The question
Does knowing a subject deeply make you better at judging what a beginner will struggle with?
The method
Two lines of evidence, from different subjects. In mathematics, 105 elementary, middle and high school teachers “ranked a set of problems from easiest for their students to solve, to most difficult” [1], and those rankings were compared against ninth-graders’ measured performance from the authors’ earlier work (Koedinger and Nathan 1999, two samples of 76 and 171) [1]. In literature, the authors re-read Grossman’s case study of six secondary English teachers, all strong in the subject, three trained in pedagogy and three not [2].
The findings
The name is the finding: expert blind spot is where “because of their advanced content knowledge in mathematics, people with greater expertise tend to make assumptions about student learning that turn out to be in conflict with students’ actual performance and developmental propensities” [1]. Students found the symbolic problems harder than the verbal ones — “students’ performance on equations is less than 30%, while verbal problems are solved correctly over 50% of the time” [1]. The high school teachers, who have the most mathematics behind them, predicted the reverse, reasoning that symbols are “pure math” while a word problem has to be translated first [1].
What makes the paper worth citing is that the error tracked training rather than teaching. “Middle school teachers were very accurate in predicting student performance, τ(6) = .733, p = .034. However, the ranking provided by high school teachers was not related to student performance at all, τ(6) = 0” [1]. Thirty middle-school teachers with less post-secondary mathematics got it right; thirty-nine high-school teachers got a result indistinguishable from noise. More subject knowledge, less signal. The authors read the collapse of New Math the same way: “the concepts that formed the foundation had been designed by mathematicians to highlight the organization of the domain, with little regard to how that domain was to be learned or taught” [1].
The literature half repeats the pattern. Grossman’s pedagogically trained teachers “chose 78% of their readings from among” adolescent literature; the equally expert but untrained teachers “chose mostly (72%) canonical texts” [3] — because, as Grossman put it in the passage the authors quote, “as successful students themselves, they expected their students to be as knowledgeable and as interested in literature as they remembered themselves being” [3]. Underneath both is a mechanism worth knowing, because it explains why asking the expert harder does not fix it: “experts are less likely to have access to memory traces of their cognitive processes when engaged in tasks within their domain of expertise” [4]. The steps have been automated away. “Among novices, these processes are deliberate and stepwise, and so they leave a memory trace which is more likely to be inspectable and verbalizable” [4]. Domain knowledge can even be a straight disadvantage: “subjects with a large amount of domain knowledge may actually be at a disadvantage when compared to novices on certain tasks” [4].
The limits
This is a short conference paper that assembles existing studies — the authors’ own algebra work and Grossman’s case study of six teachers — into a hypothesis. The teacher rankings and the student performance data come from two separate studies, so the comparison is across datasets rather than within one. It is evidence in classrooms, not in hiring. It is also not the same work as Nathan and Koedinger’s 2003 American Educational Research Journal paper on the same problem.