The block design task, a standardized test of nonverbal reasoning, is often used to characterize atypical patterns of cognition in individuals with developmental or neurological conditions. Many studies suggest that, in addition to looking at quantitative differences in block design speed or accuracy, observing qualitative differences in individuals' problem-solving strategies can provide valuable information about a person's cognition. However, it can be difficult to tie theories at the level of problem-solving strategy to predictions at the level of externally observable behaviors such as gaze shifts and patterns of errors. We present a computational architecture that is used to compare different models of problem-solving on the block design task and to generate detailed behavioral predictions for each different strategy. We describe the results of three different modeling experiments and discuss how these results provide greater insight into the analysis of gaze behavior and error patterns on the block design task.