A system has been developed which coherently converts the meaning of geometric computational representation questions by means of natural language processing techniques as well as one which draws a figure based upon an understanding of that conversion. The research covered three important areas. First, phrase structure rules and categories for parsing geometric questions were defined based upon an analysis of textbook and workbook sentences. Next, a method for producing two levels of representation were proposed. One level corresponded directly to the questions, the other handled more detailed information. In other words, the former represents the relationships among the objects specified in the sentences while the latter is generated by applying a knowledge of geometry and represents the relationships among the points, segments and lines which underlie each of the objects described at the first level. This latter area corresponds to actual geometric representation. The third area was the drawing of a figure after coordinate values of points and other information necessary had been added. The output from the system is intended for use in a geometric problem solving system as well as in a system for inputting handwriting.

View full abstract

A study was designed, using a stimulated-recall procedure, to capture the cognitive processes of fifth and sixth grade students receiving instruction in either mathematics or science. The purpose was to investigate the cognitive process in relation to lesson segments and individual student characteristics. The results included : 1. It was possible to understand changes in states of student understanding during a lesson. In other words, it was possible to learn which lesson segments most of the students were able to understand the contents of the instruction and which lesson segments many of the students were not able to understand. 2. It was possible to extract specific lesson segments, those which most all of the students understood and those which many of the students did not understand. 3. Students who are high achievers tend to more frequently use their own prior knowledge or experience as an aid in learning from the instruction. 4. Even those students who are usually high achievers on the subjects being taught became only moderate achievers because they failed to understand the contents of the more important lesson segments.

View full abstract

The purpose of this study was, based upon a model previous proposed by the author, to develop a tentative system for computer simulation of classroom instructional activities. The resulting system consists of four elements : monitoring schema, instructional plan, instructional behaviors, and instructional material knowledge. The monitoring schema serves to roles-decision making and plan execution-and has been developed as a production system. Instructional plans are used as input date outlining the instructional activities. The data format is determined and the instructional behaviors are defined as interfaces to manage the process of teacher-student interaction. These are described in script form and contain variables to explain differences in instructional purposes and behavior patterns which arise between teachers even when they are executing the same instructional plan. The data format for the domain of math education has already been prepared. It consists of two levels, textual and conceptual information, and is expressed in the form of a semantic network.

View full abstract