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This study investigated the rates of successful mathematical performance and errors of information processing in third-grade children in California and continued an investigation of these factors in sixth-grade children. The objectives were to: (1) identify areas of mathematics in which the children had recognizable strengths and weaknesses, (2) classify characteristic areas according to information-processing theory, and (3) relate the errors made by third graders in l980 with errors made by the same children as sixth graders in l983. Approximately 25,000 children in each grade were tested for each year using data from the Survey of Basic Skills in the California Assessment Program. The tests and population are first briefly discussed, followed by the results of the analyses. For each grade level, discussion focuses on: correct performance by categories --computation, counting/number property, word problems (using operations), visual problems, geometry/measurement problems, and nontraditional story problems; the most difficult items; scores on matched items (computation and applications); and errors. Then the longitudinal analysis is dicussed. Girls appear stronger than boys in grade 3 and boys were stronger than girls in grade 6. References and sample items are included in the appendix. (MNS)

This report describes a computer-based instructional system, the Story Problem Solver (SPS). SPS provides students with instruction about the semantic structure of story problems. It was developed to test a specific schema theory of knowledge organization in long-term memory. For this reason SPS depends explicitly upon a theory of the relationship between the form of instruction and the memory structures that develop as a result. The schema theory underlying SPS, the design of SPS with respect to the theory, and the system's operational features are described. The report concludes with a short description of ongoing extensions to the basic instructional program. An appendix summarizes one experimental study of the effects of sequential versus all-at-once presentation for evaluating specific design features of SPS. (Author/YP)

A 2-year study of mathematics performance of sixth-grade students was conducted to: (1) determine the extent to which previously reported sex differences in California data exist and influence student response; (2) examine the predominant successful and unsuccessful strategies used by sixth-grade students in solving story problems; (3) discover to what extent boys and girls use different strategies in solving story problems; and (4) determine whether there are underlying cognitive differences in typical strategies of boys and girls and to identify these differences if they exist. Particular emphasis was given to analysis and classification of errors made by students solving a variety of mathematical items. The research consisted of analyzing responses from all sixth-grade students on previously existing data and analyzing children's (N=93) problem-solving behaviors obtained from individual interviews. Among the results reported are those indicating that girls were more likely to make errors leading to illogical responses and errors resulting from guessing strategies and that girls performed better on computation and worse than boys on story problems. Appendices include items used in interviews; children's responses to these items; and manuscripts, prepared for journal or book publication, which contain more technical detail about the research. (JN)

This report discusses the role of affect in cognitive processing. The importance of affect in processing mathematical information is described in the context of solving arithmetic story problems. Some ideas are offered about the way affective responses to mathematical problem solving situations influence the development, maintenance, and retrieval of information stored in human memory. A model of human memory based on schema knowledge structures is outlined. A way that affective information may be stored within a schema is suggested. The report concludes with a discussion of some affective responses to mathematics evidenced by students' comments as they worked with story problems. (PK)

This report describes the first of three stages in a study in the domain of problem solving: the definition and explication of schema knowledge. One objective of this research is to understand how schema knowledge is acquired and used in the chosen domain. The focus is on ways in which instruction influences the development of specific knowledge structures in long-term memory. The problem-solving domain was first analyzed with respect to the conceptual relations that may appear in arithmetic story problems. Emphasis is placed on the underlying semantic structure that gives meaning to each problem. Next, each semantic structure was framed as a hypothetical memory object, or schema, and the relationship to accepted theories of memory was explored. Finally, a computer model was developed that details the linkage of schema knowledge to two basic components of long-term memory: semantic networks of declarative memory and production systems and procedural memory (MNS)