Described is a method using a computer for grading student work on a problem when the student's own steps are shown in detail. A reference trace is created representing a best solution path to the problem. A student trace of the student's own work is then created, which involves searching explicitly for a specific rationale for appending a step to the student trace; deeming the step a correct production provided the step was able to be reproduced and marking the step as traced; provisionally accepting the step as part of the best solution path subject to revocation if a better-quality step is later found by a step conflict check; implicitly tracing the student's work to discover implicitly taken mental steps provided the explicit tracing has failed to justify the step; appending any remaining untraced steps to the student trace and excluding them from the best solution path; computing a value of the steps in the student's work to form a student value; and, comparing the student value to a total value of the steps in the reference trace to obtain a score.