The issue of expository teaching versus independent discovery in the learning, retention, and transfer of principles is still very much in controversy. This study was designed to test the following hypotheses: (1) The children trained by discovery method would improve their subsequent ability to solve scientific reasoning problems based on the scientific concepts and principles learned in elementary school science subjects than those who were trained by traditional didactic method. (2) The relative effectiveness of discovery method would be related to the variables such as grade, sex, intelligence, and personality traits of children. One hundred fourth graders (50 boys & 50 girls) and 80 sixth graders (40 boys & 40girls) were selected from the experimental classes of discovery instruction. A matched group of children with the same number was drawn from traditional didactic method classes. The Raven´s Progressive Matrices Test and the Chinese form of the Children´s Manifest Anxidty Scale were used to determine children´s intellectual and personality traits respectively. The results of the study indicated: (1) There were no signnificant differences between performance of the groups under different types of instruction in terms of retention and transfer of principles. (2) No significant sex difference was found in fourth graders, but the boys were significantly superior to the girls in sixth grade in terms of reasoning performance. (3) The hypothseized nagative relationship between anxiety level and reasoning performance was not identified.