Many dentists and hygienists believe that electric toothbrushes can perform much better than manual toothbrushes. It is not because of the technology. Mainly it is because of the user.
Many people do not know how to brush their teeth properly. For years, they have been brushing in an incorrect fashion, but old habits are hard to change. Hence, by introducing the electric toothbrush, a new instrument, a new method of brushing can be introduced.
However, some areas in the mouth, such as the surfaces on the lower front teeth on the tongue side, should be brushed with the manual toothbrush rather than the electric toothbrush due to the contour of these teeth.
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However, note that the back and forth movement in the illustration does not mean dragging your toothbrush across the gum line. If you do that it will damage your gums and cause a groove line along the root of your tooth, which could become very sensitive. You can only drag your brush on the biting surfaces of the teeth which already has a lot of grooves.