This case study introduces the notion of an operative system to describe elementary teachers' knowledge and practice. Drawing from complex systems theory, the operative system is defined as the network of knowledge and practices that constituted teachers' work within a lesson study cycle. Data were gathered throughout a lesson study cycle in which teachers designed and implemented an inquiry-based science lesson that integrated science notebook writing. The lesson occurred in a second-grade classroom with general and special education students. The findings describe a network of nodes-teachers' knowledge and practices for science, writing, and working with their students-and the specific connections among these nodes in order to identify their operative system. The implications are discussed in terms of theoretical tools for the knowledge needed for teaching and teacher professional development, as well as the application of complex systems theory.
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