This paper proposes a technique for developing an optimal syllabus consisting of instructional items selected from a given set of such items. The problem is to locate, from the given set, those instructional items which maximize the sum of the weights for the items, subject to the given total teaching hours and the order of instruction. This technique consists of two phases : (1) the construction of a hierarchical directed graph and (2) its optimization. The hierarchical directed graph, using the interpretive structural modeling method (ISM), is constructed so as to represent the order of instruction as perceived by the teachers. The problem is formulated as a zero-one integer programming problem using precedence sets directly adjacent to each instructional item. Optimization is carried out using the branch and bound method. The latter part of this paper discusses examples of satisfactory and efficient solving of actual problems through the application of this technique.

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For videotaped examples of instruction were analyzed using the time-series categorization system (an instrument for analysis of teacher-pupil interaction). In order to make the teaching-learning process more explicit, an attempt was made to clarify differences in (1) the teaching-learning process-science versus social studies instruction, (2) teachers-experienced versus inexperienced, and (3) student development-sixth versus fourth grade children. "Hayashi's Second Family Quantification" was adapted to this study. Some of the results were : (a) In the social studies class, the children held the initiative while in the science class the instruction proceeded under the control of the teacher, (b) The younger, inexperienced teacher kept better order and a more rigid pace while the older, experienced teacher incorporated more flexibility into his instruction and encouraged his students to be more active ; but also helped them to clearly understand the essential points of the instruction, (c) The sixth grade students maintained a more composed class room atmosphere throughout the lesson while, as the teacher maintained step-by-step control, the fourth grade students were more passive in their attitudes. The results of this study show that "Hayashi's Second Family Quantification" is useful as an instrument for instructional analysis.

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