We present a theory, and its computer implementation, of how mental simulations underlie the abductions of informal algorithms and deductions from these algorithms. Three experiments tested the theory's predictions, using an environment of a single railway track and a siding. This environment is akin to a universal Turing machine, but it is simple enough for nonprogrammers to use. Participants solved problems that required use of the siding to rearrange the order of cars in a train (experiment 1). Participants abduced and described in their own words algorithms that solved such problems for trains of any length, and, as the use of simulation predicts, they favored "while-loops" over "for-loops" in their descriptions (experiment 2). Given descriptions of loops of procedures, participants deduced the consequences for given trains of six cars, doing so without access to the railway environment (experiment 3). As the theory predicts, difficulty in rearranging trains depends on the numbers of moves and cars to be moved, whereas in formulating an algorithm and deducing its consequences, it depends on the Kolmogorov complexity of the algorithm. Overall, the results corroborated the use of a kinematic mental model in creating and testing informal algorithms and showed that individuals differ reliably in the ability to carry out these tasks.

for advice.Experiments showed that ten-year old children are able to create algorithms, i.e., sequences of operations that solve problems, and that their gestures help them to do so. The theory of mental models, which is implemented in a computer program, postulates that the creation of algorithms depends on kinematic mental simulations. Gestures are outward signs of moves and they help the process. We tested ten-year children, because they can make mental simulations, and because they gesture more than adults. They readily rearranged the order of six cars in a train (using a siding), and the difficulty of the task depended on the number of moves in minimal solutions (Experiment 1). They were also able to devise informal algorithms to rearrange the order of cars when they were not allowed to move the cars, and the difficulty of the task depended on the complexity of the algorithms (Experiment 2). When children were unable to gesture as they formulated algorithms, the accuracy of their algorithms declined by13% (Experiment 3). We discuss the implications of these results for accounts of reasoning and theories of gestures.

When do children acquire the ability to understand recursion-that is, repeated loops of actions, as in cookery recipes or computer programs? Hitherto, studies have focused either on unconscious recursions in language and vision or on the difficulty of conscious recursions-even for adults-when learning to program. In contrast, we examined 10- to 11-year-old fifth-graders' ability to deduce the consequences of loops of actions in informal algorithms and to create such algorithms for themselves. In our experiments, the children tackled problems requiring the rearrangement of cars on a toy railway with a single track and a siding-an environment that in principle allows for the execution of any algorithm-that is, it has the power of a universal Turing machine. The children were not allowed to move the cars, so each problem's solution called for them to envision the movements of cars on the track. We describe a theory of recursive thinking, which is based on kinematic simulations and which we have implemented in a computer program embodying mental models of the cars and track. Experiment 1 tested children's ability to deduce rearrangements of the cars in a train from descriptions of algorithms containing a single loop of actions. Experiment 2 assessed children's spontaneous creation of similar sorts of algorithms. The results showed that fifth-grade children with no training in computer programming have systematic abilities to deduce from and to create informal recursive algorithms.

Our research focuses on the perception of difference in the evaluations of positive and negative options. The literature provides evidence for two opposite effects: on the one hand, negative objects are said to be more differentiated (e.g., density hypothesis), on the other, people are shown to see greater differences between positive options (e.g., liking-breeds-differentiation principle). In our study, we investigated the perception of difference between fictitious political candidates, hypothesizing greater differences among the evaluations of favorable candidates. Additionally, we analyzed how positive and negative information affect candidate evaluation, predicting further asymmetries. In three experiments, participants evaluated various candidate profiles presented in a numeric and narrative manner. The evaluation tasks were designed as individual or joint assessments. In all three studies, we found more differentiation between positive than negative options. Our research suggests that after exceeding a certain, relatively small level of negativity, people do not see any further increase in negativity. The increase in positivity, on the other hand, is more gradual, with greater differentiation among positive options. Our findings are discussed in light of cognitive-experiential self-theory and density hypothesis.

This article reports investigations of inferences that depend both on connectives between clauses, such as or else, and on relations between entities, such as in the same place as. Participants made more valid inferences from biconditionals—for instance, Ann is taller than Beth if and only if Beth is taller than Cath—than from exclusive disjunctions (Exp. 1). They made more valid transitive inferences from a biconditional when a categorical premise affirmed rather than denied one of its clauses, but they made more valid transitive inferences from an exclusive disjunction when a categorical premise denied rather than affirmed one of its clauses (Exp. 2). From exclusive disjunctions, such as Either Ann is not in the same place as Beth or else Beth is not in the same place as Cath, individuals tended to infer that all three individuals could be in different places, whereas in fact this was impossible (Exps. 3a and 3b). The theory of mental models predicts all of these results.