The linked concepts of "scaffolding" and the Zone of Proximal Development (ZPD) were originally applied to the context of asymmetrical teaching and learning with a teacher or adult explicitly supporting a learner, usually a child, to achieve tasks beyond their ability when working alone. In this paper we investigate how these concepts need to be reconceptualized if they are to be applied to the different context of symmetrical learning amongst groups of peers. We present two separate studies. In the first one we analyze the type of talk used by a group of children from Mexico solving the Raven's Standard Progressive Matrices (RSPM) test together both before and after an intervention program teaching "exploratory talk". Our analysis demonstrates a ZPD created by the way in which they talk together. In the second study we present the comparison of the talk of two groups of children, one from Mexico and the other from the UK, solving together a single matrix from the RSPM test. Our analysis shows how the concept of "scaffolding" can be applied to understand how these groups of children use language to support shared thinking and learning. In both studies we found that applying ideas of "scaffolding" and the ZPD to symmetrical learning required the re-conceptualization of these concepts as characterizations of dynamic processes within dialogues.