Limitations in the understanding of mathematical logic by novice computer science students

This research explored the understanding that novice computer science students have of mathematical logic. Because concepts of logic are at the heart of many areas of computer science, it was hypothesized that a solid understanding of logic would help students grasp basic computer science concepts more quickly and would better prepare them for advanced topics such as formal verification of program correctness. This exploratory study lays the groundwork for further investigation of this hypothesis. Data for the study were the publicly available versions of the Advanced Placement Examination in Computer Science (APCS examination) and files containing anonymous individual responses of students who took these examinations. A content analysis procedure was developed to provide reliable and valid classification of multiple-choice items from the APCS examinations based on the relationship between concepts covered in each item and the concepts of logic. The concepts in the computer science subdomain of logic were clarified by means of a taxonomy developed for use in this study. Thirty-eight experts in computer science education were judges in the content analysis of the multiple-choice items. The judges' ratings provided criteria for grouping items into strongly related and not strongly related partitions. In general, the mean proportion of student respondents that correctly answered the items in a partition was lower for the strongly related than for the not strongly related partition, with a smaller standard deviation. The difficulty distributions for the two partitions were shown to be non-homogeneous ($p\le .002$), with the difficulty distribution for the strongly related partition skewed more towards the "very difficult" end of the distribution. The results of this study suggest that novice computer science students experience more difficulty with concepts involving mathematical logic than they do, in general, with other concepts in computer science. This indicates a need to improve the way in which novice computer science students learn the concepts of logic. In particular, pre-college preparation in mathematical logic and the content of discrete mathematics courses taken by computer science students need to be scrutinized.

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