This study aimed to investigate the effects of using Merrill and Tennyson Model on the acquisition of mathematical concepts by 6th Grade female students and the differences in acquisition when using the cognitive style (field dependence / independence). The study attempted to answer the following questions: 1. Is the acquisition of some mathematical concepts by 6th grade female students effected by the changing the teaching method (Merrill Tennyson / the traditional method)? 2. Is the acquisition of some mathematical concepts by 6th grade female students effected by the change in the teaching method (field dependence / independence)? 3. Does the acquisition of some mathematical concepts by 6th grade female students changes according to the interaction between the teaching methods (Merrill Tennyson / the traditional method) and the knowledge method (Independent / awareness dependency)? The sample of the research consists of 141 female students at the 6" Grade in the academic year 2004/2005. In order to gain the necessary data for the study, the researcher administered an impeded shapes test and an achievement test in the geometry of quadrant shapes. The results of the two tests were as follows: 1. There were statistically significant differences at (0.05) in the mean of the students test results which is attributed to the teaching methods used. 2. There were statistically significant differences at (0.05) in the mean of the students test results which is attributed to the use of the cognitive style. 3. The absence of statistically significant effect at (0.05) in the mean of the test results which can be attributed to the interaction between the teaching strategies used and the cognitive style. The researcher recommended the necessity of re-thinking about the teaching methods used for teaching the mathematical concepts with the emphasis on pattering the examples and the non-examples together in opposite pairs. It is also important to take the individual differences between the students into consideration and using the methods that best fit the students' aptitudes. That's because no method is better than another but students with certain aptitudes will benefit more from certain method of treatment. There is also a need to find teaching methods and treatments that are appropriate with the cognitive style for students in all scientific fields to accomplish the goal of considering the individual differences between the students.