A Miss is as Good as a Mile: Off-By-One Errors and Arrays in an Introductory Programming Course

Loops and arrays are fundamental CS1 concepts, but ones that can be problematic for novice programmers. In this research, we investigate off-by-one errors - logic errors where loops perform one too few or one too many iterations - in code using an indexed loop over an array. We classify off-by-one errors, and explore the prevalence of each type, by analyzing a large set of code submissions from students in a first year programming course as they tackle a sequence of exercises. We describe an approach to reliably identify off-by-one errors through dynamic analysis, and find that off-byone errors are both common and persist across exercises. We also show that students infrequently choose to iterate over an array in reverse, but when they do they more commonly encounter off-byone errors. We conclude that teaching material should explicitly focus student attention on boundary cases, and should provide more examples that iterate through arrays in reverse.