Many mathematics educators and specialists believe that computer education at the undergraduate level should be concentrated in the mathematics and mathematics/education courses. However, the content in these courses is already crowded, and the prospective elementary school teacher still needs more mathematics than is currently taught. To add the necessary knowledge of computers to this overcrowded curriculum is unwise for two reasons. First, it could dilute rather than enhance the mathematics training, and, second, computers should be applied to all disciplines. I believe that a general education in the use of the computer needs to be introduced first and that applications should then be integrated across the curriculum. This approach will allow and encourage teachers to use the computer as a tool in each of the elementary chool subjects. This article recommends a program of computer education at the undergraduate level for elementary school teacher and elementary school computer specialists.