An examination of the relationships among type of tasks, strategies, and mental representations used by students on application tasks in symbolic logic

The purpose of the study was to extend researchers' knowledge of students' understanding of the structure of symbolic logic and to determine mental representations of content made by these students. A test of symbolic logic and its applications was administered to 154 students identified as successful by teachers of courses in which they were enrolled. Semi-structured interviews were conducted to investigate their approaches to situations taken from the research instrument. Quantatative and qualitative examinations of responses to questions of symbolic logic and applications were used to determine the role of task content, symbolic representation, and procedures of symbolic logic as indicators of ability of the subjects to determine a logical consequent to an argument. Regression analysis was performed to determine effects of characteristics of transfer on scores. Written explanations by subjects were examined to investigate mental representations of symbolic logic. To determine extent to which instruction in symbolic logic affects responses to mathematical and real world situations, a modified version of the research instrument was administered to students who had not studied symbolic logic and responses of the two groups of subjects were compared.;Results from an ANOVA showed a significant difference in scores due to procedure used by subjects but no effect due to the use of symbols. Predominate procedure used across all types of content was application of symbolic logic rules. Qualitative analysis of written responses on the research instrument and oral responses in interviews indicated that subjects often identified incorrect laws or applied inappropriate laws when attempting to determine valid conclusions to arguments. Regression analysis to determine the role of characteristics of transfer indicated no effect for the characteristics identified. An analysis of variance indicated that there was significant difference between students who had and had not studied symbolic logic as a unit in school on questions with mathematical content but not real world content. This indicates that there are implications for the teaching of symbolic logic as it affects the study of non-symbolic-logic mathematics.