Competition can be seen as Adversarial Problem Solving (APS), thus ideas from problem solving research can be applied to it. We tested if better modeling of the opponent led to better performance in APS using a zero-sum game played by pairs, but with no obvious skill component. We replicated earlier results that showed that third-order modeling (i.e., what I think my opponent thinks of me: R3MA), but not second-order model (i.e., what I think about my opponent: R2MA) correlated with performance. We also manipulated who was played (same person as in an earlier game, or a predetermined sequence) and who players were told their opponent was (same or different). Players performed better when they could apply the appropriate model (i.e., what they were told matched the opponent). Therefore, we showed that more accurate modeling of an opponent can lead to better APS. However, the critical aspect of modeling may be third-order modeling accuracy. We also found support for a game theory analysis of the task.

Dual space models of problem solving (e.g., Simon & Lea, 1974; Klahr & Dunbar, 1988) assume that the problem space for a task consists of two spaces: an hypothesis space and an experiment space. In hypothesis space, hypotheses about rules governing the task are generated, which can then be tested in experiment space. However, experiment space can be searched by applying the operators even without knowledge about the task. W e predicted that people searching hypothesis space would learn more about the task. To test this claim, two experiments were performed in which subjects had to learn to control a system consisting of three input variables that had unknown links to three output variables. Subjects first explored the task, then they had to reach goal states for the output variables. In both experiments subjects were presented with an hypothesis about one of the links, which should foster search of hypothesis space. In Experiment 1, hypothesis instruction improved performance and we showed that it had a similar effect to a manipulation of goal specificity, suggesting that both factors improve learning by encouraging search in hypothesis space. In Experiment 2 subjects were given a correct hypothesis or an incorrect hypothesis. Both groups performed better than an appropriate control. Thus instructions that encourage hypothesis testing appear to improve learning in problem solving.

Goal-specificity has been found to affect performance: In difficult tasks, specific goals may be detrimental for learning. Locke and Latham (1990) claimed that goal-specificity has an impact on performance via motivation. Vollmeyer and Rheinberg's (1998) cognitive-motivational process model proposed that cognitive and motivational processes interact. Therefore, we investigated if goal-specificity may change the nature of this interaction, by trying to fit different structural equations models for groups given a specific goal (SG) or a nonspecific goal (NSG). Before beginning a complex dynamic task, the SG group was given a specific goal to reach, but the NSG group only received a goal when they had to transfer their knowledge. We found that the SG group learnt less and had lower motivation during learning. Contrary to earlier claims, there was no direct effect of goal-specificity on initial motivation, but it did alter the interaction between strategies and motivation during learning. The empirical model for the SG group showed a strong effect of initial motivation on the learning process and goal-directed strategies were effective. For the NSG group motivation during the task and systematic strategies were important.

In our cognitive-motivational process model (Vollmeyer & Rheinberg, in press) we assumed that motivational factors have an impact on how people learn about a task and how well they can perform it. Many motivation theories (if not all) have such assumptions in common. Our approach emphasizes four task specific motivational factors: mastery confidence, incompetence fear, interest, and challenge. We investigated how these motivational factors influence the learning outcome through mediators. Our framework proposes that the motivational state and the strategy systematicity could mediate motivational effects on learning. Path analysis supported this assumption in two studies.

When adults estimate meaningful numbers their distribution of first-digits is strongly biased towards Benford's Law. Insight into why this bias emerges could be gained by examining when it emerges in children. Three hypotheses were formulated: the Representation Hypothesis predicted this distribution can be found in all grades; the Integration Hypothesis predicted a leap in Benford bias from Grade 3 to 4 due to increased mathematical knowledge; and the Distribution Hypothesis proposed a gradual increase across grades due to implicit learning. 151 children in Grades 2 to 4 were asked to estimate numbers based on images and questions. Results showed a strong Benford bias in all three grades but a significant leap from Grade 2 to 3. This was evidence for both the Representation and Integration Hypotheses. Therefore, Benford bias may develop in children due to how they represent numbers, or develop complex mathematical processes, or perhaps some combination of these.