This paper introduces a new framework for thinking about tangible interfaces in education, with specific focus on abstract problem domains.Manipulatives are physical objects specifically designed to foster learning. We offer a new classification of Manipulatives: "Froebel-inspired Manipulatives" (FiMs) and "Montessori-inspired Manipulatives" (MiMs). We argue that FiMs are design materials, fostering modeling of real-world structures, while MiMs foster modeling of more abstract structures. We show that our classification extends to computationally enhanced versions of manipulatives.We present Digital MiMs - computationally enhanced building blocks. We describe two prototypical members of the Digital MiMs class: FlowBlocks and SystemBlocks, physical, modular interactive systems that serve as general-purpose modeling and simulation tools for dynamic behavior. We present findings from qualitative studies, and conclude that digital MiMs are accessible to young children, engaging, and encourage learning of abstract structures of dynamic behavior through an iterative process of hands-on modeling, simulating, and analogizing.