identification of the students with higher abilities for reasoning, students situated from decile 8 to 10 were selected. These children were interviewed and asked to make a spontaneous drawing. A guide to observe them in class was given to the teachers, to obtain additional information about them. In order to help the teachers offer them the best learning situations, comprehensible, friendly documents were written on three themes: what is a student with high capacity for reasoning and learning, how to help these students obtain better comprehension in Mathematics and how to stimulate students for better reading and writing abilites. Important conclusions of this study are: 7,07% of the children were identified as with high learning and reasoning abilites. Among their psychopedagogical characteristics may be named the fact that they do not use reading as a recreative or academic tool and that they do not employ writing or drawing to express their interests in life. Another important result of this study is the fact that it is necessary to train teachers for better identification and academic attention to these children.Los objetivos de este estudio de perspectiva constructivista fueron: identificar niños con alta capacidad para el aprendizaje, describir sus características psicopedagógicas y elaborar una estrategia educativa para atender sus necesidades. En una primera fase cuantitativa se aplicaron la prueba de Vocabulario Escrito de Seis Minutos de Rey (1969) y la de Razonamiento Matemático (Oviedo & Méndez 1984) a estudiantes de cuarto grado de cinco escuelas. Se calcularon deciles para la población. Los niños situados del decil 8 en adelante en su grupo en ambas pruebas fueron seleccionados como estudiantes de alta capacidad para el aprendizaje. En la segunda fase, de enfoque cualitativo, fueron entrevistados y se les pidió un dibujo espontáneo. Se le entregó a las docentes una guía de observación. Se elaboraron folletos sobre estudiantes de alta capacidad para el aprendizaje, cómo mejorar la comprensión en matemática y estimular las habilidades de lectura y escritura. Un 7,07% de los niños fueron identificados con habilidades de aprendizaje. Entre sus características psicopedagógicas se encontró que no utilizan la lectura como medio de recreación ni la escritura o el dibujo para expresar sus intereses. Se identificó la necesidad de capacitar a las educadoras en la identificación y atención de estos niños.