This article describes Realistic Mathematics Education (RME), a design theory for mathematics education proposed by Hans Freudenthal and developed over 40 years of developmental research at the Freudenthal Institute for Science and Mathematics Education in the Netherlands. Activities from a unit to develop student understanding of logarithms are used to exemplify the RME design principle of progressive formalization. Starting from contexts that elicit students' informal reasoning, a series of representations and key questions were used to build connections between informal, pre-formal and formal representations of mathematics. Student and teacher comments from the pilot of this unit in a College Algebra course at a U.S. community college suggest this approach may benefit students who have been underserved by traditional approaches to mathematics instruction.