The objective of this work is examination of co-ordinance amongst assessments of logical-mathematical giftedness with young primary school students, made by four groups of evaluators: teachers, parents, coevals and self-evaluators. Teachers of 11 primary schools selected at the area of Republic Srpska were assigned to follow Instructions for Nomination and select most capable students of Years Three and Four, who would be directly involved in the research. An evaluation of logical-mathematical giftedness was performed on a sample of 151 named students, using an instrument created for the needs of this research. The results have shown a high level co-ordinance in evaluation of logical-mathematical giftedness between teachers and students and between parents and coevals, which leads to a conclusion that there is a scientific justification to innovate the teaching process while working with gifted students at primary schools, by applying a questionnaire developed for evaluation of logical-mathematical giftedness to be done by teachers, parents, students and coevals. This work allows a space for forming data bases on evaluations of students' abilities, in order to plan the next step which would be creating a predictive model based upon likelihood and expectations as to the possibility of identifying giftedness.