In my Dissertation, I used several methodologies (literature search, multivariate experiment, factor analysis, ontological deconstruction, protocol analysis, clinical study, and direct remediation) to show that almost every math error made by 7th grade algebra students is unique, arising from unique sources, contexts and motives never to be repeated. The structure that teachers see in error behavior is constructed by the teacher, presumably so that teaching is easier. Errors, however, are not about the structure of the subject matter (like negative numbers or the distributive rule), they are about the immediate and idiosyncratic social structure of the classroom.

Analyzing Errors in Elementary Mathematics, Stanford School of Education, 1987.