Problem solvers who know several different solution methods or strategies for a problem may choose a strategy flexibly for each problem in order to lessen cognitive load or to maximize accuracy of performance under time pressure. This idea is explored, and consideration is given to how this issue of multiple-strategy use will affect cognitive skill diagnosis. The "adaptive strategy choice" hypothesis is proposed, which states that if test takers know more than one solution strategy, they will tend to choose the easiest effective strategy for a particular problem. This idea is applied to a well-known problem-solving domain — that of mixed-fraction subtraction. In this domain, adaptive strategy choice leads to a hybrid strategy ("Method C") in addition to the previously recognized Methods A (convert mixed numbers to improper fractions; Tatsuoka, 1990) and B (separate mixed numbers into integer and fraction). The idea of Method C is that people can select strategies on each item, using whichever strategy is easier between Method A and B. Previous research has concluded that Method B explains the data better. However, the present results from multiple regression and mixed effects logistic regression analyses show that Method C works better than Method A or B to predict the item difficulties.

The second goal of this research is to develop methods for cognitively diagnostic testing that work effectively in the presence of multiple strategy use. A new model, the "Mix-NIDA" model, is proposed that allows the solution strategy used by problem solvers to vary so that people can be classified into different strategy groups. Two versions of this Mix-NIDA model are defined, and a fitting method is developed using a Bayesian analysis framework. The proposed fitting method is validated via simulation studies. A number of models are then defined assuming different potential mixtures of the three strategies (Methods A, B, or C) using the Mix-NIDA framework, and the models are applied to the mixed fraction subtraction data The Mix-NIDA model assuming use of all three strategies fits the data best This Mix-NIDA model classifies about 50% of the participants as Method C users.