“So my program doesn’t run!” Definition, origins, and practical expressions of students’ (mis)conceptions of correctness

We studied students' conceptions of correctness and their influence on students' correctness-related practices by examining how 159 students had analyzed the correctness of error-free and erroneous algorithms and by interviewing seven students regarding their work. We found that students conceptualized program correctness as the sum of the correctness of its constituent operations and, therefore, they rarely considered programs as incorrect. Instead, as long as they had any operations written correctly students considered the program ‘partially correct’. We suggest that this conception is a faulty extension of the concept of a program's grade, which is usually calculated as the sum of points awarded for separate aspects of a program. Thus school (unintentionally) nurtures students' misconception of correctness. This misconception is aligned with students' tendency to employ a line by line verification method – examining whether each operation is translated as a sub-requirement of the algorithm – which is inconsistent with the method of testing that they formally studied.