The conventional wisdom holds that calculus as a system of knowledge and technique is an intrinsically difficult subject. In turn, calculus as an institution has acted as a filter allowing only some students to move on to higher mathematics and the sciences. A fundamental change in calculus as a system of knowledge and technique can radically alter the role of calculus as an institution and potentially support a redistribution of opportunity for all students completing the high school mathematics sequence. In spite of the Calculus reform of the 1990s there has been no deep and lasting innovation in content – in the conceptual foundations of the elementary calculus – for some 183 years. Calculus, at both the secondary and tertiary levels, is taught today in essentially the same way Cauchy taught the calculus in 1823. Both supporters and detractors of Calculus reform have operated under the tacit assumption that the historically derived form of the calculus was immutable – close to a law of nature. We have focused not on reforming the institution of the calculus but rather the calculus as a system of knowledge and techniques. In this poster session we examine the calculus as a system of knowledge and techniques. In particular we present a re-conceptualization of the elementary calculus, without limits or infinitesimals, using only the concepts and techniques of a beginning high school Algebra course. As a consequence of our analysis we are now able to make a critical distinction between the conceptual foundations of the elementary calculus and its logical foundations. There are different conceptual foundations and the different conceptual foundations have different logical foundations. In this reformulation the algebraic notion of equivalence replaces the analytic notion of limit as a conceptual foundation of the calculus. We recognize that the conceptual architecture of a knowledge domain can act as a passive barrier to entry as surely as the architecture of a building determines the presence or absence of physical barriers to entry. Architecture, whether conceptual or physical, is intentional. The conceptual architecture of mathematics in general and of the calculus in particular is neither predetermined nor immutable. There is a conceptual architecture of the Elementary Calculus which is potentially accessible to students at the level of a high school beginning Algebra course. This work, in contradistinction to the two volumes on the didactics of mathematics by Felix Klein, is part of an on-going project to develop at the secondary level advanced mathematics from an elementary standpoint.