For example, to solve item 20 (item difficulty = −.274 logits) (outlined in section "Research questions") correctly, two mental processes are relevant: (a) matching as scientific authors' statements have to be compared with statistical values; and (b) specifying as the test persons have to "identify principles that apply to a specific situation" (Marzano and Kendall 2007, p. 50).
Respondents on level II have the ability to name the basic mechanical terms and to correctly solve items containing mechanical problems with simple connections (see e.g. the item in Figure 4).
The Rasch model's basic equation (see Eq. 1) describes the difference between the ability of a specific person n, B n, and the difficulty of a specific item i, D i, via a logarithmic function that depends upon the probability P ni of person n to correctly solve item i: {B}_n-{D}_i=ln left({P}_{ni}/left 1-{P}_{ni}right)right) (1).
Hence, in the following, we solve items 3 5 in Algorithm 1 using fixed-point search routines.
Alternatively, they might have thought that understanding of the literal meaning would suffice to solve the items.
In these tasks, students were able to solve single items independently from their performance on previous ones.
Thus, a computer simulation entails a certain degree of risk, because the information needed to solve the items is not always visible at a glance.
The selection of wrong answer alternatives and/or the omission of correct answer alternatives, in contrast, signify that a student does not yet possess the conceptual understanding necessary to solve the item correctly and the respective item is scored 0. Consequently, an item is either correct (1) or wrong (0).
More complex models may also have parameters representing the different conditions under which the persons respond to the items, properties of possible raters who evaluate the responses, specific mental operations needed to solve the item, or the speed at which the person responds.
This means that it may take (almost) as much time to try to solve an item before finally judging it to be too difficult as it does to complete it correctly.
