This is the first of a two-part article that presents a theory of unit construction and coordination that underlies radical constructivist empirical studies of student learning ranging from young students' counting strategies to high school students' algebraic reasoning. My explanation starts with the formation of arithmetical units, which presage the construction of the first numerical schemes, and continues on through the construction of a three-level structure of coordinated units, which is necessary for upper-level mathematics. Along the way I disambiguate terminology in order to increase the accessibility of this useful theory to a wider group of learning researchers.