This paper describes the problem-solving studio (PSS) learning environment. PSS was designed to teach students how to solve difficult analytical engineering problems without resorting to rote memorization of algorithms, while at the same time developing their deep conceptual understanding of the course topics. There are several key features of PSS. First, students work in teams of two to solve problems, working at the same table with another team of two. The student teams and tables are stable, remaining together for most of the semester. The teams work in a public, shared problem-solving space that allows in-class mentors (near peers of the students) and the instructor to observe and critique their work. The public nature of the work enables the instructor to provide students with real-time, situated feedback. In addition, it enables the instructor to tailor the challenge level to the needs of each team, such that the problem is too difficult for any one student to solve on their own, but reasonable enough that the team can solve it together, given the support that the PSS environment provides. We call this targeted adjustment of the problem's difficulty dynamic scaffolding. PSS provides the support students need through a specific set of participant structures that govern how the instructors, in-class mentors, and students interact during class. This paper describes the PSS approach and how it has been implemented in an entry-level course at Georgia Tech called "Conservation Principles of Biomedical Engineering (BMED 2210)". Our results show that even though PSS emphasizes engineering problem-solving skills, the students' conceptual understanding of the material significantly improves, as measured by Shallcross' material and energy balances concept inventory. The implications of our work, particularly with respect to the use of PSS in flipped classrooms, are discussed.