The study was carried out within the framework of a project that provided afterschool mathematics tutorial sessions to 10th-12th grade students by engineers in an informal setting. The participating students were selected from advanced level mathematics classes according to their need for additional support. The main goal of the study was to characterize the special learning environment that evolved within this project, and to identify distinctive elements that enhanced students learning. In our paper we present three main characteristics associated with the problem solving activities in which the tutor and students engaged, and discuss their contributions to students' learning. [For complete proceedings, see ED489597.]