This article defines constructivism and examines the theory in terms of the view of the learner, the content, teacher-student interactions, motivation, and assessment. The standards generated by the National Council of Teachers of Mathematics are reviewed in terms of their sensitivity to students with moderate to mild disabilities. Constructivistic teaching principles are abstracted from the constructivism and learning strategy literature and research. Nineteen instructional components are identified and discussed in terms of teacher behaviors, teacher modeling of explicit strategies, teacher-student interactions, instructional content, and learning factors. An analysis of these components reveals that most constructivists adopt an exogenous constructivistic approach to teaching math to students with moderate to mild disabilities. Finally, obstacles to applying research-based constructivistic components in classrooms are identified.