This study aimed at investigating basic ninth grade students' geometrical representation and their relationship with students' geometrical thinking It also investigated the differences between students performance in the geometric representation test and the geometrical thinking test... The researcher prepared two tests:- one testing the geometrical representation and the other testing the ability to think geometrically on the first three levels i.e. visualization, analysis and informal deduction, The two tests were verified for validity by a group of educators and have also been verified for reliability by the means of conducting endurance the two tests on a group of ninth grade students and calculating the internal consistency using the method of Alpha Cronbach's- that reached (0.91) and (0.7) respectively. Sample of the study consisted of(314) students distributed over (12) groups in (5) schools related to the Directorate General of Education in the Al-Dahirah region in the Sultanate of Oman and the following results were found:
According to the study there was a decline in the performance of the students in basic ninth grade in the test of geometrical representation of mathematical problems. It was found that (17.2%)did not go beyond any of the levels of geometrical thinking according to the degree of perfection(70%) for each of the levels, (73.9%) were classified in one of the levels of geometrical thinking (visualization, analysis and informal deduction), among them (8.9%) of the students did not achieve the level of geometrical thinking in the serial arrangement according to the theory of Van Hill, There is a positive statistical correlation shown statistically on the level of ( a s0.05) between the grades of the students in the test of geometrical representation and the grades of the students in the test of geometrical thinking. There are statistical differences at the level of (aso.05) between the average grades of students in the test of geometrical representation of mathematical problems and the average of students' marks at the geometrical thinking test according to students' level (high-medium – low( The study ended with several recommendations such as the fact that basic education school textbooks should include mathematical problems which require geometrical thinking in their solutions and should also focus on activities which can help develop the level of geometrical thinking of the students and characterize the ability to gradually rise from the cognitive level to the verification of the relationships and the discovery of properties.