Social scaffolding refers to the support the teacher provides that helps students learn to work with each other. Analytic scaffolding refers to the support offered to students by materials, teachers, or one another, in building mathematical understanding.
Analytic scaffolding might include physical manipulatives, models, metaphors, representations, explanations, or justifications that allow students to better understand mathematical tasks and solutions. Part of this scaffolding is provided by the tasks given to the students or by questions that help to focus attention and point out critical aspects of the mathematics being used.
-From Social and Analytic Scaffolding: the Dilemma of Telling published in Math Teacher Education (2010) 13:17-26.