L&G characterize teaching as a complex cognitive skill amenable to analysis in a manner similar to other skills described by cognitive psychology. According to L&G, teaching skill rests on two fundamental knowledge systems: lesson structure and subject matter.
L&G propose that a skilled teacher has a complex knowledge structure composed of interrelated sets of organized actions. L&G refer to these organized actions as schemata. They are applied flexibly and with little cognitive effort in circumstances that arise in the classroom. The main feature of the skilled teacher's knowledge structure is a set of schemata for teaching activities. These schemata include structures at differing levels of generality, with some schemata for quite global activities such as checking homework and some for smaller units of activity such as distributing paper to the class.
A characteristic of skilled performance is that many component actions are performed with little effort because they have become automatic through practice. L&G conclude that skilled teachers have a large repertoire of activities that they perform fluently. L&G refer to these activities as routines (Leinhardt, Weidman, & Hammond, in press). For routines to be effective, the students as well as the teacher must have developed an organization of actions or schemata for the actions that are performed. Routines play an important role in skilled performances because they allow relatively lowlevel activities to be carried out efficiently, without diverting significant mental resources from the more general and substantive activities and goals of teaching. Thus, routines reduce cognitive load and expand the teacher's facility to deal with unpredictable elements of a task.
Skilled teaching requires decisions about whether to proceed with the next component of a lesson, based on students' readiness for new material and the likelihood that students will succeed in solving instructional problems, or involving selection of students to ask questions or give special help.
The article describes a homework check activity of an expert math teacher and a novice one.
Expert teachers constructed their mathematics lessons around a core of activities. The expert teachers had, with the class, a large repertoire of routines, usually with several forms of each one. The expert's lesson can be characterized as an action agenda consisting of a list of action segments.