One debate that periodically arises in mathematics education is the issue of how to teach calculation more effectively. "Modern" approaches seem to initially favour mental calculation, informal methods, and the development of understanding before introducing written forms, while traditionalists tend to champion particular algorithms. The debate is an important one, as it links directly to the purpose of mathematics education, but the debate is not easily resolved. Recent experiences have led the author to believe that this is partially due to the significance placed on algorithms when many of today's adults were learning mathematics at school--and the constraints this has placed on one's thinking. Algorithms are designed as elegant notations by people who understand the process being presented, so tend to be useful for people with similar levels of understanding, or for people drilled in their use. In this article, the author reports on an epiphany on the road to understanding addition. (Contains 1 figure and 4 tables.)