The current research aims to identify: 1. The level of mathematical construct among the Department of Mathematics students in the colleges of education and basic education. 2. The level of effective mathematical operations in both sides of the brain at the Department of Mathematics students in the colleges of education and basic education. 3. The strength and direction of the correlation between the mathematical construct and effective mathematical operations on both sides of the brain at the Department of Mathematics students in the colleges of Education and Basic Education. To investigate the research objectives, the researcher formulated zero-main hypothesis for each aim and from the same hypothesis, three sub-zero hypotheses are derived. The current research community has included the fourth-year students (171 subjects) from the departments of mathematics students in the colleges of Education and Basic Education - Misan University (Morning Studies) for the academic year (2015-2016). Because the number of the community is small, the current research has included all fourth-year students in the mathematics department at the colleges of Education and Basic Education - Misan University except the students in the exploratory sample which are (30) subjects, were taken equally from the students of the Department of Mathematics in the two colleges. Therefore, the size of sample was (141) students; (63) students are from the College of Education and (78) students are from the College of Basic Education. The researcher had prepared a test of effective mathematical operations on both sides of the brain is composed of (34) items distributed among three fields. He proved its validity, reliability and to the statistical analysis of its items. He used a template test for mathematical construct, which was used before. He modified some its items linguistically, rearranged some of them and numbered in a different way, and check its validity, reliability and the statistical analysis to its items. The final draft of the test included (36) objective items, (23) multiple- choice items and (7) items of the pairing type (they included 55 sub-items). After the application of the two tools of the research on a sample of research and data analysis, the researcher obtained the following results: 1. The students of research sample have the mathematical construct at the required level. 2. The research sample students have effective mathematical operations on both sides of the brain at the required level. 3. Statistically, there is significant correlation between the mathematical construct and the effective mathematical operations on both sides of the brain among the students of the research sample. Based on the research results, the researcher formulated a number of conclusions, recommendations and suggestions