He allocated students to one of four groups based on their response patterns, as in
Table 1. The first group (referred to as Experts in this paper, and Level 3 by Fujii)
consisted of students who were correct on both items. He referred to another group as
Level 1; these students circled all answers in both problems and hence were incorrect on
Problem 1 and yet correct on Problem 2. We will label this misconception Empty Boxes
(EB), as these students appear to treat the letters x and y as they might treat empty boxes
(i.e. interpret Problem 1 as □ + □ + □ = 12) in a primary school “fill the gaps” exercise.
The next group (Level 2 by Fujii) correctly answered Problem 1 but were incorrect on
Problem 2, by making a particular error; omitting to circle part c. We will label this
misconception Different Letter means Different Number (DLDN). These students reject the