We examine the structure and objectives of our first-year service courses. The literature suggests that these are well out of date and do a poor job of preparing our students for the life of work and play that awaits them. In these courses, our curricula are based on the acquisition of knowledge, knowledge that very few of our students will ever need. As a consequence, they generally fail to give our students the performance capacities that they will need to flourish in an ever-changing environment. Building on past work, we use the image of a tree to depict the many rich branches and branchlets of the wonderful discipline of mathematics. The problem is that we make our students spend their beginning years climbing up the trunk of the tree, such that very few of them ever manage to experience the joy of doing authentic mathematics. To break away from this, we need to let go of the narrow logical structure of the subject found in introductory text-books, and engage our service-course students instead in the play of complex structures.