In most developmental studies the only error children could make on counterfactual tasks was to answer with the current state of affairs. It was concluded that children who did not show this error are able to reason counterfactually. However, children might have avoided this error by using basic conditional reasoning (Rafetseder, Cristi-Vargas, & Perner, 2010). Basic conditional reasoning takes an antecedent, which like in counterfactual reasoning can be counter to fact, and combines it with a conditional (or set of conditionals reflecting knowledge of how the world works) to draw a likely conclusion. A critical feature of counterfactual reasoning then is that these additional assumptions be modelled after the actual events to which the counterfactual is taken to be counterfactual. In contrast in basic conditional reasoning one enriches the given antecedent with any plausible assumptions. In our tasks basic conditional reasoning leads to different answers than counterfactual reasoning. For instance, a doctor, sitting in the park with the intention to read a paper, is called to an emergency at the swimming pool. The question, "if there had been no emergency, where would the doctor be?" should counterfactually be answered "in the park". But ignoring the doctor's intentions and just reasoning on plausible grounds one might answer: "in the hospital". Only by 6 years, did children give mostly correct answers.

How accurate are insights compared to analytical solutions? In four experiments, we investigated how participants' solving strategies influenced their solution accuracies across different types of problems, including one that was linguistic, one that was visual and two that were mixed visual-linguistic. In each experiment, participants' self-judged insight solutions were, on average, more accurate than their analytic ones. We hypothesised that insight solutions have superior accuracy because they emerge into consciousness in an all-or-nothing fashion when the unconscious solving process is complete, whereas analytic solutions can be guesses based on conscious, prematurely terminated, processing. This hypothesis is supported by the finding that participants' analytic solutions included relatively more incorrect responses (i.e., errors of commission) than timeouts (i.e., errors of omission) compared to their insight responses.

The Representational Distortion (RD) approach to similarity (e.g., Hahn, Chater, & Richardson, 2003) proposes that similarity is computed using the transformation distance between two entities. We argue that researchers who adopt this approach need to be concerned with how representational transformations can be determined a priori. We discuss several roadblocks to using this approach. Specifically, we demonstrate the difficulties inherent in determining what transformations are psychologically salient and the importance of considering the directionality of transformations.

Individual differences in Executive Function (EF) are well established to be related to overall mathematics achievement, yet the mechanisms by which this occurs are not well understood. Comparing representations (problems, solutions, concepts) is central to mathematical thinking, and relational reasoning is known to rely upon EF resources. The current manuscript explored whether individual differences in EF predicted learning from a conceptually demanding mathematics lesson that required relational reasoning. Analyses revealed that variations in EF predicted learning when measured at a delay, controlling for pretest scores. Thus, EF capacity may impact students' overall mathematics achievement by constraining their resources available to learn from cognitively demanding reasoning opportunities in everyday lessons. To assess the ecological validity of this interpretation, we report follow-up interviews with mathematics teachers who raised similar concerns that cognitively demanding activities such as comparing multiple representations in mathematics may differentially benefit their high versus struggling learners. Broader implications for ensuring that all students have access to, and benefit from, conceptually rich mathematics lessons are discussed. We also highlight the utility of integrating methods in Science of Learning (SL) research.

The neural basis of developmental changes in transitive reasoning in parietal regions was examined, using voxel-based morphometry. Young adolescents and adults performed a transitive reasoning task, subsequent to undergoing anatomical magnetic resonance imaging (MRI) brain scans. Behaviorally, adults reasoned more accurately than did the young adolescents. Neural results showed (i) less grey matter density in superior parietal cortex in the adults than in the young adolescents, possibly due to a developmental period of synaptic pruning; (ii) improved performance in the reasoning task was negatively correlated with grey matter density in superior parietal cortex in the adolescents, but not in the adult group; and (iii) the latter results were driven by the more difficult trials, requiring greater spatial manipulation. Taken together, the results support the idea that during development, regions in superior parietal cortex are fine-tuned, to support more robust spatial manipulation, resulting in greater accuracy and efficiency in transitive reasoning.

Despite its theoretical importance, little is known about how semantic memory structure facilitates and constrains creative idea production. We examine whether the semantic richness of a concept has both benefits and costs to creative idea production. Specifically, we tested whether cue set-size-an index of semantic richness reflecting the average number of elements associated with a given concept-impacts the quantity (fluency) and quality (originality) of responses generated during the alternate uses task (AUT). Across four studies, we show that low-association, sparse, AUT cues benefit originality at the cost of fluency compared to high-association, rich, AUT cues. Furthermore, we found an interaction with individual differences in fluid intelligence in the low-association AUT cues, suggesting that constraints of sparse semantic knowledge can be overcome with top-down intervention. The findings indicate that semantic richness differentially impacts the quality and quantity of generated ideas, and that cognitive control processes can facilitate idea production when conceptual knowledge is limited.

The information humans are exposed to has grown exponentially. This has placed increased demands upon our information selection strategies resulting in reduced fact-checking and critical-thinking time. Prior research shows that problem solving (traditionally measured using the Cognitive Reflection Test-CRT) negatively correlates with believing in false information. We argue that this result is specifically related to insight problem solving. Solutions via insight are the result of parallel processing, characterized by filtering external noise, and, unlike cognitively controlled thinking, it does not suffer from the cognitive overload associated with processing multiple sources of information. We administered the Compound Remote Associate Test (problems used to investigate insight problem solving) as well as the CRT, 20 fake and real news headlines, the bullshit, and overclaiming scales to a sample of 61 participants. Results show that insight problem solving predicts better identification of fake news and bullshit (over and above traditional measures i.e., the CRT), and is associated with reduced overclaiming. These results have implications for understanding individual differences in susceptibility to believing false information.

Solving problems with insight culminates in an " moment": a feeling of confidence and pleasure. In daily life, insights are often followed by important decisions, such as deciding what to do with a new idea. Here, we investigated whether having an Aha! moment affects subsequent decision-making. Because Aha! moments tend to elicit positive affect, which is generally associated with an increased risk-taking tendency, we hypothesized that people would favor a monetary payout with more upside despite greater uncertainty after solving a problem with insight. Participants were asked to solve verbal puzzles and report whether they solved them with insight or without insight. After each puzzle, they chose between two bonuses: a or a with 50% chance of receiving a high or a low payout. Participants were more likely to choose the risk payout after they solved with insight compared to without, suggesting a temporarily higher risk preference. The study provided preliminary evidence of a carryover effect - the impact of an Aha! moment on the subsequent risk choice - that can have implications in everyday decision-making.