The purpose was to define and determine the influence which different perceptions of mathematics held by elementary teachers may have on student computational ability, comprehension of mathematical concepts, and attitudes, at grade levels three and six. The perception factor was contrasted in the design with teacher attitude toward mathematics. Data were obtained from 62 third- and 51 sixth-grade classes (approximately 3,100 students). Six student instruments were adapted from attitude scales taken from the National Longitudinal Study of Mathematical Abilities (NLSMA), computation items from Seeing Through Arithmetic Tests, and comprehension tests from the Wisconsin Contemporary Test of Elementary Mathematics. Sixteen items measuring teacher perception of elementary school mathematics were selected from scales used in the Collier, NLSMA, and Rettig studies; teacher attitude was measured by the Revised Mathematics Attitude Scale. Results showed that no significant causal relations can be inferred between teacher attitude and perception and student achievement. It was found that teachers with informal perceptions of mathematics taught students who scored significantly higher on attitude, computation, and comprehension at the third-grade level. No significant differences were observed at the sixth-grade level. (DT)